Handbook of Engineering Tables

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CRC

HANDBOOK OF

ENGINEERING tables

© 2004 by CRC Press LLC

The Electrical Engineering Handbook Series Series Editor

Richard C. Dorf University of California, Davis

Titles Included in the Series The Handbook of Ad Hoc Wireless Networks, Mohammad Ilyas The Avionics Handbook, Cary R. Spitzer The Biomedical Engineering Handbook, Second Edition, Joseph D. Bronzino The Circuits and Filters Handbook, Second Edition, Wai-Kai Chen The Communications Handbook, Second Edition, Jerry Gibson The Computer Engineering Handbook, Vojin G. Oklobdzija The Control Handbook, William S. Levine The CRC Handbook of Engineering Tables, Richard C. Dorf The Digital Signal Processing Handbook, Vijay K. Madisetti and Douglas Williams The Electrical Engineering Handbook, Second Edition, Richard C. Dorf The Electric Power Engineering Handbook, Leo L. Grigsby The Electronics Handbook, Jerry C. Whitaker The Engineering Handbook, Richard C. Dorf The Handbook of Formulas and Tables for Signal Processing, Alexander D. Poularikas The Handbook of Nanoscience, Engineering, and Technology, William A. Goddard, III, Donald W. Brenner, Sergey E. Lyshevski, and Gerald J. Iafrate The Handbook of Optical Communication Networks, Mohammad Ilyas and Hussein T. Mouftah The Industrial Electronics Handbook, J. David Irwin The Measurement, Instrumentation, and Sensors Handbook, John G. Webster The Mechanical Systems Design Handbook, Osita D.I. Nwokah and Yidirim Hurmuzlu The Mechatronics Handbook, Robert H. Bishop The Mobile Communications Handbook, Second Edition, Jerry D. Gibson The Ocean Engineering Handbook, Ferial El-Hawary The RF and Microwave Handbook, Mike Golio The Technology Management Handbook, Richard C. Dorf The Transforms and Applications Handbook, Second Edition, Alexander D. Poularikas The VLSI Handbook, Wai-Kai Chen

Forthcoming Titles The Electrical Engineering Handbook, Third Edition, Richard C. Dorf The Electronics Handbook, Second Edition, Jerry C. Whitaker The Engineering Handbook, Second Edition, Richard C. Dorf

© 2004 by CRC Press LLC

CRC

HANDBOOK OF

ENGINEERING tables editor-in-chief

Richard c. dorf University of California, Davis

CRC PR E S S Boca Raton London New York Washington, D.C.

© 2004 by CRC Press LLC

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Library of Congress Cataloging-in-Publication Data CRC handbook of engineering tables / edited by Richard C. Dorf. p. cm. — (Electrical engineering handbook series) Includes index. ISBN 0-8493-1587-5 (alk. paper) 1. Engineering—Tables. I. Dorf, Richard C. II. Series. TA151.C76 2003 620¢.002¢1—dc21

2003055215

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $1.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 0-8493-1587-5/04/$0.00+$1.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com © 2004 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1587-5 Library of Congress Card Number 2003055215 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

© 2004 by CRC Press LLC

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Preface

Purpose The purpose of the CRC Handbook of Engineering Tables is to provide in a single volume a ready reference for the practicing engineer in industry, government, and academia. The tables and figures provided in this book include data and information from all fields of engineering in a comprehensive format. This information is organized into five sections: Electrical and Computer Engineering; Civil and Environmental Engineering; Chemical Engineering, Chemistry and Material Science; Mechanical Engineering; and General Engineering and Mathematics. The 450 tables and figures are compiled from 51 books and are inclusive of most ready available, important data widely used by the engineering practitioner.

Locating Your Topic Two avenues of access to information are provided. A complete table of contents is provided at the front of the book. An index is provided at the end of the book. The CRC Handbook of Engineering Tables provides answers to most engineering data with reference to the original source. The reader may find it valuable to refer to the original source for a fuller discussion of the underlying theory. We hope that this handbook will be ready at hand to provide data on engineering methods, devices, materials, chemistry, and mathematics.

Acknowledgement The handbook was compiled with the generous help of the editors and authors of the original sources and I am grateful for their assistance. I wish to acknowledge the diligent help of my editor, Nora Konopka, and my editorial project development supervisor, Helena Redshaw.

Richard C. Dorf Davis, California [email protected]

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Dedication

I wish to dedicate this book to the memory of my mother and father, Marion Fraser Dorf and William Carl Dorf.

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Editor-in-Chief

Richard C. Dorf, professor of electrical and computer engineering at the University of California, Davis, teaches graduate and undergraduate courses in electrical engineering in the fields of circuits and control systems. He earned a Ph.D. in electrical engineering from the U.S. Naval Postgraduate School, an M.S. from the University of Colorado, and a B.S. from Clarkson University. Highly concerned with the discipline of engineering and its wide value to social and economic needs, he has written and lectured internationally on the contributions and advances in engineering and their value to society. Professor Dorf has extensive experience with education and industry and is professionally active in the fields of robotics, automation, electric circuits, and communications. He has served as a visiting professor at the University of Edinburgh, Scotland; the Massachusetts Institute of Technology; Stanford University; and the University of California, Berkeley. A Fellow of The Institute of Electrical and Electronics Engineers, Dr. Dorf is widely known to the profession for his Modern Control Systems, 10th Edition (Prentice Hall 2004) and Introduction to Electric Circuits, 6th Edition (Wiley 2004). He is the Editor-inChief of the Electrical Engineering Handbook, 2nd Edition (CRC Press 1997), the Technology Management Handbook (CRC Press 1999), and the Engineering Handbook, 2nd Edition (CRC Press 2004).

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Original Source Page

Material from the following titles appears in the CRC Handbook of Engineering Tables AC Power Systems Handbook, Second Edition, Jerry C. Whitaker, Technical Press Avionics Handbook, Cary R. Spitzer, AvioniCon, Inc. Biomedical Engineering Handbook, Second Edition, Joseph D. Bronzino, Trinity College and Biomedical Engineering Alliance for Connecticut Circuits and Filters Handbook, Second Edition, Wai-Kai Chen, University of Illinois Civil Engineering Handbook, Second Edition, Wai-Fai Chen, University of Hawaii, and J. Y. Richard Liew, National University of Singapore Communications Handbook, Second Edition, Jerry D. Gibson, Southern Methodist University Comprehensive Dictionary of Electrical Engineering, Philip A. Laplante, Pennsylvania Institute of Technology Computer Engineering Handbook, Vojin G. Oklobdzija, University of California Concrete Construction Engineering Handbook, Edward G. Nawy, Rutgers University Control Handbook, William E. Levine, University of Maryland CRC Handbook of Tables for Applied Engineering Science, Ray E. Bolz, Worcester Polytechnic Institute, and George L Tuve, Case Institute of Technology CRC Handbook of Mechanical Engineering, Frank Kreith, University of Colorado CRC Materials Science and Engineering Handbook, James F. Shackelford and William Alexander, University of California CRC Standard Mathematical Tables and Formulae, 31st Edition, Daniel Zwillinger, Rensselaer Polytechnic Insitute Digital Color Imaging Handbook, Gaurav Sharma, Xerox Corporation Digital Signal Processing Handbook, Vijay K. Madisetti and Douglas B. Williams, Georgia Institute of Technology Earthquake Engineering Handbook, Wai-Fai Chen, University of Hawaii, and Charles Scawthorn Electric and Hybrid Vehicles: Design Fundamentals, Iqbal Husain, University of Akron Electric Power Engineering Handbook, Leo L. Grigsby, Auburn University Electrical Engineering Handbook, Second Edition, Richard C. Dorf, University of California Electronic Packaging Handbook, Glenn R. Blackwell, Purdue University Electronics Handbook, Jerry C. Whitaker, Technical Press Engineering Handbook, Richard C. Dorf, University of California Environmental Engineers' Handbook, Second Edition, David H. F. Liu, J.T. Baker, Inc., and Béla G. Lipták, Liptak Associates Fuel Cell Technology Handbook, Gregory Hoogers, Trier University of Applied Sciences Handbook of Ad hoc Wireless Networks, Mohammad Ilyas, Florida Atlantic Univeristy Handbook of Antennas in Wireless Communications, Lal Chand Godara, University of New South Wales xi © 2004 by CRC Press LLC

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Handbook of Chemistry and Physics, 83rd Edition, David R. Lide, National Institute of Standards and Technology Handbook of Formulas and Tables for Signal Processing, Alexander Poularikas, The University of Alabama in Huntsville Handbook of Lasers, Marvin J. Weber, Lawrence Berkeley National Laboratory, University of California Handbook of Nanoscience, Engineering, and Technology, William A. Goddard III, California Institute of Technology, Donald W. Brenner, North Carolina State University, Sergey Edward Lyshevski, Rochester Institute of Technology, and Gerald J. Iafrate, North Carolina State University Handbook of Photonics, Mool C. Gupta, Eastman Kodak Company Handbook of Structural Engineering , Wai-Fai Chen, Purdue University Image Processing Handbook, Third Edition, John C. Russ, North Carolina State University Industrial Electronics Handbook, J. David Irwin, Auburn University Instrument Engineers' Handbook: Process Software and Digital Networks, Third Edition, Béla G. Lipták, Lipták Associates Laws and Models: Science, Engineering, and Technology, Carl W. Hall, Consultant Measurement, Instrumentation and Sensors Handbook, John G. Webster, University of Wisconsin — Madison Mechanical Systems Design Handbook, Osita D. I. Nwokah and Yildrim Hurmuzlu, Southern Methodist University Mechatronics Handbook, Robert H. Bishop, The University of Texas at Austin MEMS Handbook, Mohamed Gal-el-Hak, University of Notre Dame Ocean Engineering Handbook, Ferial El-Hawary, BH Engineering Systems, Ltd. Optical Communications Handbook, Mohammad Ilyas, Florida Atlantic University Power Electronics Handbook, Timothy L. Skvarenina, Purdue University Resource Handbook of Electronics, Jerry C. Whitaker, Technical Press RF and Microwave Handbook, Mike Golio, Motorola Corporation RF Transmission Systems Handbook, Jerry C. Whitaker, Technical Press Technology Management Handbook, Richard C. Dorf, University of California Telecommunications Handbook, Kornel Terplan and Patricia Morreale, Stevens Institute of Technology VLSI Handbook, Wai-Kai Chen, University of Illinois Wind and Solar Power Systems, Mukund R. Patel, U.S. Merchant Marine Academy

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Table of Contents

SECTION 1

Electrical and Computer Engineering

Parameters and Characteristics of Discrete Capacitors ............................................................................1-7 Electrical Properties of Common Insulating Liquids...............................................................................1-8 Types of Systemwide Protection Equipment Available to Facility Managers and the AC Line Abnormalitites That Each Approach Can Handle ...............................................................................1-8 Comparison of System Grounding Methods ............................................................................................1-9 Typical Resistivity of Common Soil Types ...............................................................................................1-9 Specifications of Standard Cooper Wire .................................................................................................1-10 Parameters of Some First-Generation Cellular Standards .....................................................................1-11 Parameters of Some Second-Generation Cellular Standards .................................................................1-11 Comparison of Satellite Systems as a Function of Orbit .......................................................................1-12 Summary of Transmission Media Characteristics ..................................................................................1-12 CSDB Physical Characteristics.................................................................................................................1-12 Sensor Data Required for Full Flight Regime Operation.......................................................................1-13 Categorization of Fault-Tolerant Software Techniques ..........................................................................1-14 The Discipline of Biomedical Engineering .............................................................................................1-15 Hematocytes .............................................................................................................................................1-16 Plasma.......................................................................................................................................................1-17 Arterial System .........................................................................................................................................1-18 Venous System ..........................................................................................................................................1-19 Main Endocrine Glands and the Hormones They Produce and Release ..............................................1-20 Typical Lung Volumes for Normal, Healthy Males ................................................................................1-20 Molecular Masses, Gas Constants, and Volume Fractions for Air and Constituents ...........................1-21 Conductivity Values for Cardiac Bidomain ............................................................................................1-21 Schematic of Energy Transformations Leading to Muscular Mechanical Work ...................................1-22 Typical Values and Estimates for Young's Modulus E ............................................................................1-22 Properties of Bone, Teeth, and Biomaterials...........................................................................................1-23 Biomedical Signals ...................................................................................................................................1-23 Amplitudes and Spectral Range of Some Important Biosignals ...........................................................1-24 Representative Thermal Property Values ................................................................................................1-25 Summary of Several Types of Wavelet Bases for L2(R) ..........................................................................1-25 Debye Temperature and Resistivity of Nonmagnetic Metals .................................................................1-26 Comparison of Capacitor Dielectric Constants .....................................................................................1-26 υ′ Index of Various Capacitors ................................................................................................................1-26 Capicitors..................................................................................................................................................1-27

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Inductor Qualifiers and Attributes ..........................................................................................................1-28 Inductance L0 of Various Air Inductors Dimensionally Similar but Having the Same Number of Turns ................................................................................................................................................1-29 Basic Characteristics of Magnetic Materials Essential for Inductor Applications ................................1-30 Ideal Op Amp Types ................................................................................................................................1-31 The Four Possible Op Amp Configurations ...........................................................................................1-31 ITRS Microprocessor Roadmap ..............................................................................................................1-31 Properties of the Relative Sensitivity.......................................................................................................1-32 Portion of the Electromagnetic Spectrum ..............................................................................................1-32 The General Arrangement of the Frequency Spectrum that is Applied to Satellite Communications and Other Radiocommunications Services ..........................................................1-33 The Primary Strengths of Satellite Communications ............................................................................1-33 Access Time ..............................................................................................................................................1-34 Active Filter ..............................................................................................................................................1-34 Algorithm .................................................................................................................................................1-34 Address .....................................................................................................................................................1-34 Antenna ....................................................................................................................................................1-34 Appropriate Technology ..........................................................................................................................1-34 Attenuation ...............................................................................................................................................1-34 Automation ..............................................................................................................................................1-34 Base ...........................................................................................................................................................1-34 Bayesian Theory .......................................................................................................................................1-34 Binary-Coded Decimal ............................................................................................................................1-34 Bit..............................................................................................................................................................1-34 Boundary Condition ................................................................................................................................1-34 Broadcasting .............................................................................................................................................1-35 Bus ............................................................................................................................................................1-35 Byte ...........................................................................................................................................................1-35 Cache ........................................................................................................................................................1-35 Capacitance ..............................................................................................................................................1-35 Causal System ...........................................................................................................................................1-35 Central Processing Unit ...........................................................................................................................1-35 Channel ....................................................................................................................................................1-35 Chaos ........................................................................................................................................................1-35 Circuit .......................................................................................................................................................1-35 Code ..........................................................................................................................................................1-35 Computer .................................................................................................................................................1-36 Conductivity .............................................................................................................................................1-36 Dielectric ..................................................................................................................................................1-36 Electric Field .............................................................................................................................................1-36 Electromagnetic Energy ...........................................................................................................................1-36 Ethernet ....................................................................................................................................................1-36 Gate ...........................................................................................................................................................1-36 Ground .....................................................................................................................................................1-36 Hologram .................................................................................................................................................1-36 Laser ..........................................................................................................................................................1-36

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Node .........................................................................................................................................................1-36 Noise .........................................................................................................................................................1-36 Permeability ..............................................................................................................................................1-36 Port ...........................................................................................................................................................1-36 Random Signal .........................................................................................................................................1-36 Resolution .................................................................................................................................................1-36 Sensor .......................................................................................................................................................1-36 Traveling Wave .........................................................................................................................................1-37 Waveguide.................................................................................................................................................1-37 Cost of Selected Memory Devices ...........................................................................................................1-37 4-Bit Fractional Two's Complement Numbers .......................................................................................1-38 DFT Parameters .......................................................................................................................................1-38 Typical Underdamped Unit-Step Response of a Control System ..........................................................1-39 Sequences Corresponding to Various z-Transform Pole Locations .......................................................1-40 Transfer Functions of Dynamic Elements and Networks ......................................................................1-43 Block Diagram Transformations .............................................................................................................1-47 Transfer Function Plots for Typical Transfer Functions ........................................................................1-48 Fraction of Area Occupied by the Eight Primaries of the Neugebauer Model.....................................1-56 Characterization vs. Calibration..............................................................................................................1-56 Block Diagram of the Hardware Components Used in a Typical Digital Camera...............................1-57 Some Basic DTFT Pairs ...........................................................................................................................1-57 Properties of the DTFT ...........................................................................................................................1-58 Properties of the DFT..............................................................................................................................1-59 Summary of the Four Types of Linear-Phase FIR Filters ......................................................................1-60 Basic Parameters for Three Classes of Acoustic Signals.........................................................................1-60 CD and DAT Bit Rates.............................................................................................................................1-61 Summary of the Functionalities and Characteristics of the Existing Standards...................................1-61 EV and ICEV Efficiencies from Crude Oil to Traction Effort ...............................................................1-62 Nominal Energy Density of Sources .......................................................................................................1-62 Specific Energy of Batteries .....................................................................................................................1-62 USABC Objectives for EV Battery Packs ................................................................................................1-63 Properties of EV and HEV Batteries .......................................................................................................1-63 Fuel Cell Types .........................................................................................................................................1-63 Summary of Power Devices.....................................................................................................................1-64 Wind Power Installed Capacity ...............................................................................................................1-65 Comparison of Five Fuel Cell Technologies ...........................................................................................1-65 Distributed Generation Technology Chart .............................................................................................1-66 Basic Fuel Cell Operation ........................................................................................................................1-66 Usual Operating Conditions for Transformers.......................................................................................1-67 Resistivity and Temperature Coefficient of Some Materials ..................................................................1-67 Most Commonly Found Relays for Generator Protection.....................................................................1-67 Appliances and Sectors under Direct Utility Control, U.S. — 1983 .....................................................1-68 Typical Characteristics of Integrated Circuit Resistors ..........................................................................1-68 Speech Coder Performance Comparisons ..............................................................................................1-69 Surface Mount Substrate Material ..........................................................................................................1-69 Emissivities of Some Common Materials...............................................................................................1-69 xv © 2004 by CRC Press LLC

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Thermal Conductivities of Typical Packaging Materials at Room Temperature ..................................1-70 Relative Permeability, mr of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials............1-71 “Hard” and “Soft” Magnetic Materials....................................................................................................1-71 Standard Rectangular Waveguides...........................................................................................................1-72 Material Parameters for Several Semiconductors...................................................................................1-73 Absorption Loss Is a Function of Type of Material and Frequency......................................................1-74 Filters Provide a Variety of Frequency Characteristics...........................................................................1-75 Radar Bands .............................................................................................................................................1-76 Typical Acoustic Properties......................................................................................................................1-77 Ferroelectric, Piezoelectric, and Electrostrictive Materials.....................................................................1-77 Material Parameters for Type 1 Superconductors ..................................................................................1-78 Material Parameters for Conventional Type II Superconductors ..........................................................1-78 Spontaneous Polarizations and Curie Temperatures for a Range of Ferroelectrics .............................1-78 Pyroelectric Properties of Selected Materials .........................................................................................1-79 Electrical Properties of a Number of Representative Insulating Liquids ..............................................1-79 Electrical and Physical Properties of Some Common Solid Insulating Materials ................................1-80 Physical and Chemical Transduction Principles.....................................................................................1-82 Electrical Properties of Metals Used in Transmission Lines ..................................................................1-83 Typical Synchronous Generate Parameters.............................................................................................1-83 Excitation Methods and Voltage Current Characteristics for DC Generators ......................................1-84 Complex Envelope Functions for Various Types of Modulation ..........................................................1-85 Protected Service Signal Intensities for Standard Broadcasting (AM) ..................................................1-86 Coding Gains with BPSK and QPSK ......................................................................................................1-87 Comparison of Orbit and Link Parameters for LEO, MEO, and GEO for the Particular Case of Circular Orbits (eccentricity, e, = 0) and for Elevation Angle (el = 10) ......................................1-87 Partial List of Satellite Frequency Allocations ........................................................................................1-88 Specifications of TDMA and CDMA Systems........................................................................................1-88 Switching Algebra Summary ...................................................................................................................1-89 Binary-to-Decimal Conversion ...............................................................................................................1-89 DFs of Single-Valued Nonlinearities .......................................................................................................1-90 Illuminance Categories and Illuminance Values for Genetic Types of Activities in Interiors..............1-92 Representative Transducers......................................................................................................................1-92 Worldwide Radio Navigation Aids ..........................................................................................................1-93 Classifications of Chemical Biomedical Sensors.....................................................................................1-93 Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristics Impedance for Water and Selected Tissues at 3.5 MHz..............................................................................................1-94 Parasitics in Various Electronic Packages................................................................................................1-94 Wiring Board Material Properties...........................................................................................................1-94 Interconnect Models ................................................................................................................................1-95 Dielectric Constants and Wave Velocities within Various PCB Materials.............................................1-97 Wire Ampacity and Size ..........................................................................................................................1-97 Parameters for Multimode and Single-Mode Fiber ...............................................................................1-97 Standard Optical Cable Color Coding ....................................................................................................1-98 Common Tests for Optical Fiber.............................................................................................................1-98 Common Tests for Optical Cable Design ...............................................................................................1-99 Cable Interconnects..................................................................................................................................1-99

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The Electromagnetic Spectrum .............................................................................................................1-100 Properties of Magnetic Materials and Magnetic Alloys .......................................................................1-101 Units .......................................................................................................................................................1-102 Summary of Capacitor Properties.........................................................................................................1-102 Frequency Response Magnitude Functions for Butterworth LP Prototype Filters.............................1-103 Frequency Response Magnitude Functions for Chebyshev LP Prototype Filters ...............................1-103 Op-amp Circuits ....................................................................................................................................1-104 Operating Characteristics of Common Battery Types .........................................................................1-108 Example Fourier Transform Pairs .........................................................................................................1-109 Advantages and Disadvantages of Satellites..........................................................................................1-110 Satellites Frequency Allocations ............................................................................................................1-110 Typical Uplink and Downlink Satellite Frequencies (GHz).................................................................1-110 Frequency Allocations for FSS (Below ~30 GHz) ................................................................................1-110 Characteristics of Satellite PCS Systems ...............................................................................................1-111 Table of Laplace Operations ..................................................................................................................1-111 Table of Laplace Transforms..................................................................................................................1-112 Properties of Fourier Transform ...........................................................................................................1-132 Table of Fourier Transforms (x = t; y = w) ..........................................................................................1-133 Examples of Display Transfer Functions ..............................................................................................1-157 Common Fourier Transforms ...............................................................................................................1-157 Common Laplace Transforms ...............................................................................................................1-158 Important Properties of Laplace Transforms .......................................................................................1-158 Representation Values of Absolute Seebeck Thermoelectric Coefficients of Some Materials Used in Industrial Electronic Circuits ..............................................................................................1-159 Power Definitions (Single-Phase Circuits)............................................................................................1-159 Power Definitions (Three-Phase Circuits)............................................................................................1-160 Summary of Describing Differential Equations for Ideal Elements....................................................1-160 Properties of the Wave Types for Time-of-Flight Measuring ..............................................................1-161 Comparison of Strain Sensors...............................................................................................................1-162 Pressure-Sensing Elements ....................................................................................................................1-163 Permittivity (Dielectric Constants of Materials Used in Capacitors)..................................................1-164 The Key Elements of Mechatronics.......................................................................................................1-164 Mechanical Process and Information Processing Develop Towards Mechatronic Systems................1-165 Generalized Through and Across Variables for Processes with Energy Flow......................................1-165 Power and Energy Variables for Mechnical Systems ............................................................................1-165 Mechanical Dissipative Elements ..........................................................................................................1-166 Typical Coefficient of Friction Values ...................................................................................................1-166 Mechanical Potential Energy Storage Elements (Integral Form).........................................................1-167 Mechanical Kinetic Energy Storage Elements (Integral Form) ...........................................................1-167 Resistance of Copper Wire ....................................................................................................................1-168 Type of Sensors for Various Measurement Objectives .........................................................................1-168 Type of Actuators and Their Features...................................................................................................1-170 Performance of Two Deep-Sea Armored Coaxes .................................................................................1-171 Past and Projected Future Growth of Data and Voice Traffic .............................................................1-172 Nominal Geographical Spans of Access, Metro-Core/Regional, and Long-Haul Networks...............1-172 ITU-T-Approved Band Assignment in the Low Attenuation Window of the Silica Fibers ...............1-173

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Fiber Optics Chemical Sensors..............................................................................................................1-174 Typical Components of Various Glass Systems ....................................................................................1-175 Thyristor Symbol and Volt-Ampere Characteristics ............................................................................1-175 Triac Symbol and Volt-Ampere Characteristics....................................................................................1-176 GTO Symbol and Turn-Off Characteristics .........................................................................................1-176 Power MOSFET Circuit Symbol ...........................................................................................................1-177 Total Elongation at Failure of Selected Polymers .................................................................................1-177 Tensile Strength of Selected Wrought Aluminum Alloys .....................................................................1-178 Density of Selected Materials, mg/m2 ...................................................................................................1-178 Applications in the Microwave Bands...................................................................................................1-179 The Electromagnetic Spectrum .............................................................................................................1-180 Typical Luminance Values .....................................................................................................................1-180 Resistivity of Selected Ceramics ............................................................................................................1-181 Properties of Magnetic Materials and Magnetic Alloys .......................................................................1-181 Thermal Conductivity of Common Materials......................................................................................1-182 Relative Thermal Conductivity of Various Materials As a Percentage of the Thermal Conductivity of Copper ....................................................................................................................1-182 Variation of Electrical and Thermal Properties of Common Insulators As a Function of Temperature .......................................................................................................................................1-182 Common Op-Amp Circuits ..................................................................................................................1-183 Electromagnetic Frequency Spectrum and Associated Wavelengths ...................................................1-187 Modulation Schemes, Glossary of Terms..............................................................................................1-187 Radar Bands ...........................................................................................................................................1-188 Thermal Conductivities of Typical Metals (W/m K) at Room Temperature .....................................1-189 Thermal Coefficient of Linear Expansion of Some of the Materials Used in Microwave and RF Packaging Applications (at Room Temperature, in 10–6/K) ............................................................1-189 Properties of Some Typical Engineering Insulating Materials.............................................................1-190 Selected Material Properties of Semiconductor for Microwave and RF Applications........................1-190 Channel Designations for VHF and UHF Television Stations in the U. S. ........................................1-191 Radar Frequency Bands .........................................................................................................................1-192 Common-Carrier Microwave Frequencies Used in the U.S. ..............................................................1-192 Comparison of Amplitude Modulation Techniques ............................................................................1-193 Representative Specifications for Various Types of Flexible Air-Dielectric Coaxial Cable.................1-193 Four Drives of Change in Telecommunications...................................................................................1-194 Summary and Comparison of Second-Generation TDMA-Based System Parameters ......................1-194 Some Milestones for Multimedia ..........................................................................................................1-195 Comparison of Interconnect Characteristics for A1 and Cu...............................................................1-195 Comparison of High-Permittivity Constant Materials for DRAM Cell Capacitors ...........................1-195 Summary of Some Architectures and Applications Possible from a Molecular Computing System ................................................................................................................................................1-196 Comparison of Selected Important Semiconductors of Major SiC Polytypes with Silicon and GaAs............................................................................................................................................1-196 MEMS Processing Technologies ............................................................................................................1-197 Materials Properties of LPCVD Deposited MEMS Materials..............................................................1-198 Wafer Bonding Techniques....................................................................................................................1-198 Microrelays .............................................................................................................................................1-199

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Electronic Packaging Requirements ......................................................................................................1-200 Thermal and Electrical Properties of Materials Used in Packaging ....................................................1-200 Some Properties of Ceramic Packaging Materials................................................................................1-201 Interconnect Technologies .....................................................................................................................1-201 Voltage Buffer Performance...................................................................................................................1-201 Embedded Memory Technologies and Applications............................................................................1-202 Recent High-Speed ADC Applications .................................................................................................1-202 Microprocessor Statistics .......................................................................................................................1-203 Comparing Electrical Parameters for BJT/HBT vs. FET......................................................................1-203 Status of Conventional and Renewable Power Sources........................................................................1-204 Benefits of Using Renewable Electricity................................................................................................1-204 Electromagnetic Radiation and Stable Elementary Particles ...............................................................1-205 Electromagnetic Frequency Spectra ......................................................................................................1-206 Dynamic Response of RCL System to a Step-Change Input ...............................................................1-207 Amplitude Response — Second-Order System ....................................................................................1-208 Phase Response — Second-Order System ............................................................................................1-209 Frequency-Response Approximations and Corrections .......................................................................1-210 Corrections to the Log Magnitude and Phase Diagram ......................................................................1-211 Block and Signal-Flow Diagrams ..........................................................................................................1-212 Block-Diagram Manipulations ..............................................................................................................1-213 Signal-Flow Diagrams............................................................................................................................1-215 Root Loci ................................................................................................................................................1-218 Transfer Function Plots for Typical Transfer Function........................................................................1-224

SECTION 2

Civil and Environmental Engineering

Properties of Dressed Lumber...................................................................................................................2-3 Beam Formulas ..........................................................................................................................................2-4 Phases in the Value Engineering Job Plan ................................................................................................2-5 Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) ......................2-6 National Ambient Air Quality Standards................................................................................................2-10 Standard Normal Probability ..................................................................................................................2-11 Typical Values of Elastic Modulus and Poisson's Ratio for Granular Soils...........................................2-12 Representative Applications and Controlling Functions of Geotextiles ................................................2-13 Physical Properties of Water in SI Units.................................................................................................2-14 Physical Properties of Air at Standard Atmospheric Pressure in English Units ...................................2-14 Physical Properties of Common Liquids at Standard Atmospheric Pressure in SI Units ....................2-15 Physical Properties of Common Gases at Standard Sea-Level Atmosphere and 68°F in English Units .....................................................................................................................................................2-15 Typical Physical Properties of and Allowable Stresses for Some Common Materials (in U.S. Customary System Units)....................................................................................................................2-16 Typical Physical Properties of and Allowable Stresses for Some Common Materials (in SI System Units).......................................................................................................................................2-17

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Probability Distribution Types ................................................................................................................2-18 Typical Compound Composition of Ordinary Portland Cement .........................................................2-19 Properties of Some Lightweight Concretes.............................................................................................2-19 Mechanical Properties of Hardened Concrete........................................................................................2-20 ACI 318 Maximum Chloride-Ion Content for Corrosion Protection...................................................2-21 Properties of Typical Air-Entraining Admixtures...................................................................................2-21 Total Target Air Content for Concrete ....................................................................................................2-21 Beam Formulas for One-, Two-, and Three-Span Conditions ..............................................................2-22 Theoretical Maximum Load Ratios on Floor and Prop for Various Shore/Reshore Combinations .....2-23 Selected Earthquakes Since 1900 (Fatalities Greater then 1,000) ..........................................................2-23 Selected U.S. Earthquakes........................................................................................................................2-26 Earthquake Loss Process ..........................................................................................................................2-28 Earthquake Risk Management Decision Process....................................................................................2-29 Principle Elemental Components of Structural Steel ............................................................................2-30 Three Levels of Analysis in the EIA Process ...........................................................................................2-30 Public Participation in Environmental Impact Assessment...................................................................2-31 Priority Chemicals Targeted in the 33/50 Project for the Industrial Sector Pollution Preventation Strategy.................................................................................................................................................2-32 Main Membrane Separation Processes: Operating Principles and Application....................................2-32 Summary of NAAQSs ..............................................................................................................................2-33 National Emission Standards for Hazardous Air Pollutants..................................................................2-33 Molecular and Aerosol Particle Diameters .............................................................................................2-37 Radon Risk Evaluation Chart ..................................................................................................................2-38 Mechanical Characteristics of Sound Waves...........................................................................................2-38 Representative Sound Pressures and Sound Levels ................................................................................2-39 Typical Wastewater Flow Rates from Residential Sources......................................................................2-39 Estimated Distribution of World's Water ...............................................................................................2-40 Currently Developed Types of Fuel Cells and Their Characteristics and Applications........................2-40 Hydrogen Storage Properties for a Range of Metal Hydrides ...............................................................2-41 Typical Gas Composition of Biogas from Organic Household Waste ..................................................2-41 Performance of Different Battery Types .................................................................................................2-42 Thermodynamic Data for Selected Chemical Compounds ...................................................................2-42 Shear Force and Bending Moment Diagrams for Beams with Simple Boundary Conditions Subjected to Selected Loading Cases ..................................................................................................2-43 Shear Force and Bending Moment Diagrams for Built-Up Beams Subjected to Typical Loading Cases.....................................................................................................................................................2-46 Typical Loading on Plates and Loading Functions ................................................................................2-48 Typical Loading and Boundary Conditions for Rectangular Plates ......................................................2-50 Typical Loading and Boundary Conditions for Circular Plates ............................................................2-51 Frequencies and Mode Shapes of Beams in Flexural Vibration ............................................................2-52 Fundamental Frequencies of Portal Frames in Asymmetrical Mode of Vibration...............................2-53 Basic Weld Symbols .................................................................................................................................2-54 Strength of Welds.....................................................................................................................................2-55 Reinforcing Bar Dimensions and Weights ..............................................................................................2-56 Eurocode 4 Maximum Width-to-Thickness Ratios for Steel Webs .......................................................2-56 Mechanical Properties of Steels Referred to in the AISI 1996 Specification.........................................2-57

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Some Nominal Properties of Aluminum Alloys.....................................................................................2-59 Minimum Mechanical Properties............................................................................................................2-59 Steel Plate Materials .................................................................................................................................2-60 Mechanical Properties of Common Design Materials ...........................................................................2-61 Properties of Sections ..............................................................................................................................2-61 Components of the Atmosphere .............................................................................................................2-63 Sound Transmission Through Partition Walls .......................................................................................2-64 Sound-Absorption Coefficients ...............................................................................................................2-65

SECTION 3 Chemical Engineering, Chemistry and Materials Science International System of Units (SI) ............................................................................................................3-3 Conversion Factors...................................................................................................................................3-11 Periodic Table of Elements ......................................................................................................................3-23 Properties of Semiconductors .................................................................................................................3-24 Solid State Lasers......................................................................................................................................3-45 III-V Material Systems with Important Optoelectronic Applications...................................................3-46 Energy Gap and Lattice Parameters for Cubic Group IV, III-V, and II-VI Semiconductors ...............3-47 Important Parameters of Semiconductors of Interest for Conventional Electronics and Emerging High Temperature Electronics ...........................................................................................3-47 Properties of GaN(a), AIN (b), and InN(c) ...........................................................................................3-48 List of Ferroelectric Materials and Their Crystal Growth Methods ......................................................3-49 General Physical Properties of Ferroelectric Materials ..........................................................................3-50 Applications of the Ferroelectric Thin Films..........................................................................................3-51 The Principal Photometric Units ............................................................................................................3-52 Dielectric Constants of Common Materials...........................................................................................3-52 Characteristics of Coaxial Cables ............................................................................................................3-52 Dry Saturated Steam: Temperature Table ...............................................................................................3-53 Properties of Superheated Steam ............................................................................................................3-55 Properties of Water at Various Temperatures from 40 to 540°F (44 to 282.2°C).................................3-59 Atomic Mass of Selected Elements..........................................................................................................3-60 Solid Density of Selected Elements .........................................................................................................3-62 Thermal Conductivity of Metals (Part 1)...............................................................................................3-63 Thermal Conductivity of Metals (Part 2)...............................................................................................3-64 Thermal Conductivity of Metals (Part 3)...............................................................................................3-65 Thermal Conductivity of Metals (Part 4)...............................................................................................3-66 General Properties of Refrigerants ..........................................................................................................3-68 Thermodynamic Properties of Saturated Mercury ................................................................................3-70 Properties of Rare-Earth Metals..............................................................................................................3-71 Products of Powder Metallurgy...............................................................................................................3-72 Fiber-Reinforced Metals...........................................................................................................................3-73 Properties of Commercial Plastics ..........................................................................................................3-74

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Rubbers and Elastomers ..........................................................................................................................3-85 Electrical Properties of Various Kinds of Glass ......................................................................................3-87 Properties of the Chemical Elements......................................................................................................3-88 Additional Properties of the Chemical Elements ...................................................................................3-90 Available Stable Isotopes of the Elements...............................................................................................3-93 Energy Absorption Mass Attenuation Coefficient In cm2/g...................................................................3-96 Gamma-Ray Absorption Cross Section In cm–1 .....................................................................................3-97 Removal Cross Sections for Various Materials .......................................................................................3-98 Diffusion of Gases and Vapors into Air ..................................................................................................3-99 Speed of Sound in Water and Steam (m·s–1)........................................................................................3-100 Dynamic Viscosity of Water and Steam (mPa·s)..................................................................................3-101

SECTION 4

Mechanical Engineering

Basic Mechanical Properties ......................................................................................................................4-3 Symbols and Definitions for Selected Properties .....................................................................................4-4 Heating Values in kJ/kg of Selected Hydrocarbons at 25°C.....................................................................4-4 Some Fuel Properties of Four Different Biomass Types ..........................................................................4-5 Physical Properties of Selected Ceramics..................................................................................................4-5 Steel Pipe Sizes ...........................................................................................................................................4-6 Commercial Copper Tubing......................................................................................................................4-7 Summary of Definitions ............................................................................................................................4-8 CAPP System Characteristics and Their Effects .......................................................................................4-9 System's View of the Injection Molding Process ....................................................................................4-10 Magnitude of Process Variation by Machine Input ...............................................................................4-11 Visualization of Accuracy, Repeatability, and Resolution ......................................................................4-11 Anthropomorphic Robot with Frame Assignment ................................................................................4-12 Denavit-Hartenberg Parameters of the Anthropomorphic Robot ........................................................4-12 Basic Grip and Trigger Concepts.............................................................................................................4-13 Examples of Specialization of Robot Designs ........................................................................................4-13 Typical Arm and Wrist Configurations of Industrial Robots ................................................................4-14 From Industrial Robots to Service Robots — The Evolution of Machine Intelligence .......................4-15 Scale of Things, in Meters .......................................................................................................................4-16 Metals .......................................................................................................................................................4-17 Molecular and Continuum Flow Models................................................................................................4-17 Knudsen Number Regimes......................................................................................................................4-18 The Operation Range for Typical MEMS and Nanotechnology Applications Under Standard Conditions Spans the Entire Knudsen Regime ..................................................................................4-18 Classification of Microrobots According to Size and Fabrication Technology .....................................4-19 Classification of Microrobots by Functionality ......................................................................................4-19 Thermal Conductivity, Coefficient of Thermal Expansion, Cost Estimates, and Scaling Trends of Current and Potential Substrate Materials .........................................................................................4-20 Tools for Soft Computing........................................................................................................................4-20 Saturated Steam, Water, and Ice — SI Units ..........................................................................................4-21 xxii © 2004 by CRC Press LLC

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Viscosity and Thermal Conductivity of Steam and Water — SI Units.................................................4-23 Properties of Gases...................................................................................................................................4-24 Mechanical Properties of Metals and Alloys...........................................................................................4-34 Thermal Properties of Pure Metals — Metric Units..............................................................................4-46 Terms and Units for Radiant Energy and Illumination .........................................................................4-48 Blackbody Radiation ................................................................................................................................4-49 Thermodynamic Nonflow Process Equations ........................................................................................4-50 Thermodynamic Cycle Efficiencies .........................................................................................................4-51 Heat of Fusion of Some Inorganic Compounds ....................................................................................4-52 Conservation Equations of a Viscous, Heat-Conducting Fluid.............................................................4-59 Energy Conversions .................................................................................................................................4-65 Helical Steel Springs.................................................................................................................................4-66 Ultrasonic Energy and Applications .......................................................................................................4-68 Mechanical Components .........................................................................................................................4-69 Pneumatic Compensating Components .................................................................................................4-71 Dynamic Elements and Networks...........................................................................................................4-73 Properties of Saturated Water and Steam (Temperature)......................................................................4-76 Properties of Saturated Water and Steam (Pressure) .............................................................................4-81 Thermal Conductivity of Water and Steam (mW·m1·K–1) ....................................................................4-87

SECTION 5

General Engineering and Mathematics

Constants — Types of Numbers ...............................................................................................................5-3 Decimal Multiples and Prefixes .................................................................................................................5-4 Powers of 10 in Hexadecimal Scale...........................................................................................................5-4 Factorials ....................................................................................................................................................5-5 Prime Numbers ..........................................................................................................................................5-7 Reliability....................................................................................................................................................5-7 Conversion: Metric to English...................................................................................................................5-7 Conversion: English to Metric...................................................................................................................5-7 Interpretations of Powers of 10.................................................................................................................5-8 Typical Values for Coefficients of Static Friction .....................................................................................5-8 Properties of Plane Areas...........................................................................................................................5-9 Moments of Inertia of Homogeneous Solids .........................................................................................5-10 Dynamic Viscosity of Liquids..................................................................................................................5-14 Resistor Color Code .................................................................................................................................5-14 The Problem of Total Cost Visbility........................................................................................................5-15 Trigonometry ...........................................................................................................................................5-15 Series.........................................................................................................................................................5-19 Differential Calculus ................................................................................................................................5-26 Integral Calculus ......................................................................................................................................5-30 Special Functions .....................................................................................................................................5-35 xxiii © 2004 by CRC Press LLC

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Moore’s Laws ............................................................................................................................................5-44 Approximate Current Densities in Electrons per Second per Square Nanometer Calculated from Experimental Data for Selected Molecular Electronic and Macroscopic Metal Devices .................5-44 Comparison of Memory Technologies for the Year 2011 ......................................................................5-45 Size and Scale of Naturally Occurring Structures as Compared With Human-Made Structures .......5-45 Trends in Miniaturization of Integrated Circuits in the Last 25 Years..................................................5-46 Civilizations, Technology Periods (Ages), and Historical Revolutions as a Function of Time ............5-47 Abbreviations ...........................................................................................................................................5-48 Boiling Point Law, General ......................................................................................................................5-49 Hall Effect.................................................................................................................................................5-50 Ideal Mixtures, Law of .............................................................................................................................5-50 Large Numbers, Law of............................................................................................................................5-51 Maxwell Electromagnetic Field Equations..............................................................................................5-51 Moore Law................................................................................................................................................5-51 Newton Laws of Motion..........................................................................................................................5-52 Normal Law..............................................................................................................................................5-53 Photoelectric Effect, Laws of ...................................................................................................................5-54 Shannon Law or Formula or Theorem...................................................................................................5-54 Skin Effect ................................................................................................................................................5-55 Snell Law...................................................................................................................................................5-55 Thermodynamics, Laws of.......................................................................................................................5-56 Young Modulus, E....................................................................................................................................5-57 Types of Manufacturing — Characteristics and Examples....................................................................5-58 Coefficient of Friction — Identical Metals.............................................................................................5-59 Coefficient of Friction — Identical Alloy Pairs ......................................................................................5-60 Coefficient of Friction — Dissimilar Metals ..........................................................................................5-61 Coefficient of Friction — Single Crystals ...............................................................................................5-62 Coefficients of Friction — Non-Metals ..................................................................................................5-63 Coefficient of Friction — Lubricating Powders .....................................................................................5-64 Coefficients of Static and Sliding Friction ..............................................................................................5-64 The Greek and Russian Alphabets ..........................................................................................................5-66 Units and Their Conversion ....................................................................................................................5-67 International System (SI) Metric Units...................................................................................................5-69 Conversions to SI Units ...........................................................................................................................5-72 Fundamental Physical Constants.............................................................................................................5-81 Numerical Constants ...............................................................................................................................5-83 Mathematical Constants ..........................................................................................................................5-85 Derivatives ................................................................................................................................................5-86 Facts from Algebra ...................................................................................................................................5-89 Integrals — Elementary Forms ...............................................................................................................5-90 Series.........................................................................................................................................................5-92 Tables of Statistical Probability .............................................................................................................5-100 Ordinates and Areas for Normal or Gaussian Probability Distribution .............................................5-102 Student's t-Distribution .........................................................................................................................5-105 Chi-Square Distribution ........................................................................................................................5-106 F-Distribution ........................................................................................................................................5-107

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Binomial Distribution — Cumulative Probabilities: P ........................................................................5-111 Poisson Distribution — Cumulative Probabilities: P...........................................................................5-113 Critical Values for the Sign Test ............................................................................................................5-116 Factors for Computing Control Limits.................................................................................................5-117 Number Systems and Change of Base ..................................................................................................5-120 Binary, Octal, and Decimal Numbers ...................................................................................................5-122 Octal-Decimal Integer Conversion........................................................................................................5-124 Boolean Theorems .................................................................................................................................5-128 Applications and Functions of Two Variables ......................................................................................5-129

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1 Electrical and Computer Engineering Parameters and Characteristics of Discrete Capacitors ............................................................................1-7 Electrical Properties of Common Insulating Liquids...............................................................................1-8 Types of Systemwide Protection Equipment Available to Facility Managers and the AC Line Abnormalitites That Each Approach Can Handle ...............................................................................1-8 Comparison of System Grounding Methods ............................................................................................1-9 Typical Resistivity of Common Soil Types ...............................................................................................1-9 Specifications of Standard Cooper Wire .................................................................................................1-10 Parameters of Some First-Generation Cellular Standards .....................................................................1-11 Parameters of Some Second-Generation Cellular Standards .................................................................1-11 Comparison of Satellite Systems as a Function of Orbit .......................................................................1-12 Summary of Transmission Media Characteristics ..................................................................................1-12 CSDB Physical Characteristics.................................................................................................................1-12 Sensor Data Required for Full Flight Regime Operation.......................................................................1-13 Categorization of Fault-Tolerant Software Techniques ..........................................................................1-14 The Discipline of Biomedical Engineering .............................................................................................1-15 Hematocytes .............................................................................................................................................1-16 Plasma.......................................................................................................................................................1-17 Arterial System .........................................................................................................................................1-18 Venous System ..........................................................................................................................................1-19 Main Endocrine Glands and the Hormones They Produce and Release ..............................................1-20 Typical Lung Volumes for Normal, Healthy Males ................................................................................1-20 Molecular Masses, Gas Constants, and Volume Fractions for Air and Constituents ...........................1-21 Conductivity Values for Cardiac Bidomain ............................................................................................1-21 Schematic of Energy Transformations Leading to Muscuar Mechanical Work ....................................1-22 Typical Values and Estimates for Young's Modulus E ............................................................................1-22 Properties of Bone, Teeth, and Biomaterials...........................................................................................1-23 Biomedical Signals ...................................................................................................................................1-23 Amplitudes and Spectral Range of Some Important Biosignals ...........................................................1-24 Representative Thermal Property Values ................................................................................................1-25 Summary of Several Types of Wavelet Bases for L2(R) ..........................................................................1-25

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Debye Temperature and Resistivity of Nonmagnetic Metals .................................................................1-26 Comparison of Capacitor Dielectric Constants .....................................................................................1-26 υ′ Index of Various Capacitors ................................................................................................................1-26 Capacitors .................................................................................................................................................1-27 Inductor Qualifiers and Attributes ..........................................................................................................1-28 Inductance L0 of Various Air Inductors Dimensionally Similar but Having the Same Number of Turns ................................................................................................................................................1-29 Basic Characteristics of Magnetic Materials Essential for Inductor Applications ................................1-30 Ideal Op Amp Types ................................................................................................................................1-31 The Four Possible Op Amp Configurations ...........................................................................................1-31 ITRS Microprocessor Roadmap ..............................................................................................................1-31 Properties of the Relative Sensitivity.......................................................................................................1-32 Portion of the Electromagnetic Spectrum ..............................................................................................1-32 The General Arrangement of the Frequency Spectrum that is Applied to Satellite Communications and Other Radiocommunications Services ..........................................................1-33 The Primary Strengths of Satellite Communications ............................................................................1-33 Access Time ..............................................................................................................................................1-34 Active Filter ..............................................................................................................................................1-34 Algorithm .................................................................................................................................................1-34 Address .....................................................................................................................................................1-34 Antenna ....................................................................................................................................................1-34 Appropriate Technology ..........................................................................................................................1-34 Attenuation ...............................................................................................................................................1-34 Automation ..............................................................................................................................................1-34 Base ...........................................................................................................................................................1-34 Bayesian Theory .......................................................................................................................................1-34 Binary-Coded Decimal ............................................................................................................................1-34 Bit..............................................................................................................................................................1-34 Boundary Condition ................................................................................................................................1-34 Broadcasting .............................................................................................................................................1-35 Bus ............................................................................................................................................................1-35 Byte ...........................................................................................................................................................1-35 Cache ........................................................................................................................................................1-35 Capacitance ..............................................................................................................................................1-35 Causal System ...........................................................................................................................................1-35 Central Processing Unit ...........................................................................................................................1-35 Channel ....................................................................................................................................................1-35 Chaos ........................................................................................................................................................1-35 Circuit .......................................................................................................................................................1-35 Code ..........................................................................................................................................................1-35 Computer .................................................................................................................................................1-36 Conductivity .............................................................................................................................................1-36 Dielectric ..................................................................................................................................................1-36 Electric field..............................................................................................................................................1-36 Electromagnetic Energy ...........................................................................................................................1-36 Ethernet ....................................................................................................................................................1-36 Gate ...........................................................................................................................................................1-36 Ground .....................................................................................................................................................1-36 Hologram .................................................................................................................................................1-36 Laser ..........................................................................................................................................................1-36 Node .........................................................................................................................................................1-36 Noise .........................................................................................................................................................1-36 Permeability ..............................................................................................................................................1-36

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Port ...........................................................................................................................................................1-36 Random Signal .........................................................................................................................................1-36 Resolution .................................................................................................................................................1-36 Sensor .......................................................................................................................................................1-36 Traveling Wave .........................................................................................................................................1-37 Waveguide.................................................................................................................................................1-37 Cost of Selected Memory Devices ...........................................................................................................1-37 4-Bit Fractional Two's Complement Numbers .......................................................................................1-38 DFT Parameters .......................................................................................................................................1-38 Typical Underdamped Unit-Step Response of a Control System ..........................................................1-39 Sequences Corresponding to Various z-Transform Pole Locations .......................................................1-40 Transfer Functions of Dynamic Elements and Networks ......................................................................1-43 Block Diagram Transformations .............................................................................................................1-47 Transfer Function Plots for Typical Transfer Functions ........................................................................1-48 Fraction of Area Occupied by the Eight Primaries of the Neugebauer Model .....................................1-56 Characterization vs. Calibration ..............................................................................................................1-56 Block Diagram of the Hardware Components Used in a Typical Digital Camera ...............................1-57 Some Basic DTFT Pairs ...........................................................................................................................1-57 Properties of the DTFT ...........................................................................................................................1-58 Properties of the DFT ..............................................................................................................................1-59 Summary of the Four Types of Linear-Phase FIR Filters ......................................................................1-60 Basic Parameters for Three Classes of Acoustic Signals .........................................................................1-60 CD and DAT Bit Rates .............................................................................................................................1-61 Summary of the Functionalities and Characteristics of the Existing Standards...................................1-61 EV and ICEV Efficiencies from Crude Oil to Traction Effort ...............................................................1-62 Nominal Energy Density of Sources .......................................................................................................1-62 Specific Energy of Batteries .....................................................................................................................1-62 USABC Objectives for EV Battery Packs ................................................................................................1-63 Properties of EV and HEV Batteries .......................................................................................................1-63 Fuel Cell Types .........................................................................................................................................1-63 Summary of Power Devices .....................................................................................................................1-64 Wind Power Installed Capacity ...............................................................................................................1-65 Comparison of Five Fuel Cell Technologies ...........................................................................................1-65 Distributed Generation Technology Chart .............................................................................................1-66 Basic Fuel Cell Operation ........................................................................................................................1-66 Usual Operating Conditions for Transformers.......................................................................................1-67 Resistivity and Temperature Coefficient of Some Materials ..................................................................1-67 Most Common Found Relays for Generator Protection........................................................................1-67 Appliances and Sectors under Direct Utility Control, U.S. — 1983 .....................................................1-68 Typical Characteristics of Integrated Circuit Resistors ..........................................................................1-68 Speech Coder Performance Comparisons ..............................................................................................1-69 Surface Mount Substrate Material ..........................................................................................................1-69 Emissivities of Some Common Materials...............................................................................................1-69 Thermal Conductivities of Typical Packaging Materials at Room Temperature ..................................1-70 Relative Permeability, mr of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials............1-71 “Hard” and “Soft” Magnetic Materials....................................................................................................1-71 Standard Rectangular Waveguides...........................................................................................................1-72 Material Parameters for Several Semiconductors...................................................................................1-73 Absorption Loss Is a Function of Type of Material and Frequency......................................................1-74 Filters Provide a Variety of Frequency Characteristics...........................................................................1-75 Radar Bands .............................................................................................................................................1-76 Typical Acoustic Properties......................................................................................................................1-77 Ferroelectric, Piezoelectric, and Electrostrictive Materials.....................................................................1-77

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Material Parameters for Type 1 Superconductors ..................................................................................1-78 Material Parameters for Conventional Type II Superconductors ..........................................................1-78 Spontaneous Polarizations and Curie Temperatures for a Range of Ferroelectrics .............................1-78 Pyroelectric Properties of Selected Materials .........................................................................................1-79 Electrical Properties of a Number of Representative Insulating Liquids ..............................................1-79 Electrical and Physical Properties of Some Common Solid Insulating Materials ................................1-80 Physical and Chemical Transduction Principles .....................................................................................1-82 Electrical Properties of Metals Used in Transmission Lines ..................................................................1-83 Typical Synchronous Generate Parameters .............................................................................................1-83 Excitation Methods and Voltage Current Characteristics for DC Generators ......................................1-84 Complex Envelope Functions for Various Types of Modulation ..........................................................1-85 Protected Service Signal Intensities for Standard Broadcasting (AM) ..................................................1-86 Coding Gains with BPSK and QPSK ......................................................................................................1-87 Comparison of Orbit and Link Parameters for LEO, MEO, and GEO for the Particular Case of Circular Orbits (eccentricity, e, = 0) and for Elevation Angle (el = 10) ......................................1-87 Partial List of Satellite Frequency Allocation ..........................................................................................1-88 Specifications of TDMA and CDMA Systems ........................................................................................1-88 Switching Algebra Summary ...................................................................................................................1-89 Binary-to-Decimal Conversion ...............................................................................................................1-89 DFs of Single-Valued Nonlinearities .......................................................................................................1-90 Illuminance Categories and Illuminance Values for Genetic Types of Activities in Interiors ..............1-92 Representative Transducers ......................................................................................................................1-92 Worldwide Radio Navigation Aids ..........................................................................................................1-93 Classifications of Chemical Biomedical Sensors.....................................................................................1-93 Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristics Impedance for Water and Selected Tissues at 3.5 MHz..............................................................................................1-94 Parasitics in Various Electronic Packages ................................................................................................1-94 Wiring Board Material Properties ...........................................................................................................1-94 Interconnect Models ................................................................................................................................1-95 Dielectric Constants and Wave Velocities within Various PCB Materials .............................................1-97 Wire Ampacity and Size ..........................................................................................................................1-97 Parameters for Multimode and Single-Mode Fiber ...............................................................................1-97 Standard Optical Cable Color Coding ....................................................................................................1-98 Common Tests for Optical Fiber.............................................................................................................1-98 Common Tests for Optical Cable Design ...............................................................................................1-99 Cable Interconnects..................................................................................................................................1-99 The Electromagnetic Spectrum .............................................................................................................1-100 Properties of Magnetic Materials and Magnetic Alloys .......................................................................1-101 Units .......................................................................................................................................................1-102 Summary of Capacitor Properties.........................................................................................................1-102 Frequency Response Magnitude Functions for Butterworth LP Prototype Filters .............................1-103 Frequency Response Magnitude Functions for Chebyshev LP Prototype Filters ...............................1-103 Op-amp Circuits ....................................................................................................................................1-104 Operating Characteristics of Common Battery Types .........................................................................1-108 Example Fourier Transform Pairs .........................................................................................................1-109 Advantages and Disadvantages of Satellites ..........................................................................................1-110 Satellites Frequency Allocations ............................................................................................................1-110 Typical Uplink and Downlink Satellite Frequencies (GHz).................................................................1-110 Frequency Allocations for FSS (Below ~30 GHz) ................................................................................1-110 Characteristics of Satellite PCS Systems ...............................................................................................1-111 Table of Laplace Operations ..................................................................................................................1-111 Table of Laplace Transforms ..................................................................................................................1-112 Properties of Fourier Transform ...........................................................................................................1-132

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Table of Fourier Transforms (x = t; y = w) ..........................................................................................1-133 Examples of Display Transfer Functions ..............................................................................................1-157 Common Fourier Transforms ...............................................................................................................1-157 Common Laplace Transforms ...............................................................................................................1-158 Important Properties of Laplace Transforms .......................................................................................1-158 Representation Values of Absolute Seebeck Thermoelectric Coefficients of Some Materials Used in Industrial Electronic Circuits ..............................................................................................1-159 Power Definitions (Single-Phase Circuits)............................................................................................1-159 Power Definitions (Three-Phase Circuits)............................................................................................1-160 Summary of Describing Differential Equations for Ideal Elements....................................................1-160 Properties of the Wave Types for Time-of-Flight Measuring ..............................................................1-161 Comparison of Strain Sensors...............................................................................................................1-162 Pressure-Sensing Elements ....................................................................................................................1-163 Permittivity (Dielectric Constants of Materials Used in Capacitors)..................................................1-164 The Key Elements of Mechatronics.......................................................................................................1-164 Mechanical Process and Information Processing Develop Towards Mechatronic Systems................1-165 Generalized Through and Across Variables for Processes with Energy Flow......................................1-165 Power and Energy Variables for Mechnical Systems ............................................................................1-165 Mechanical Dissipative Elements ..........................................................................................................1-166 Typical Coefficient of Friction Values ...................................................................................................1-166 Mechanical Potential Energy Storage Elemnents (Integral Form) ......................................................1-167 Mechanical Kinetic Energy Storage Elements (Integral Form) ...........................................................1-167 Resistance of Copper Wire ....................................................................................................................1-168 Type of Sensors for Various Measurement Objectives .........................................................................1-168 Type of Actuators and Their Features...................................................................................................1-170 Performance of Two Deep-Sea Armored Coaxes .................................................................................1-171 Past and Projected Future Growth of Data and Voice Traffic .............................................................1-172 Nominal Geographical Spans of Access, Metro-Core/Regional, and Long-Haul Networks...............1-172 ITU-T-Approved Band Assignment in the Low Attenuation Window of the Silica Fibers ...............1-173 Fiber Optics Chemical Sensors..............................................................................................................1-174 Typical Components of Various Glass Systems ....................................................................................1-175 Thyristor Symbol and Volt-Ampere Characteristics ............................................................................1-175 Triac Symbol and Volt-Ampere Characteristics....................................................................................1-176 GTO Symbol and Turn-Off Characteristics .........................................................................................1-176 Power MOSFET Circuit Symbol ...........................................................................................................1-177 Total Elongation at Failure of Selected Polymers .................................................................................1-177 Tensile Strength of Selected Wrought Aluminum Alloys .....................................................................1-178 Density of Selected Materials, Mg/m3 ...................................................................................................1-178 Applications in the Microwave Bands...................................................................................................1-179 The Elecromagnetic Spectrum ..............................................................................................................1-180 Typical Luminance Values .....................................................................................................................1-180 Resistivity of Selected Ceramics ............................................................................................................1-181 Properties of Magnetic Materials and Magnetic Alloys .......................................................................1-181 Thermal Conductivity of Common Materials......................................................................................1-182 Relative Thermal Conductivity of Various Materials as a Percentage of the Thermal Conductivity of Copper ....................................................................................................................1-182 Variation of Electrical and Thermal Properties of Common Insulators as a Function of Temperature .......................................................................................................................................1-182 Common Op-Amp Circuits ..................................................................................................................1-183 Electromagnetic Frequency Spectrum and Associated Wavelengths ...................................................1-187 Modulation Schemes, Glossary of Terms..............................................................................................1-187 Radar Bands ...........................................................................................................................................1-188 Thermal Conductivities of Typical Metals (W/m K) at Room Temperature .....................................1-189

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CRC Handbook of Engineering Tables

Thermal Coefficient of Linear Expansion of Some of the Materials Used in Microwave and RF Packaging Applications (at Room Temperature, in 10–6/K) ............................................................1-189 Properties of Some Typical Engineering Insulating Materials.............................................................1-190 Selected Material Properties of Semiconductor for Microwave and RF Applications........................1-190 Channel Designations for VHF and UHF Television Stations in the U. S. ........................................1-191 Radar Frequency Bands .........................................................................................................................1-192 Common-Carrier Microwave Frequencies Used in the U.S. ..............................................................1-192 Comparison of Amplitude Modulation Techniques ............................................................................1-193 Representative Specifications for Various Types of Flexible Air-Dielectric Coaxial Cable.................1-193 Four Drives of Change in Telecommunications...................................................................................1-194 Summary and Comparison of Second-Generation TDMA-Based System Parameters ......................1-194 Some Milestones for Multimedia ..........................................................................................................1-195 Comparison of Interconnect Characteristics for A1 and Cu...............................................................1-195 Comparison of High-Permittivity Constant Materials for DRAM Cell Capacitors ...........................1-195 Summary of Some Architectures and Applications Possible from a Molecular Computing System ................................................................................................................................................1-196 Comparison of Selected Important Semiconductors of Major SiC Polytypes with Silicon and GaAs............................................................................................................................................1-196 MEMS Processing Technologies ............................................................................................................1-197 Materials Properties of LPCVD Deposited MEMS Materials..............................................................1-198 Wafer Bonding Techniques....................................................................................................................1-198 Microrelays .............................................................................................................................................1-199 Electronic Packaging Requirements ......................................................................................................1-200 Thermal and Electrical Properties of Materials Used in Packaging ....................................................1-200 Some Properties of Ceramic Packaging Materials................................................................................1-201 Interconnect Technologies .....................................................................................................................1-201 Voltage Buffer Performance...................................................................................................................1-201 Embedded Memory Technologies and Applications............................................................................1-202 Recent High-Speed ADC Applications .................................................................................................1-202 Microprocessor Statistics .......................................................................................................................1-203 Comparing Electrical Parameters for BJT/HBT vs. FET......................................................................1-203 Status of Conventional and Renewable Power Sources........................................................................1-204 Benefits of Using Renewable Electricity................................................................................................1-204 Electromagnetic Radiation and Stable Elementary Particles ...............................................................1-205 Electromagnetic Frequency Spectra ......................................................................................................1-206 Dynamic Response of RCL System to a Step-Change Input ...............................................................1-207 Amplitude Response — Second-Order System ....................................................................................1-208 Phase Response — Second-Order System ............................................................................................1-209 Frequency-Response Approximations and Corrections .......................................................................1-210 Corrections to the Log Magnitude and Phase Diagram ......................................................................1-211 Block and Signal-Flow Diagrams ..........................................................................................................1-212 Block-Diagram Manipulations ..............................................................................................................1-213 Signal-Flow Diagrams............................................................................................................................1-215 Root Loci ................................................................................................................................................1-218 Transfer Function Plots for Typical Transfer Function........................................................................1-224

© 2004 by CRC Press LLC

Range

Rated Voltage, VR

Polycarbonate Polyester/Mylar Polypropylene Polystyrene

100 pF–30 mF 1000 pF–50 mF 100 pF–50 mF 10 pF–2.7 mF

Polysulfone Parylene Kapton Teflon

1000 pF–1 mF 5000 pF–1 mF 1000 pF–1 mF 1000 pF–2 mF

Mica Glass Porcelain Ceramic (NPO) Ceramic

5 pF–0.01 mF 5 pF–1000 pF 100 pF–0.1 mF 100 pF–1 mF 10 pF–1 mF

100–600 100–600 50–400 50–400 50–30,000

Paper Aluminum Tantalum (Foil)

0.01 mF–10 mF 0.1 mF–1.6 F 0.1 mF–1000 mF

200–1600 3–600 6–100

Thin-film Oil

10 pF–200 pF 0.1 mF–20 mF

6–30 200–10,000

Vacuum

1 pF–1000 pF

TTC ppm/˚C

Tolerance ±%

Insulation Resistance, MWmF

Dissipation Factor, %

Dielectric Absorption %

Temperature Range, ˚C

Comments, Applications

5

0.2 0.75 0.2 0.05

0.1 0.3 0.1 0.04

–55/+125 –55/+125 –55/+105 –55/+85

High quality, small, low TC Good, popular High quality low absorption High quality, large, low TC, signal filters High temperature

50–800 50–600 100–800 100–600

±50 +400 –200 –100

10 10 10 10

5 ¥ 10 105 105 106

50–200

+80 ±100 +100 –200

5 10 10 10

105 105 105 5 ¥ 106

0.3 0.1 0.3 0.04

0.2 0.1 0.3 0.04

–55/+150 –55/+125 –55/+220 –70/+250

–50 +140 +120 ±30

5 5 5 10

2.5 ¥ 104 106 5 ¥ 105 5 ¥ 103

0.001 0.001 0.10 0.02

0.75

–55/+125 –55/+125 –55/+125 –55/+125 –55/+125

2000–3600

±800 +2500 +800 +100

10 –10/+100 –10/+100 10

5 ¥ 103 100 20 106

1.0 10 4.0 0.01 0.5

4.2 0.75

2.5 8.0 8.5

–55/+125 –40/+85 –55/+85

High temperature High temperature lowest absorption Good at RF, low TC Excellent long-term stability Good long-term stability Active filters, low TC Small, very popular selectable TC Motor capacitors Power supply filters short life High capacitance small size, low inductance

–55/+125

Cost High Medium High Medium High High High High High High High Medium Low Low High High High

High voltage filters, large, long life Transmitters

From Whitaker, J.C., The origins of AC line disturbances, in AC Power Systems Handbook, 2nd ed., CRC Press, Boca Raton, FL, 1999, p. 56. Originally published in Filanovsky, I.M., Capacitance and Capacitors, in The Electronics Handbooks, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 371. With permission.

1-7

© 2004 by CRC Press LLC

1587_Book.fm Page 7 Sunday, August 31, 2003 9:44 PM

Capacitor Type

Electrical and Computer Engineering

Parameters and Characteristics of Discrete Capacitors

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1-8

CRC Handbook of Engineering Tables

Electrical Properties of Common Insulating Liquids Viscosity cST (37.8˚C)

Dielectric Constant (at 60 Hz, 25˚C)

Dissipation Factor (at 60 Hz, 100˚C)

Breakdown Strength (kV cm–1)

21 170 49.7 2365 9.75 6.0 110 (SUS) 2200 (SUS at 100˚C) 50 98 (100˚C) 0.64

2.2 2.15 2.3 2.23 2.25 2.1 2.14 (at 1 MHz) 2.22 (at 1 MHz) 2.7 3.74 1.86

0.001 0.001 0.001 0.001 0.001 0.0004 0.0003 0.0005 0.00015 0.06 <0.0005

>118 >118 >118 >118 >128 >138 >138 >138 >138 >138 >138

Liquid Capacitor oil Pipe cable oil Self-contained cable oil Heavy cable oil Transformer oil Alkyl benzene Polybutene pipe cable oil Polybutene capacitor oil Silicone fluid Castor oil C8F16O fluorocarbon

From Whitaker, J.C., The origins of AC line disturbances, in AC Power Systems Handbook, 2nd ed., CRC Press, Boca Raton, FL, 1999, p. 64. Originally published in Bartnikas, R., Dielectrics and Insulators, in The Electrical Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1993, p. 1132. With permission.

Types of Systemwide Protection Equipment Available to Facility Managers and the AC Line Abnormalities That Each Approach Can Handle System UPS system and standby generator UPS system Secondary spot network1 Secondary selective network2 Motor-generator set Shielded isolation transformer Suppressors, filters, lightning arrestors Solid-state line voltage regulator/filter 1

Type 1

Type 2

All source transients; no load transients All source transients; no load transients None

None

None

Most

All source transients; no load transients Most source transients; no load transients Most transients Most source transients; no load transients

Type 3

All

All

All

Most

All outages shorter than the battery supply discharge time Most, depending on the type of outage Most, depending on the type of outage Only brown-out conditions

None

None

None

None

Some, depending on the response time of the system

Only brown-out conditions

Dual power feeder network. Dual power feeder network using a static (solid-state) transfer switch. From Whitaker, J.C., Power system protection alternatives, in AC Power Systems Handbook, 2nd ed., CRC Press, Boca Raton, FL, 1999, p. 267. After Key, Lt. Thomas, “The Effects of Power Disturbances on Computer Operation,” IEEE Industrial and Commercial Power Systems Conference, Cincinnati, June 7, 1978, and Federal Information Processing Standards Publication No. 94, Guideline on Electrical Power for ADP Installations, U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., 1983. 2

© 2004 by CRC Press LLC

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1-9

Electrical and Computer Engineering

Comparison of System Grounding Methods System Grounding Method Characteristic Assuming No Fault Escalation

Solidly Grounded

Operation of overcurrent device on first ground fault Control of internally generated transient overvoltages Control of steady-state overvoltages Flash hazard Equipment damage from arcing ground-faults Overvoltage (on unfaulted phases) from ground-fault1 Can serve line-to-neutral loads

Ungrounded

High Resistance

Yes

No

No

Yes

No

Yes

Yes Yes Yes

No No No

Yes No No

L-N Voltage

>>L-L-Voltage

L-L Voltage

Yes

No

No

1

L = line, N = neutral From Whitaker, J.C., Facility grounding, in AC Power Systems Handbook, 2nd ed., CRC Press, Boca Raton, FL:, 1999, p. 373. After IEEE Standard 142, “Recommended Practice for Grounding Industrial and Commercial Power Systems,” IEEE, New York, 1982.

Typical Resistivity of Common Soil Types Type of Soil Resistivity in W/cm

Average

Minimum

Maximum

Filled land, ashes, salt marsh Top soils, loam Hybrid soils Sand and gravel

2400 4100 6000 90,000

600 340 1000 60,000

7000 16,000 135,000 460,000

From Whitaker, J.C., Facility grounding, in AC Power Systems Handbook, 2nd ed., CRC Press, Boca Raton, FL, 1999, p. 379.

© 2004 by CRC Press LLC

1587_Book.fm Page 10 Sunday, August 31, 2003 9:44 PM

1-10

CRC Handbook of Engineering Tables

Specifications of Standard Copper Wire Turns per Linear Inch1

Wire Size AWG

Dia. in Mils

Cir. Mil Area

Enamel

S.C.E.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

289.3 257.6 229.4 204.3 181.9 162.0 144.3 128.5 114.4 101.9 90.7 80.8 72.0 64.1 57.1 50.8 45.3 40.3 35.9 32.0 28.5 25.3 22.6 20.1 17.9 15.9 14.2 12.6 11.3 10.0 8.9 8.0 7.1 6.3 5.6 5.0 4.5 4.0 3.5

83810 05370 62640 41740 33100 26250 20820 16510 13090 10380 8234 6530 5178 4107 3257 2583 2048 1624 1288 1022 810 642 510 404 320 254 202 160 127 101 50 63 50 40 32 25 20 16 12

— — — — — — — 7.6 8.6 9.6 10.7 12.0 13.5 15.0 16.8 18.9 21.2 23.6 26.4 29.4 33.1 37.0 41.3 46.3 51.7 58.0 64.9 72.7 81.6 90.5 101 113 127 143 158 175 198 224 248

— — — — — — — — — 9.1 — 11.3 — 14.0 — 17.3 — 21.2 — 25.8 — 321.3 — 37.6 — 46.1 — 54.6 — 64.1 — 74.1 — 86.2 — 103.1 — 116.3 —

D.C.C.

Ohms per 100 ft2

Current Carry Capacity3

Dia. in mm

— — — — — — — 7.1 7.8 8.9 9.8 10.9 12.8 13.8 14.7 16.4 18.1 19.8 21.8 23.8 26.0 30.0 37.6 35.6 38.6 41.8 45.0 48.5 51.8 55.5 59.2 61.6 66.3 70.0 73.5 77.0 80.3 83.6 86.6

0.1239 0.1563 0.1970 0.2485 0.3133 0.3951 0.4982 0.6282 0.7921 0.9989 1.26 1.588 2.003 2.525 3.184 4.016 5.064 6.386 8.051 10.15 12.8 16.14 20.36 25.67 32.37 40.81 51.47 64.9 81.83 103.2 130.1 164.1 206.9 260.9 329.0 414.8 523.1 659.6 831.8

119.6 94.8 75.2 59.6 47.3 37.5 29.7 23.6 18.7 14.8 11.8 9.33 7.40 5.87 4.65 3.69 2.93 2.32 1.84 1.46 1.16 0.918 0.728 0.577 0.458 0.363 0.288 0.228 0.181 0.144 0.114 0.090 0.072 0.057 0.045 0.036 0.028 0.022 0.018

7.348 6.544 5.827 5.189 4.621 4.115 3.665 3.264 2.906 2.588 2.305 2.063 1.828 1.628 1.450 1.291 1.150 1.024 0.912 0.812 0.723 0.644 0.573 0.511 0.455 0.406 0.361 0.321 0.286 0.255 0.227 0.202 0.180 0.160 0.143 0.127 0.113 0.101 0.090

Notes: 1 Based on 25.4 mm. 2 Ohms per 1000 ft measured at 20˚C. 3 Current carrying capacity at 700 C.M./A. From Whitaker, J.C., Conversion tables, in AC Power Systems Handbook, 2nd., CRC Press, Boca Raton, FL, 1999, pp. 528–529.

© 2004 by CRC Press LLC

1587_Book.fm Page 11 Sunday, August 31, 2003 9:44 PM

1-11

Electrical and Computer Engineering

Parameters of Some First-Generation Cellular Standards Parameters Tx Frequency (MHz) Mobile Base Station Channel bandwidth (kHz) Spacing between forward and reverse channels (MHz) Speech signal FM deviation Control signal data rate (kbps) Handoff decision is based on

AMPS

C450

NMT 450

NTT

TACS

824–849 869–894 30

450–455.74 460–465.74 20

453–457.5 463–467.5 25

925–940 870–885 25

890–915 935–960 25

45

10

10

55

45

±12

±5

±5

±5

±9.5

10

5.28

Power received at base

1.2

Round-trip delay

Power received at base

0.3

8

Power received at base

Power received at base

From Godara, L.C., Cellular systems, in Handbook of Antennas in Wireless Communications, Godara, L.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-15.

Parameters of Some Second-Generation Cellular Standards Parameters TX frequencies (MHz) Mobile Base station Channel bandwidth (kHz) Spacing between forward and reverse channels (MHz) Modulation Frame duration (ms)

IS-54

GSM

IS-95

PDC

824–849 869–894 30 kHz 45

890–915 935–960 200 kHz 45

824–849 869–894 1250 kHz 45

940–956 and 1429–1453 810–826 and 1477–1501 25 kHz 30/48

p/4 DQPSK 40

GMSK

BPSK/QPSK

4.615

20

p/4 DQPSK 20

From Godara, L.C., Cellular systems, in Handbook of Antennas in Wireless Communications, Godara, L.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-16.

© 2004 by CRC Press LLC

1587_Book.fm Page 12 Sunday, August 31, 2003 9:44 PM

1-12

CRC Handbook of Engineering Tables

Comparison of Satellite Systems as a Function of Orbit Characteristic Satellite height (km) Orbital period (hr) Number of satellites Two-way propagation delay (ms) Satellite life (years) Elevation angle Visibility of satellite Handheld terminal Handover Cost of satellite Gateway cost Network complexity Radio frequency output power Propagation loss

LEO

MEO

GEO

600–1,500 1–2 40–80 10–15 3–7 Medium Short Possible Frequent Maximum Highest Complex Low Low

9,000–11,000 6–8 8–20 150–250 10–15 Best Medium Possible Infrequent Minimum Medium Medium Medium Medium

35,800 24 2–4 480–540 10–15 Good Permanent Restricted None Medium Lowest Simplest High High

From Ryan, M.J., Satellite-based mobile communications, in Handbook of Antennas in Wireless Communications, Godara, L.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 2-8.

Summary of Transmission Media Characteristics Cable Type Capacitance Characteristic Impedance Cable Attenuation Cable Twists Shield Coverage Cable Termination Direct Coupled Stub Length Transformer Coupled Stub Length

Twisted Shielded Pair 30.0 pF/ft max — wire to wire 70.0 to 85.0 ohms at 1 MHz 1.5 dbm/100 ft at 1 MHz 4 twists per foot maximum 90% minimum Cable impedance (±2%) Maximum of 1 ft Maximum of 20 ft

From deLong, C., AS 15531/MIL-STD-1553B digital time division command/response multiplex data bus, in The Avionics Handbook, Spitzer, C.R., Ed., CRC Press, Boca Raton, FL, 2001, , p. 1-5.

CSDB Physical Characteristics Modulation Technique Logic Sense for Logic “0” Logic Sense for Logic “1” Bus Receiver Bus Transmitter Bus Signal Rates Signal Rise-Time and Fall-Time Receiver Capacitance Loading Transmitter Driver Capability

Non-Return to Zero (NRZ) Line B Positive with Respect to Line A Line A Positive with Respect to Line B High Impedance, Differential Input Differential Line Driver Low Speed: 12,500 bps High Speed: 50,000 bps Low Speed: 8 ms High-Speed: 0.8–1.0 ms Typical: 600 pF Maximum: 1,200 pF Maximum: 12,000 pF

From Harrison, L.H., Commercial standard digital bus, in The Avionics Handbook, Spitzer, C.R., Ed., CRC Press, Boca Raton, FL, 2001, p. 3-4. Originally published in Commercial Standard Digital Bus, 8th ed., Collins General Aviation Division, Rockwell International Corporation, Cedar Rapids, IA, January 30, 1991.

© 2004 by CRC Press LLC

1587_Book.fm Page 13 Sunday, August 31, 2003 9:44 PM

1-13

Electrical and Computer Engineering

Sensor Data Required for Full Flight Regime Operation Input Data Attitude Airspeed

Altitude Vertical Speed Slip/Skid Heading

Navigation

Reference Information

Flight Path

Flight Path Acceleration

Automatic Flight Control System Miscellaneous

Data Source Pitch and Roll Angles — 2 independent sources Calibrated Airspeed Low Speed Awareness Speed(s) (e.g., Vstall) High Speed Awareness Speed(s) (e.g., Vmo) Barometric Altitude (pressure altitude corrected with altimeter setting) Radio Altitude Vertical Speed (inertial if available, otherwise raw air data) Lateral Acceleration Magnetic Heading True Heading or other heading (if selectable) Heading Source Selection (if other than Magnetic selectable) Selected Course VOR Bearing/Deviation DME Distance Localizer Deviation Glideslope Deviation Marker Beacons Bearings/Deviations/Distances for any other desired nav signals (e.g., ADF, TACAN, RNAV/FMS) Selected Airspeed Selected Altitude Selected Heading Other Reference Speed Information (e.g., V1, VR, Vapch) Other Reference Altitude Information (e.g., landing minimums [DH/MDA], altimeter setting) Pitch Angle Roll Angle Heading (Magnetic or True, same as Track) Ground Speed (inertial or equivalent) Track Angle (Magnetic or True, same as Heading) Vertical Speed (inertial or equivalent) Pitch Rate, Yaw Rate Longitudinal Acceleration Lateral Acceleration Normal Acceleration Pitch Angle Roll Angle Heading (Magnetic or True, same as Track) Ground Speed (inertial or equivalent) Track Angle (Magnetic or True, same as Heading) Vertical Speed (inertial or equivalent) Flight Director Guidance Commands Autopilot/Flight Director Modes Autothrottle Modes Wind Speed Wind Direction (and appropriate heading reference) Mach Windshear Warning(s) Ground Proximity Warning(s) TCAS Resolution Advisory Information

From Wood, R.B. and Howells, P.J., Head-up displays, in The Avionics Handbook, Spitzer, C.R., Ed., CRC Press, Boca Raton, FL, 2001, p. 4-14.

© 2004 by CRC Press LLC

1587_Book.fm Page 14 Sunday, August 31, 2003 9:44 PM

1-14

CRC Handbook of Engineering Tables

Categorization of Fault-Tolerant Software Techniques Multiversion Software N-Version Program Cranfield Algorithm for Fault-Tolerance (CRAFT) Food Taster Distinct and Dissimilar Software Recovery Blocks Deadline Mechanism Dissimilar Backup Software Exception Handlers Hardened Kernel Robust Data Structures and Audit Routines Run Time Assertionsa Hybrid Multiversion Software and Recovery Block Techniques Tandem Consensus Recovery Blocks a

Not a complete fault-tolerant software technique as it only detects errors. From Hitt, E.F. and Mulcare, D., Fault-tolerant avionics, in The Avionics Handbook, Spitzer, C.R., Ed., CRC Press, Boca Raton, FL, 2001, p. 28-20. Originally from Hitt, E. et al., Study of Fault-Tolerant Software Technology, NASA CR 172385.

© 2004 by CRC Press LLC

1-15

© 2004 by CRC Press LLC

1587_Book.fm Page 15 Sunday, August 31, 2003 9:44 PM

Electrical and Computer Engineering

From The Biomedical Engineering Handbook, 2nd ed., Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000. p. x.

Cell Type Erythrocytes (red blood cells)

Corpuscular Diameter (mm)*

Corpuscular Surface Area (mm2)*

Corpuscular Volume (mm3)*

Mass Density (g/cm3)*

Percent Water*

Percent Protein*

Percent Extractives*†

4.2–5.4 ¥ 106 4.6–6.2 ¥ 106 (5 ¥ 106) 4000–11000 (7500)

6–9 (7.5) Thickness 1.84–2.84 “Neck” 0.81–1.44 6–10

120–163 (140)

80–100 (90)

1.089–1.100 (1.098)

64–68 (66)

29–35 (32)

1.6–2.8 (2)

300–625

160–450

1.055–1.085

52–60 (56)

30–36 (33)

4–18 (11)

2–6 ¥ 103 (4875) 45–480 (225) 0–113 (75)

8–8.6 (8.3) 8–9 (8.5) 7.7–8.5 (8.1)

422–511 (467) 422–560 (491) 391–500 (445)

268–333 (300) 268–382 (321) 239–321 (278)

1.075–1.085 (1.080) 1.075–1.085 (1.080) 1.075–1.085 (1.080)

—

—

—

—

—

—

—

—

—

1000–4800 (1875) 100–800 (450) (1.4 ), 2.14 ()–5 ¥105

6.75–7.34 (7.06) 9–9.5 (9.25) 2–4 (3) Thickness 0.9–1.3

300–372 (336) 534–624 (579) 16–35 (25)

161–207 (184) 382–449 (414) 5–10 (7.5)

1.055–1.070 (1.063) 1.055–1.070 (1.063) 1.04–1.06 (1.05)

—

—

—

—

—

—

60–68 (64)

32–40 (36)

Neg.

*Normal physiologic range, with “typical” value in parentheses. †Extractives include mostly minerals (ash), carbohydrates, and fats (lipids). From Schneck, D.J., An outline of cardiovascular structure and function, in The Biomedical Engineering Handbook, 2nd ed., vol. 1., Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-2.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Leukocytes (white blood cells) Granulocytes Neutrophils: 55–70% WBC (65%) Eosinophils: 1–4% WBC (3%) Basophils: 0–1.5% WBC (1%) Agranulocytes Lymphocytes: 20–35% WBC (25%) Monocytes: 3–8% WBC (6%) Thrombocytes (platelets) (2.675 ¥ 105)

Number Cells per mm3 Blood*

1587_Book.fm Page 16 Friday, September 26, 2003 12:10 PM

1-16

Hematocytes

1587_Book.fm Page 17 Friday, September 26, 2003 12:10 PM

1-17

Electrical and Computer Engineering

Plasma

Constituent Total protein, 7% by weight Albumin (56% TP) a1-Globulin (5.5% TP) a2-Globulin (7.5% TP) b-Globulin (13% TP) g-Globulin (12% TP) Fibrinogen (4% TP) Other (2% TP) Inorganic ash, 0.95% by weight Sodium Potassium Calcium Magnesium Chloride Bicarbonate Phosphate Sulfate Other Lipids (fats), 0.80% by weight Cholesterol (34% TL) Phospholipid (35% TL) Triglyceride (26% TL) Other (5% TL) Extractives, 0.25% by weight Glucose Urea Carbohydrate Other

Concentration Range (mg/dl plasma)

Typical Plasma Value (mg/dl)

Molecular Weight Range

Typical Value

Typical size (nm)

6400–8300

7245

21,000–1,200,000

—

—

2800–5600

4057

66,500–69,000

69,000

15 ¥ 4

300–600

400

21,000–435,000

60,000

5–12

400–900

542

100,000–725,000

200,000

50–500

500–1230

942

90,000–1,200,000

100,000

18–50

500–1800

869

150,000–196,000

150,000

23 ¥ 4

150–470

290

330,000–450,000

390,000

(50–60) ¥ (3–8)

70–210

145

70,000–1,000,000

200,000

(15–25) ¥ (2–6)

930–1140

983

20–100

300–340 13–21 8.4–11.0 1.5–3.0 336–390 110–240 2.7–4.5 0.5–1.5 0–100 541–1000

325 17 10 2 369 175 3.6 1.0 80.4 828

12–105 “free” 72–259 esterified, 84–364 “total” 150–331

59 224 283 292

386.67

65–240

215

400–1370

0–80

38

280–1500

200–500

259

60–120, fasting 20–30 60–105 11–111

90 25 83 61

— — — — — — — — —

20–100 44,000–3,200,000

690–1010

— — — 180.16–342.3 —

22.98977 39.09800 40.08000 24.30500 35.45300 61.01710 95.97926 96.05760 — = Lipoproteins

— (Radius) 0.102 (Na+) 0.138 (K+) 0.099 (Ca2+) 0.072 (Mg2+) 0.181 (Cl–) 0.163 (HCO3–) 0.210 (HPO42–) 0.230 (SO42–) 0.1–0.3 Up to 200 or more

Contained mostly in intermediate to LDL b-lipoproteins; higher in women Contained mainly in HDL to VHDL a1-lipoproteins Contained mainly in VLDL a2-lipoproteins and chylomicrons Fat-soluble vitamins, prostaglandins, fatty acids — — 180.1572 60.0554 — —

0.86 D 0.36 D 0.74–0.108 D —

From Schneck, D.J., An outline of cardiovascular structure and function, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-3.

© 2004 by CRC Press LLC

1587_Book.fm Page 18 Friday, September 26, 2003 12:10 PM

1-18

CRC Handbook of Engineering Tables

Arterial System* Blood Vessel Type

(Systemic) Typical Number

Internal Diameter Range

Length Range†

Wall Thickness

Systemic Volume

(Pulmonary) Typical Number

Pulmonary Volume

Aorta 1 1.0–3.0 cm 30–65 cm 2–3 mm 156 ml — — Pulmonary artery — 2.5–3.1 cm 6–9 cm 2–3 cm — 1 52 ml Wall morphology: Complete tunica adventitia, external elastic lamina, tunica media, internal elastic lamina, tunica intima, subendothelium, endothelium, and vasa vasorum vascular supply Main branches 32 5 mm–2.25 cm 3.3–6 cm 2 mm 83.2 ml 6 41.6 ml (Along with the aorta and pulmonary artery, the largest, most well-developed of all blood vessels) Large arteries 288 4.0–5.0 mm 1.4–2.8 cm 1 mm 104 ml 64 23.5 ml (A well-developed tunica adventitia and vasa vasorum, although wall layers are gradually thinning) Medium arteries 1152 2.5–4.0 mm 1.0–2.2 cm 0.75 mm 117 ml 144 7.3 ml Small arteries 3456 1.0–2.5 mm 0.6–1.7 cm 0.50 mm 104 ml 432 5.7 ml Tributaries 20,736 0.5–1.0 mm 0.3–1.3 cm 0.25 mm 91 ml 5184 7.3 ml (Well-developed tunica media and external elastic lamina, but tunica adventitia virtually nonexistent) Small rami 82,944 250–500 mm 0.2–0.8 cm 125 mm 57.2 ml 11,664 2.3 ml Terminal branches 497,664 100–250 mm 1.0–6.0 mm 60 mm 52 ml 139,968 3.0 ml (A well-developed endothelium, subendothelium, and internal elastic lamina, plus about two to three 15-mm-thick concentric layers forming just a very thin tunica media; no external elastic lamina) Arterioles 18,579,456 25–100 mm 0.2–3.8 mm 20–30 mm 52 ml 4,094,064 2.3 ml Wall morphology: More than one smooth muscle layer (with nerve association in the outermost muscle layer), a welldeveloped internal elastic lamina; gradually thinning in 25- to 50-mm vessels to a single layer of smooth muscle tissue, connective tissue, and scant supporting tissue. Metarterioles 238,878,720 10–25 mm 0.1–1.8 mm 5–15 mm 41.6 ml 157,306,536 4.0 ml (Well-developed subendothelium; discontinuous contractile muscle elements; one layer of connective tissue) Capillaries 16,124,431,360 3.5–10 mm 0.5–1.1 mm 0.5–1 mm 260 ml 3,218,406,696 104 ml (Simple endothelial tubes devoid of smooth muscle tissue; one-cell-layer-thick walls) *Vales are approximate for a 68.7-kg individual having a total blood volume of 5200 ml. †Average uninterrupted distance between branch origins (except aorta and pulmonary artery, which are total length). From Schneck, D.J., An outline of cardiovascular structure and functions, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-8.

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Electrical and Computer Engineering

Venous System Blood Vessel Type

(Systemic) Typical Number

Internal Diameter Range

Length Range

Wall Thickness

Systemic Volume

(Pulmonary) Typical Pulmonary Number Volume

Postcapillary venules 4,408,161,734 8–30 mm 0.1–0.6 mm 1.0–5.0 mm 166.7 ml 306,110,016 10.4 ml (Wall consists of thin endothelium exhibiting occasional pericytes (pericapillary connective tissue cells) which increase in number as the vessel lumen gradually increases) Collecting venules 160,444,500 30–50 mm 0.1–0.8 mm 5.0–10 mm 161.3 ml 8,503,056 1.2 ml (One complete layer of pericytes, one complete layer of veil cells (veil-like cells forming a thin membrane), occasional primitive smooth muscle tissue fibers that increase in number with vessel size) Muscular venules 32,088,900 50–100 mm 0.2–1.0 mm 10–25 mm 141.8 ml 3,779,136 3.7 ml (Relatively thick wall of smooth muscle tissue) Small collecting veins 10,241,508 100–200 mm 0.5–3.2 mm 30 mm 329.6 ml 419,904 6.7 ml (Prominent tunica media of continuous layers of smooth muscle cells) Terminal branches 496,900 200–600 mm 1.0–6.0 mm 30–150 mm 206.6 ml 34,992 5.2 ml (A well-developed endothelium, subendothelium, and internal elastic lamina; well-developed tunica media but fewer elastic fibers than corresponding arteries and much thinner walls) Small veins 19,968 600 mm–1.1 mm 2.0–9.0 mm 0.25 mm 63.5 ml 17,280 44.9 ml Medium veins 512 1–5 mm 1–2 cm 0.50 mm 67.0 ml 144 22.0 ml Large veins 256 5–9 mm 1.4–3.7 cm 0.75 mm 476.1 ml 48 29.5 ml (Well-developed wall layers comparable to large arteries but about 25% thinner) Main branches 224 9.0 mm–2.0 cm 2.0–10 cm 1.00 mm 1538.1 ml 16 39.4 ml (Along with the vena cava and pulmonary veins, the largest, most well-developed of all blood vessels) Vena cava 1 2.0–3.5 cm 20–50 cm 1.50 mm 125.3 ml — — Pulmonary veins — 1.7–2.5 cm 5–8 cm 1.50 mm — 4 52 ml Wall morphology: Essentially the same as comparable major arteries but a much thinner tunica intima, a much thinner tunica media, and a somewhat thicker tunica adventitia; contains a vasa vasorum Total systemic blood volume: 4394 ml—84.5% of total blood volume; 19.5% in arteries (~3:2 large:small), 5.9% in capillaries, 74.6% in veins (~3:1 large:small); 63% of volume is in vessels greater than 1 mm internal diameter Total pulmonary blood volume: 468 ml—9.0% of total blood volume; 31.8% in arteries, 22.2% in capillaries, 46% in veins; 58.3% of volume is in vessels greater than 1 mm internal diameter; remainder of blood in heart, about 338 ml (6.5% of total blood volume) From Schneck, D.J., An outline of cardiovascular structure and functions, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-8.

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CRC Handbook of Engineering Tables

Main Endocrine Glands and the Hormones They Produce and Release Gland

Hormone

Hypothalamus/median eminence

Anterior pituitary

Posterior pituitary Thyroid Parathyroid Adrenal cortex Adrenal medulla Pancreas

Gonads: Testes Ovaries

Chemical Characteristics

Thyrotropin-releasing hormone (TRH) Somatostatin Gonadotropin-releasing hormone Growth hormone-releasing hormone Corticotropin-releasing hormone Prolactin inhibitor factor Thyrotropin (TSH) Luteinizing hormone Follicle-stimulating hormone (FSH) Growth hormone Prolactin Adrenocorticotropin (ACTH) Vasopressin (antidiuretic hormone, ADH) Oxytocin Triidothyronine (T3) Thyroxine (T4) Parathyroid hormone (PTH) Cortisol Aldosterone Epinephrine Norepinephrine Insulin Glucagon Somatostatin Testosterone Oestrogen Progesterone

Peptides Amine

Glycoproteins Proteins

Peptides Tyrosine derivatives Peptide Steroids Catecolamines Proteins

Steroids

From Cramp, D.G. and Carson, E.R., Endocrine system, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 2-3.

Typical Lung Volumes for Normal, Healthy Males Lung Volume Total lung capacity (TLC) Residual volume (RV) Vital capacity (VC) Inspiratory reserve volume (IRV) Expiratory reserve volume (ERV) Functional residual capacity (FRC) Anatomic dead volume (VD) Upper airways volume Lower airways volume Physiologic dead volume (VD) · Minute volume (Ve) at rest Respiratory period (T) at rest Tidal volume (VT) at rest Alveolar ventilation volume (VA) at rest Minute volume during heavy exercise Respiratory period during heavy exercise Tidal volume during heavy exercise Alveolar ventilation volume during exercise

Normal Values 6.0 ¥ 10–3 m3 1.2 ¥ 10–3 m3 4.8 ¥ 10–3 m3 3.6 ¥ 10–3 m3 1.2 ¥ 10–3 m3 2.4 ¥ 10–3 m3 1.5 ¥ 10–4 m3 8.0 ¥ 10–5 m3 7.0 ¥ 10–5 m3 1.8 ¥ 10–4 m3 1.0 ¥ 10–4 m3/s 4s 4.0 ¥ 10–4 m3 2.5 ¥ 10–4 m3 1.7 ¥ 10–3 m3/s 1.2 s 2.0 ¥ 10–3 m3 1.8 ¥ 10–3 m3

(6,000 cm3) (1,200 cm3) (4,800 cm3) (3,600 cm3) (1,200 cm3) (2,400 cm3) (150 cm3) (80 cm3) (70 cm3) (180 cm3) (6,000 cm3/min) (400 cm3) (250 cm3) (10,000 cm3/min) (2,000 cm3) (1,820 cm3)

From Johnson, A.T., Lausted, C.G., and Bronzino, J.D., Respiratory system, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 7-7.

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Electrical and Computer Engineering

Molecular Masses, Gas Constants, and Volume Fractions for Air and Constituents

Constituent Air Ammonia Argon Carbon dioxide Carbon monoxide Helium Hydrogen Nitrogen Oxygen

Molecular Mass kg/mol

Gas Constant, N·m/(mol·K)

Volume Fraction in Air, m3/m3

29.0 17.0 39.9 44.0 28.0 4.0 2.0 28.0 32.0

286.7 489.1 208.4 189.0 296.9 2078.6 4157.2 296.9 259.8

1.0000 0.0000 0.0093 0.0003 0.0000 0.0000 0.0000 0.7808 0.2095

Note: Universal gas constant is 8314.43 N·m/kg·mol·K. From Johnson, A.T., Lausted, C.G., and Bronzino, J.D., Respiratory system, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 7-9.

Conductivity Values for Cardiac Bidomain S/mm

Clerc [1976]

Roberts [1982]

gix giy gax gay

1.74 ¥ 10–4 1.93 ¥ 10–5 6.25 ¥ 10–4 2.36 ¥ 10–4

3.44 ¥ 10–4 5.96 ¥ 10–5 1.17 ¥ 10–4 8.02 ¥ 10–5

From Plonsey, R., Volume conductor theory, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 9-5.

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CRC Handbook of Engineering Tables

Schematic of energy transformations leading to muscular mechanical work. (From Johnson, A.T. and Hurley, B.F., Factors affecting mechanical work in humans, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 27-2.)

Typical Values and Estimates for Young’s Modulus E Compact bone Keratin Basilar membrane fibers Microtubules Collagen Reissner’s membrane Actin Red blood cell, extended (assuming thickness = 10 nm) Rubber, elastin Basilar membrane ground substance Tectorial membrane Jell-O Henson’s cells

20 3 1.9 1.2 1 60 50 45 4 200 30 3 1

GPa GPa GPa GPa GPa MPa MPa MPa MPa kPa kPa kPa kPa

From Steele, C.R., Baker, G.J., Tolomeo, J.A., and Zetes-Tolomeo, D.E., Cochlear mechanics, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 35-4.

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Electrical and Computer Engineering

Properties of Bone, Teeth, and Biomaterials

Material Hard Tissue Tooth, bone, human compact bone, longitudinal direction Tooth dentin Tooth enamel Polymers Polyethylene (UHMW) Polymethyl methacrylate, PMMA PMMA bone cement Metals 316L Stainless steel (wrought) Co-Cr-Mo (cast) Co Ni Cr Mo (wrought) Ti6A14V Composites Graphite-epoxy (unidirectional fibrous, high modulus) Graphite-epoxy (quasi-isotropic fibrous) Dental composite resins (particulate) Foams Polymer foams

Young’s modulus E[GPa]

Density r (g/cm3)

17

1.8

130 (tension)

18 50

2.1 2.9

138 (compression)

1 3 2

0.94 1.1 1.18

30 (tension) 65 (tension) 30 (tension)

200 230 230 110

7.9 8.3 9.2 4.5

1000 (tension) 660 (tension) 1800 (tension) 900 (tension)

215

1.63

1240 (tension)

46 10-16

1.55

579 (tension) 170-260 (compression)

10–4–1

0.002–0.8

Strength (MPa)

0.01–1 (tension)

From Lakes, R., Composite biomaterials, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 40-6.

Biomedical Signals Classification Bioelectric Action potential Electroneurogram (ENG) Electroretinogram (ERG) Electro-oculogram (EOG) Electroencephalogram (EEG) Surface

Acquisition

Frequency Range

10 mV–100 mV

Needle electrode Microelectrode Surface electrodes

100 Hz–1 kHz 0.2–200 Hz dc–100 Hz

5 mV–10 mV 0.5 mV–1 mV 10 mV–5 mV

Surface electrodes

0.5–100 Hz

2–100 mV

Multichannel (6–32) scalp potential Young children, deep sleep and pathologies Temporal and central areas during alert states Awake, relaxed, closed eyes

50–100 mV 100–200 mV

Bursts of about 0.2 to 0.6 s Bursts during moderate and deep sleep Response of brain potential to stimulus Occipital lobe recordings, 200-ms duration Sensory cortex Vertex recordings

Theta range

4–8 Hz

Alpha range Beta range Sleep spindles K-complexes

Somatosensory (SEP) Auditory (AEP)

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Invasive measurement of cell membrane potential Potential of a nerve bundle Evoked flash potential Steady-corneal-retinal potential

100 Hz–2 kHz

0.5–4 Hz

Visual (VEP)

Comments

Microelectrodes

Delta range

Evoked potentials (EP)

Dynamic Range

8–13 Hz 13–22 Hz 6–15 Hz 12–14 Hz

0.1–20 mV

Surface electrodes 1–300 Hz 2 Hz–3 kHz 100 Hz–3 kHz

1–20 mV 0.5–10 mV

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CRC Handbook of Engineering Tables

Biomedical Signals (continued) Classification

Acquisition

Frequency Range

Dynamic Range

Electrocorticogram

Needle electrodes

100 Hz–5 kHz

Electromyography (EMG) Single-fiber (SFEMG)

Needle electrode

500 Hz–10 kHz

1–10 mV

Needle electrode

5 Hz–10 kHz

100 mV–2 mV

2–500 Hz 0.01–1 Hz 0.05–100 Hz 100 Hz–1 kHz

50 mV–5 mV

Motor unit action potential (MUAP) Surface EMG (SEMG) Skeletal muscle Smooth muscle Electrocardiogram (ECG) High-Frequency ECG

Comments Recordings from exposed surface of brain Action potentials from single muscle fiber

Surface electrodes

Surface electrodes Surface electrodes

1–10 mV 100 mV–2 mV

Notchs and slus waveforms superimposed on the ECG.

From Cohen, A., Biomedical signals: Origin and dynamic characteristics; frequency-domain analysis, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 52-4.

Amplitudes and spectral range of some important biosignals. The various biopotentials completely cover the area 10–6 V to almost 1 V and from dc to 10 kHz. (From Nagel, J.H., Biopotential amplifiers, in The Biomedical Engineering Handbook, 2nd ed., vol. 1, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 70-5.)

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Electrical and Computer Engineering

Representative Thermal Property Values

Tissue

Thermal Conductivity (W/m-K)

Thermal Diffusivity (m2/s)

Aorta Fat of spleen Spleen Pancreas Cerebral cortex Renal cortex Myocardium Liver Lung Adenocarcinoma of breast Resting muscle bone Whole blood (21˚C) Plasma (21˚C) Water

0.461 [16] 0.3337 [44] 0.5394 [44] 0.5417 [44] 0.5153 [44] 0.5466 [44] 0.5367 [44] 0.5122 [44] 0.4506 [44] 0.5641 [44] 0.478 [50] 0.492 [50] 0.570 [50] 0.628 [6]

1.25 ¥ 10–7 [16] 1.314 ¥ 10–7 [44] 1.444 ¥ 10–7 [44] 1.702 ¥ 10–7 [44] 1.468 ¥ 10–7 [44] 1.470 ¥ 10–7 [44] 1.474 ¥ 10–7 [44] 1.412 ¥ 10–7 [44] 1.307 ¥ 10–7 [44] 1.436 ¥ 10–7 [44] 1.59 ¥ 10–7 [50] 1.19 ¥ 10–7 [50] 1.21 ¥ 10–7 [50] 1.5136 ¥ 10–7 [6]

Perfusion (m3/m3-sec)

0.023 [45] 0.0091 [45] 0.0067 [46] 0.077 [47] 0.0188 [48] 0.0233 [49]

0.0007 [48]

All conductivities and diffusivities are from humans at 37˚C except the value for skeletal muscle which is from sheep at 21˚C. Perfusion values are from various mammals as noted in the references. Significant digits do not imply accuracy. The temperature coefficient for thermal conductivity ranges from –0.000254 to 0.0039 W/m-K-˚C with 0.001265 W/m-K-˚C typical of most tissues as compared to 0.001575 W/m-K-˚C for water [44]. The temperature coefficient for thermal diffusivity ranges from –4.9 ¥ 10–10 m2/s-˚C to 8.4 ¥ 10–10 m2/s-˚C with 5.19 ¥ 10–10 m2/s-˚C typical of most tissues as compared to 4.73 ¥ 10–10 m2/s-˚C for water [44]. The values provided in this table are representative values presented for tutorial purposes. The reader is referred to the primary literature for values appropriate for specific design applications. From Baish, J.W., Microvascular heat transfer, in The Biomedical Engineering Handbook, 2nd ed., vol. 2, Bronzino, J.D., Ed., CRC Press, Boca Raton, FL, 2000, p. 98-6.

Summary of Several Types of Wavelet Bases for L2(R) Type of Wavelet

Decay of y(t) in Time

Stromberg, 1982

Exponential

Meyer, 1985

Faster than any chosen inverse polynomial Exponential

Battle–Lemarié, 1987, 1988 (splines) Daubechies, 1988

Compactly supported

Regularity of y(t) in Time

Type of Wavelet Basis

y(t) ŒC k ; k can be chosen arbitrarily large y(t) ŒC • (band limited)

Orthonormal

y(t) ŒC k ; k can be chosen arbitarily large y(t) ŒC a ; a can be chosen as large as we please

Orthonormal Orthonormal Orthonormal

From Vaidyanathan, P.P. and Djokovic, I., Wavelet transforms, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 212.

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CRC Handbook of Engineering Tables

Debye Temperature and Resistivity of Nonmagnetic Metals Metal

r20 at T = 293 K [10–8 W * m]

Q [K]

0.15 Q [K]

r at Q [10–8 W * m]

Ag Cu Au Al Zn Pt Pb W

1.62 1.68 2.22 2.73 6.12 10.6 20.8 5.39

214 320 160 374 180 220 84.5 346

32 48 24 56 27 33 12.7 52

1.16 1.94 1.17 3.79 3.65 7.91 5.5 6.76

From Nowak, S., Resistor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 284.

Comparison of Capacitor Dielectric Constants er (Dielectric Constant)

Dielectric Air or vacuum Paper Plastic Mineral oil Silicone oil Quartz Glass Porcelain Mica Aluminium oxide Tantalum pentoxide Ceramic

1.0 2.0–6.0 2.1–6.0 2.2–2.3 2.7–2.8 3.8–4.4 4.8–8.0 5.1–5.9 5.4–8.7 8.4 26 12–400,000

From Nowak, S., Capacitor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 295. Originally from The Electrical Engineering Handbook, Dorf, R., Ed., CRC Press, Boca Raton, FL, 1993.

u¢ Index of Various Capacitors Capacitor Definition Variable air Mica Ceramic (rutile) Ferroelectronic Ferroelectric multilayer Polystyrene Polyester (mylar) Polycarbonate — metalized Electrolytic Al(HV)a Electrolytic Al(LV)a “Golden” capacitor Electrolytic Ta (wet) Electrolytic Ta (dry) a

Main Parameters

u¢ [cm3/mF]

500 pF/250 V 10 nF/500 V 1000 pF/500 V 40 nF /250 V 0.68 mF/50 V 2 mF/160 V 0.1 mF/160 V 0.15 mF/160 V 40 mF/350 V 120 mF/7 V 1 F/5.5 V 10 mF/100 V 5.6 mF/10 V

200,000 250 600 50 1.5 300 12.4 5.6 1.3 0.008 0.00001 0.038 0.0026

HV: High voltage, LV: low voltage. From Nowak, S., Capacitor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 296. Originally from Badian, L., Handbuch der Electronik., FranzisVerlag, Munich, Vol. 3, 1979.

© 2004 by CRC Press LLC

Capacitor Name Polystyrene Teflon Polyethylene Polypropylene Metalized polypropylene Metalized Polyester Polyester (polyethylene tereftalate) Polycarbonate Metalized polycarbonate

Class

deltamax after 1000 h [%]

Smallest t δp [%]

300 300 200 50

1 1 1 2

0.5 0.5 1 5

±0.5 ±0.5 ±1 ±5

10

2

5

±0.5

5.6 12

2 2

10 5

12

2 2

υ′ cm3/µF

5.6

TCC ppm/K

Maximum Work Temperature [˚C]

2–5 6 5 6–8

–100 –150 –500 –200

70 280 100 110

6–8

–200

85

±10 ±10

50 (200 at 1 MHz) 50 (200 at 1 MHz)

— Large

— 150

10

±10

20

Large

100

10

±10

20

Large

100

Power Factor × 10–4

Remarks For telecommunications filter Special applications

Neutral polymer

For ac pulse

Polar polymer

From Nowak, S., Capacitor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 306.

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Capacitors

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Inductor Qualifiers and Attributes Inductor Qualifier Ideal, perfect

Nonideal

Linear

Nonlinear

Real

Air Cored

Lumped or discrete Distributed

Inductor: Attribute or Quality Linear inductor having only a “pure” inductance, i.e., no power loss is related to the flow of time-varying current through the inductor winding. In the ideal inductor, the current of sine wave lags the induced voltage by angle j = 90˚ (p/2 rad). The concept of the ideal inductor is used only in idealized or simplified circuit analysis. Usually, a linear inductor in which the power loss in the winding and core is taken into account. The current of sine wave lags the induced voltage by angle 0˚ £ j < 90˚ (90˚ for ideal, power lossfree inductor; 0˚ for pure resistor). The concept of nonideal inductor is used as a first order approximation of a real inductor. Inductor, ideal or nonideal, for which the induced voltage drop across it is proportional to the flowing time-varying current in its steady state. Linear inductor can be described or be used to describe the circuit in terms of transfer function. An air inductor is an example of linear inductor. Inductor for which the induced voltage drop is not proportional to the time-varying current flowing by it. As a rule, cored inductors (specifically if a core forms a closed magnetic circuit) are nonlinear. This is a consequence of the strong nonlinear dependence of magnetic induction B, proportional to voltage u = dL/dt, on magnetic field strength H, proportional to current i. Inductor with electrically behavioral aspects and characteristics that are all taken into account, e.g., magnetic power loss, magnetic flux leakage, self-winding and interwinding capacitances and related dielectric power loss, radiation power loss, parasitic couplings, and so on, and dependences of these factors on frequency, induction, temperature, time, etc. Inductor not containing magnetic materials as constituents or in its magnetically perceptible vicinity Inductor in which a magnetic material in the form of a core serves intentionally as a path, complete or partial, for guidance of magnetic flux generated by current flowing through inductor winding Inductor assumed to be concentrated at a single point Inductor with inductance and other properties that are distributed over a physical distance(s) which is(are) comparable to a wavelength

From Nowak, S., Capacitor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 314.

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Electrical and Computer Engineering

Inductance L0 of Various Air Inductors Dimensionally Similar but Having the Same Number of Turns When Coil Dimensions Are:

Winding (Coil) Dimensions

Inductance L0 for n=100 Turns Is:

l (a)

D

λ

S1

d

(b)

S2 l

(c)

D1 D2

h

(d) D1 D2

D1 = 2 cm l = 10 cm

19 µH

S1 = 1.5 cm S2 = 2.5 cm λ = 0.05 cm l = 10 cm d = 0.05 cm G (0.6;4) = 0.4 H (1;100) = 0

32 µH

D1 = 1 cm D2 = 3 cm

10.3 µH

D1 = 2 cm D2 = 3 cm

41 µH

D1 = 2 cm D2 = 4 cm h = 1 cm

13.9 µH

D1 = 1 cm D2 = 5 cm h = 2 cm

64.4 µH

D = 2 cm h = 0.5 cm l = 4 cm

74 µH

D = 2 cm h = 0.5 cm l = 0.2 cm

245 µH

l (e)

h D

l h (f) D

From Postupolski, T.W., Inductor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 316.

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−

µ′ and µ″ (log scale)

Series complex

permeability components

Magnetic field strength,

µ′ (1)

µ″ (1)

µ′ (2)

µ″

µ

µ Amplitude permeability,

µ=tg α

µ0

µ

Magnetic field strength,

µ =

/

µ0

µ

µ

Magnetic induction,

(1)

disaccomodation

µ = (1g)

µ

/

(2)

µ″ δµ = µ µ′µ′

tg

Permeability,

−

µ =

(magnetic) Loss factor

Magnetic induction,

Amplitude permeability,

µ

CRC Handbook of Engineering Tables

(2)

log of frequency

log of time

Temperature,

0

log of induction

µ

µ = log of power loss

Power loss,

log of power loss

2

>

log of power loss

µ =

2

>

Curie point

Temperature,

µ

Bias dc field,

Saturation induction,

gapped

µ ( )

µ =1

µ = ( 0)

Permeability,

Permeability,

µ

µ

ungapped core

Curie point

log of frequency

µ =

= 2

>

Temperature,

Basic characteristics of magnetic materials essential for inductor applications. (From Postupolski, T.W., Inductor, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 331.)

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Electrical and Computer Engineering

Ideal Op Amp Types Input

Output

Gain

Type

V I I V

V V I I

Av Rm Ai Gm

Voltage Transimpedance Current Transconductance

From Nairn, D.G., The ideal operational amplifier, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 428.

in-

in-

out

vd in+

+

Av vd

out ii

in+

+ -

(a)

in-

-

out in+

+ -

(b)

inii

Rm ii

in+

Ai ii

out

vd +

(c)

Gm vd

(d)

The four possible op amp configurations: (a) the voltage op amp, (b) the transimpedance op amp, (c) the current op amp, and (d) the transconductance op amp. (From Nairn, D.G., The ideal operational amplifier, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 428.)

ITRS Microprocessor Roadmap Characteristic Transistor gate length (nm) Feature size scale factor (Sfeature) Chip size (mm2) Million transistors/mm2 Million transistors/chip Clock frequency (GHz) Supply voltage (V) Maximum power (W)

2001

2004

2007

2010

2013

2016

90 1 310 0.89 275.9 1.684 1.1 130

53 0.59 310 1.78 551.8 3.99 1 160

35 0.39 310 3.1 961 6.739 0.7 190

25 0.28 310 7.14 2213.4 11.511 0.6 218

18 0.20 310 14.27 4423.7 19.348 0.5 251

13 0.14 310 28.54 8847.4 28.751 0.4 288

From Cottrell, D., Design automation technology roadmap, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 2161.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Properties of the Relative Sensitivity Property Number

Relation

Property Number

Relation

1

S xky = Skxy = S xy

10

S xy1 / y 2 = S xy1 - S xy 2

2

S xx = S xkx = Skxx = 1

11

S xy1 = S xy2 S xx12

3

S1y x = S 1x y = -S xy

12a

S xy = S |xy| + j arg yS xarg y

4

S xy1y 2 = S xy1 + S xy 2

13a

S xarg y =

5

S x i =1 i =

14a

S |xy| = Re S xy

15

S xy + z =

Pn y

1 Im S xy arg y

n

ÂS

yi x

i =1

6

n

S xy = n S xy

(

1 y S xy + z S xz y+z

)

n

Ây S i

7

n

n

S xx = n S xkx = n

16

S ni =1yi

Sx

=

i =1

yi x

n

Ây

i

i =1

1 y S n x

8

S xyn =

9

S xxn = Skxxn =

17

S xln y =

1 y S ln y x

1 n

a

In this relation, y is a complex quantity and x is a real quantity. From Filanovsky, I., Sensitivity and selectivity, in The Circuits and Filters Handbook, 2nd ed., Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2003, p. 2294.

Portion of the electromagnetic spectrum. (From Palais, J., Fiber optic communications systems, in The Communications Handbook, 2nd ed., Gibson, J.D., Ed., CRC Press, Boca Raton, FL, 2002, p. 44-2.)

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Electrical and Computer Engineering

The general arrangement of the frequency spectrum that is applied to satellite communications and other radiocommunications services. Indicated are the short-hand letter designations along with an explanation of the typical applications. Note that the frequency ranges indicated are the general ranges and do not correspond exactly to the ITU frequency allocations and allotments. (From Elbert, B.R., Geostationary communications satellites and applications, in The Communications Handbook, 2nd ed., Gibson, J.D., Ed., CRC Press, Boca Raton, FL, 2002, p. 56-5.)

The Primary Strengths of Satellite Communications Feature of Satellite Service

Application

Wide-area coverage Wide bandwidth Independent of land-based networks Rapid installation

Domestic, regional, global Up to 1 GHz per coverage Does not require connection to terrestrial infrastructure Individual sites can be installed and activated in one day for VSAT or two months of major hub Depends on type of service; can be as low as $600 for DTH Determined by coverage and type of transmission system By the satellite operator or a separate organization that leases transponder capacity Requires line-of-sight path over the coverage area

Low cost per added site Uniform service characteristics Total service from a single provider Mobile Communication

From Elbert, B.R., Geostationary communications satellites and applications, in The Communications Handbook, 2nd ed., Gibson, J.D., Ed., CRC Press, Boca Raton, FL, 2002, p. 56-7.

© 2004 by CRC Press LLC

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Access time The total time needed to retrieve data from memory. For a disk drive this is the sum of the time to position the read/write head over the desired track and the time until the desired data rotates under the head. Active filter A form of power electronic converter designed to effectively cancel harmonic currents by injecting currents that are equal and opposite to, or 180˚ out of phase with, the target harmonics. Active filters allow the output current to be controlled and provide stable operation against AC source impedance variations without interfering with the system impedance. The main type of active filter is the series type in which a voltage is added in series with an existing bus voltage. The other type is the parallel type in which a current is injected into the bus and cancels the line current harmonics. Algorithm A systematic and precise, step-by-step procedure (such as a recipe, a program, or set of programs) for solving a certain kind of problem or accomplishing a task, for instance converting a particular kind of input data to a particular kind of output data, or controlling a machine tool. An algorithm can be executed by a machine. Address A unique identifier for the place where information is stored (as opposed to the contents actually stored there). Most storage devices may be regarded by the user as a linear array, such as bytes or words in RAM or sectors on a disk. The address is then just an ordinal number of the physical or logical position. In some disks, the address may be compound, consisting of the cylinder or track and the sector within that cylinder. In more complex systems, the address may be a “name” that is more relevant to the user but must be translated by the underlying software or hardware. Antenna A device used to couple energy from a guiding structure (transmission line, waveguide, etc.) into a propagation medium, such as free space, and vice versa. It provides directivity and gain for the transmission and reception of electromagnetic waves. Appropriate technology The technolog y that w ill accomplish a task adequately given the resources available. Adequacy can be verified by determining that increasing the technological content of the solution results in diminishing gains or increasing costs. Attenuation The exponential decrease, with distance, in the amplitude of an electric signal traveling along a very long transmission line due to losses in the supporting medium. In electromagnetic systems attenuation is due to conductor and dielectric losses. In fiber optic systems attenuation arises from intrinsic material properties (absorption and Rayleigh scattering) and from waveguide properties such as bending, microbending, splices, and connectors. Automation Refers to the bringing together of machine tools, materials handling process, and controls with little worker intervention, including 1. a continuous flow production process that integrates various mechanisms to produce an item with relatively few or no worker operations, usually through electronic control;

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

2. self-regulating machines (feedback) that can perform highly precise operations in sequence; and 3. electronic computing machines. In common use, however, the term is often used in reference to any type of advanced mechanization or as a synonym for technological progress; more specifically, it is usually associated with cybernetics. Base (1) The number of digits in a number system (10 for decimal, 2 for binary). (2) One of the three terminals of a bipolar transistor. (3) A register’s value that is added to an immediate value or to the value in an index register in order to form the effective address for an instruction such as LOAD or STORE. Bayesian theory Theory based on Bayes’ rule, which allows one to relate the a priori and a posteriori probabilities. If P (ci) is the a priori probability that a pattern belongs to class ci, P(xk) is the probability of pattern xk, P (xk|ci) is the class conditional probability that the pattern is xk provided that it belongs to class ci , P (ci|xk) is the a posteriori conditional probability that the given pattern class membership is ci, given pattern xk, then P x c P (c ) ( ) ( P(x) ) k i

P ci x k =

i

k

The membership of the given pattern is determined by

( )

( )

max P c i x k = max P x k c i P (c i ) ci

ci

Hence, the a posteriori probability can be determined as a function of the a priori probability. Binary-coded decimal (BCD) A weighted code using patterns of four bits to represent each decimal position of a number. Bit (1) The fundamental unit of information representation in a computer, short for “binary digit” and with two values usually represented by “0” and “1.” Bits are usually aggregated into “bytes” (7 or 8 bits) or “words” (12–60 bits). A single bit within a word may represent the coefficient of a power of 2 (in numbers), a logical TRUE/FALSE quantity (masks and Boolean quantities), or part of a character or other compound quantity. In practice, these uses are often confused and interchanged. (2) In Information Theory, the unit of information. If an event E occurs with a probability P (E), it conveys information of log2 (1/P (E)) binary units or bits. When a bit (binary digit) has equiprobable 0 and 1 values, it conveys exactly 1.0 bit (binary unit) of information; the average information is usually less than this. Boundary condition (1) The conditions satisfied by a function at the boundary of its interval of definition. They are generally distinguished in hard or soft also called Neumann (the normal derivative of the function is equal to zero) or Dirichlet (the function itself is equal to zero). (2) The conditions satisfied from the electromagnetic field at the boundary between two different media.

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Electrical and Computer Engineering (3) Rules that govern the behavior of electromagnetic fields as they move from one medium into another medium. Broadcasting

Sending a message to multiple receivers.

Bus (1) A data path connecting the different subsystems or modules within a computer system. A computer system will usually have more than one bus; each bus will be customized to fit the data transfer needs between the modules that it connects. (2) A conducting system or supply point, usually of large capacity. May be composed of one or more conductors, which may be wires, cables, or metal bars (busbars). (3) A node in a power system problem. (4) A heavy conductor, typically used with generating and substation equipment. Byte In most computers, the unit of memory addressing and the smallest quantity directly manipulated by instructions. The term byte is of doubtful origin, but was used in some early computers to denote any field within a word (e.g., DEC PDP-10). Since its use on the IBM “Stretch” computer (IBM 7030) and especially the IBM System/360 in the early 1960s, a byte is now generally understood to be 8 bits, although 7 bits is also a possibility. Cache An intermediate memory store having storage capacity and access times somewhere in between the general register set and main memory. The cache is usually invisible to the programmer, and its effectiveness comes from being able to exploit program locality to anticipate memoryaccess patterns and to hold closer to the CPU: most accesses to main memory can be satisfied by the cache, thus making main memory appear to be faster than it actually is. A hit occurs when a reference can be satisfied by the cache; otherwise a miss occurs. The proportion of hits (relative to the total number of memory accesses) is the hit ratio of the cache. Capacitance The measure of the electrical size of a capacitor, in units of farads. Thus a capacitor with a large capacitance stores more electrons (coulombs of charge) at a given voltage than one with a smaller capacitance. In a multiconductor system separated by nonconductive mediums, capacitance (C) is the proportionality constant between the charge (q) on each conductor and the voltage (V) between each conductor. The total equilibrium system charge is zero. Capacitance is dependent on conductor geometry, conductor spatial relationships, and the material properties surrounding the conductors. Capacitors are constructed as two metal surfaces separated by a nonconducting electrolytic material. When a voltage is applied to the capacitor, the electrical charge accumulates in the metals on either side of the nonconducting material, negative charge on one side and positive on the other. If this material is a fluid then the capacitor is electrolytic; otherwise, it is nonelectrolytic. Causal system A system whose output does not depend on future input; the output at time t may depend only on the input signal {f (t) : t £ t}. For example, the voltage measured across a particular element in a passive electric circuit does not depend upon future inputs applied to the circuit and hence is a causal system.

© 2004 by CRC Press LLC

If a system is not causal, then it is noncausal. An ideal filter which will filter in real time all frequencies present in a signal f (t) requires knowledge of {f (t) : t > t} and is an example of a noncausal system. Central processing unit (CPU) A part of a computer that performs the actual data processing operations and controls the whole computing system. It is subdivided into two major parts: 1. The arithmetic and logic unit (ALU), which performs all arithmetic, logic, and other processing operations. 2. The control unit (CU), which sequences the order of execution of instructions, fetches the instructions from memory, decodes the instructions, and issues control signals to all other parts of the computing system. These control signals activate the operations performed by the system. Channel (1) The medium along which data travel between the transmitter and receiver in a communication system. This could be a wire, coaxial cable, free space, etc. (2) The conductivity path between the source and the drain of a field effect transistor. (3) A single path for transmitting electrical signals. Example 1: The band of frequencies from 50 Hz to 15 KHz (Channel A) and 15 KHz to 75 KHz (Channel B) which frequency modulates the main carrier of an FM stereo transmitter. Example 2: A portion of the electromagnetic spectrum assigned for operation of a specific carrier from the FM broadcast band (88 to 108 MHz) of frequencies 200 KHz wide designated by the center frequency beginning at 88.1 MHz and continuing in successive steps to 107.9 MHz. Chaos (1) Erratic and unpredictable dynamic behavior of a deterministic system that never repeats itself. Necessary conditions for a system to exhibit such behavior are that it be nonlinear and have at least three independent dynamic variables. (2) In microelectronics, deterministic motion, in which the statistics are essentially those of a Gaussian random process. Circuit A physical device consisting of an interconnection of elements, or a topological model of such a device. For example, an electric circuit may be constructed by interconnecting a resistor and a capacitor to a voltage source. A representation of this circuit is shown by the diagram in the figure.

Circuit example. Code (1) A technique for representing information in a form suitable for storage or transmission. (2) A mapping from a set of messages into binary strings.

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CRC Handbook of Engineering Tables

Computer (1) An electronic, electromechanical, or purely mechanical device that accepts input, performs some computational operations on the input, and produces some output. (2) Functional unit that can perform substantial computations, including numerous arithmetic operations, or logic operations, without human intervention during a run. (3) General or special-purpose programmable system that is able to execute programs automatically. It has one or more associated processing units, memory, and peripheral equipment for input and output. Uses internal memory for storing programs and/or data. Conductivity (1) The reciprocal of resistivity. (2) A measure of a material’s ability to conduct electrical current. Conductivity s is the ratio of the conduction current to the electric field in Ohm’s Law: Jc = s E Dielectric (1) A medium that exhibits negligible or no electrical conductivity and thus acts as a good electrical insulator. (2) A medium characterized by zero conductivity, unity relative permeability, and a relative permittivity greater than one. Also known as an insulator. Dielectries are usually used to separate two conducting bodies such as to form a capacitor. Electric field In a region of space, if a test charge q experiences a force F, then the region is said to be characterized by an electric field of intensity E given by E=

F q

Electromagnetic energy Energy contained in electromagnetic fields and associated polarizable and magnetizable media. Ethernet A standard for interconnecting devices on a local area network (LAN). Gate (1) A logical or physical entity that performs one logical operation, such as AND, NOT, or OR. (2) The terminal of a FET which controls the flow of electrons from source to drain. It is usually considered to be the metal contact at the surface of the die. The gate is usually so thin and narrow that if any appreciable current is allowed to flow, it will rapidly heat up and self-destruct due to I-R loss. This same resistance is a continuing problem in low noise devices and has resulted in the creation of numerous methods to alter the gate structure and reduce this effect. Ground (1) An earth-connected electrical conducting connection that may be designed or nonintentionally created. (2) The electrical “zero” state, used as the reference voltage in computer systems. Hologram Medium that when illuminated optically, provides a three-dimensional image of stored information, sometimes called holograph.

© 2004 by CRC Press LLC

Laser Acronym that stands for light amplification by stimulated emission of radiation. Usually refers to an oscillator rather than an amplifier; commonly also refers to similar systems that operate at non-optical frequencies or with nonelectromagnetic wave fields. Node A symbol representing a physical connection between two electrical components in a circuit. Noise (1) Any undesired disturbance, whether originating from the transmission medium or the electronics of the receiver itself, that gets superimposed onto the original transmitted signal by the time it reaches the receiver. These disturbances tend to interfere with the information content of the original signal and will usually define the minimum detectable signal level of the receiver. (2) Any undesired disturbance superimposed onto the original input signal of an electronic device; noise is generally categorized as being either external (disturbances superimposed onto the signal before it reaches the device) or internal (disturbances added to the signal by the receiving device itself). Some common examples of external noise are crosstalk and impulse noise as a result of atmospheric disturbances or manmade electrical devices. Some examples of internal noise include thermal noise, shot noise, l/f noise, and intermodulation distortion. Permeability Tensor relationship between the magnetic field vector and the magnetic flux density vector in a medium with no hysteresis; flux density divided by the magnetic field in scalar media. Permeability indicates the ease with which a magnetic material can be magnetized. An electromagnet with a higher permeable core material will produce a stronger magnetic field than one with a lower permeable core material. Permeability is analogous to conductance when describing electron flow through a material. Port (1) A terminal pair. (2) A place of connection between one electronic device and another. (3) A point in a computer system where external devices can be connected. Random signal A signal X(t) that is either noise N(t), an interfering signal s(t), or a sum of these: X (t ) = s1 (t ) + L + sm (t ) + N1 (t ) + L + N n (t ) Resolution (1) The act of deriving from a sound, scene, or other form of intelligence, a series of discrete elements from which the original may subsequently be reconstructed. The degree to which nearly equal values of a quantity can be discriminated. (2) The fineness of detail in a measurement. For continuous systems, the minimum increment that can be discerned. (3) The ability to distinguish between two units of measurement. (4) The number of pixels per linear unit (or per dimension) in a digital image. (5) The smallest feature of a given type that can be printed with acceptable quality and control. Sensor A transducer or other device whose input is a physical phenomenon and whose output is a quantitative

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1-37

Electrical and Computer Engineering measurement of that physical phenomenon. Physical phenomena that are typically measured by a sensor include temperature or pressure to an internal, measurable value such as voltage or current. Traveling wave An electromagnetic signal that propagates energy through space or a dielectric material. Waveguide A system of conductive or dielectric materials in which boundaries and related dimensions are defined such that electromagnetic waves propagate within the

bounded region of the structure. Although most waveguides utilize a hollow or dielectric filled conductive metal tube, a solid dielectric rod in which the dielectric constant of the rod is very much different from the dielectric constant of the surrounding medium can also be used to guide a wave. Waveguides rapidly attenuate energy at frequencies below the waveguide lower cut-off frequency, and are limited in bandwidth at the upper end of the frequency spectrum due to wave attenuation as well as undesired mode propagation.

From Comprehensive Dictionary of Electrical Engineering, Laplante, P.A., Ed., CRC Press, Boca Raton, FL, 1999.

Cost of Selected Memory Devices Year

Device

Size (bits)

Cost ($)

Cost ($/MB)

Speed (ns)

1943 1958 1959 1960 1964 1966 1970 1972 1975 1977 1977 1979 1982 1985 1989 1991 1995 1999 2001 2002 2005

Relay Magnetic drum (IBM650) Vacuum tube flip-flop Core Transistor flip-flop I.C. flip-flop Core I.C. flip-flop 256 bit static RAM 1 Kbit static RAM 4 Kbit DRAM 16 Kbit DRAM 64 Kbit DRAM 256 Kbit DRAM 1 Mbit DRAM 4 M x 9 DRAM SIMM 16 MB ECC DRAM DIMM 64 MB PC-100 DIMM 256 MB PC-133 DIMM 1 Gbit chip 4 Gbit chip

1 80,000 1 8 1 1 8 1 256 1,024 4,096 16,384 65,536 262,144 1,048,576 37,748,736 150,994,944 536,870,912 2,147,483,648 1,073,741,824 4,294,967,296

— 157,400 8.10 5.00 59.00 6.80 0.70 3.30 — 1.62 16.40 9.95 6.85 6.00 20.00 165.00 489.00 55.00 88.00 — —

— 1.7E+07 6.8E+07 5.2E+06 4.9E+08 5.7E+07 7.3E+05 2.8E+07 — 1.3E+04 3.4E+04 5.1E+03 8.8E+02 1.9E+02 1.6E+02 3.7E+01 2.7E+01 8.6E-01 3.4E-01 — —

100,000,000 4,800,000 10,000 11,500 200 200 770 170 1,000 500 270 350 200 200 120 80 70 60/10 45/7 — —

From McCallum, J.C., Price-performance of computer technology, in The Computer Engineering Handbook, Oklobdzija, V.G., Ed., CRC Press, Boca Raton, FL, 2002, p. 4-10.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

4-Bit Fractional Two’s Complement Numbers Decimal Fraction

Binary Representation

+7/8 +3/4 +5/8 +1/2 +3/8 +1/4 +1/8 +0 -1/8 -1/4 -3/8 -1/2 -5/8 -3/4 -7/8 -1

0111 0110 0101 0100 0011 0010 0001 0000 1111 1110 1101 1100 1011 1010 1001 1000

From Swartzlander, E.E. Jr., High-speed computer arithmetic, in The Computer Engineering Handbook, Oklobdzija, V.G., Ed., CRC Press, Boca Raton, FL, 2002, p. 9-2.

DFT Parameters DFT Parameter Sample size Sample period Record length Number of harmonics Number of positive (negative) harmonics Frequency spacing between harmonics DFT frequency (one-sided baseband range) DFT frequency (two-sided baseband range) Frequency of the kth harmonic

Notation or Units N samples Ts seconds T = NTs seconds N harmonics N/2 harmonics Df = 1/T = 1/NTs = fs /N Hz f [0, fs /2) Hz f [-fs /2, fs /2) Hz fk = kfs /N Hz

From Taylor, F.J., Digital signal processing, in The Computer Engineering Handbook, Oklobdzija, V.G., Ed., CRC Press, Boca Raton, FL, 2002, p. 24-9.

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Electrical and Computer Engineering

1-39

Typical underdamped unit-step response of a control system. An overdamped unit-step response would not have a peak. (From Yang, J.-S. and Levine, W.S., Specification of control systems, in The Control Handbook, Levine, W.S., Ed., CRC Press, Boca Raton, FL, 1996, p. 158.)

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CRC Handbook of Engineering Tables

Sequences corresponding to various z-transform pole locations. (From Santina, M.S., Stubberud, A.R., and Hostetter, G.H., Discrete-time systems, in The Control Handbook, Levine, W.S., Ed., CRC Press, Boca Raton, FL, 1996, pp. 243-245.)

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Pole location(s) on the complex plane

Sequence

Im 1

1

Re

k Constant sequence A (1)k = A

Im 1 Ω 1

Re

k Sinusoidal sequence A cos (Ω k + θ)

Im 1

x

Re

1

k

Alernating sequence A (–1)k Im

c

Ω Re

k

Damped sinusoidal sequence A c k cos (Ωk + θ)

(Continued) Sequences corresponding to various z-transform pole locations.

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CRC Handbook of Engineering Tables

Pole location(s) on the complex plane

Sequence

Im 1 Ω 1

Re

k

Exponentially expanding sinusoidal sequence Ak cos (Ω k + θ)

Im 1

1

Re

k

Ramp sequence Ak (1)k = Ak

Im 1

c

1

Re

k

Ramp-weighted geometric sequence Akc k

(Continued) Sequences corresponding to various z-transform pole locations.

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Electrical and Computer Engineering

Transfer Functions of Dynamic Elements and Networks Element or System

G(s)

1. Integrating circuit, filter C R

−

+

+

+

V1(s) −

V2(s)

V2 ( s )

=

V2 ( s )

= RCs

V2 ( s )

=-

R2 (R1Cs + 1)

V2 ( s )

=-

(R C s + 1)(R C s + 1)

q( s )

=

V1 ( s )

1 RCs

−

2. Differentiating circuit R C −

+

+

+

V1(s) −

V2(s)

V1 ( s )

−

3. Differentiating circuit R1

R2

C −

+

+ V2(s) −

+

V1(s) −

V1 ( s )

R1

4. Integrating filter R1

R2 −

+

+ V2(s) −

+

C1

V1(s) −

C2

V1 ( s )

1 1

2 2

R1C2 s

5. dc motor, field-controlled, rotational actuator Ia

+

j, b

Rf Vf (s) −

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Lf If

θ, ω

V f (s)

Km

(

s( Js + b) L f s + R f

)

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CRC Handbook of Engineering Tables

Transfer Functions of Dynamic Elements and Networks (continued) Element or System

G(s)

6. dc motor, armature-controlled, rotational actuator La

+ Ra

+

Ia

Vb −

Va (s) −

If q( s )

Va ( s )

θ, ω j, b

Km

=

s (Ra + La s )( Js + b) + K b K m

=

Km s( ts + 1)

[

]

7. ac motor, two-phase control field, rotational actuator q( s )

+

Vc ( s )

j, b VC (s)

t = J (b - m)

ω

−

m = slope of linearized torque-speed curve (normally negative)

Reference field

8. Amplidyne, voltage and power amplifier id

−

Lc 4 Rc

Vc ( s )

3

1 Vc

Vo ( s )

Ld

ic

+

+

Rd

Vo(s)

2

=

(K R R ) ( ) c

q

(stc + 1) stq + 1

t c = Lc Rc , t q = Lq Rq For the unloaded case, id 0, tc tq, 0.05 s < tc < 0.5s V12 = Vq, V34 = Vd

Lq

iq Rq

−

9. Hydraulic actuator x (t), Control valve displacement Return Pressure source

Piston

Return M, b Load

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y(t)

Y (s)

X (s)

=

K s( Ms + B )

K=

Ê Akx A2 ˆ , B = Áb + kp k p ˜¯ Ë

kx =

∂g ∂x

, kp = x0

∂g , ∂P Po

g = g ( x , P ) = flow A = area of piston

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Electrical and Computer Engineering

Transfer Functions of Dynamic Elements and Networks (continued) Element or System

G(s)

10. Gear train, rotational transformer Gear 1 N1 r1 θm, ωm

Gear ratio = n = θL, ωL

N1 N2

N 2q L = N1qm , q L = nqm

r2

w L = nw m

N2 Gear 2 11. Potentiometer, voltage control θ

V2 ( s )

+

V1 ( s )

R1

V1(s) R −

+ R2 V (s) 2 −

V2

=

R2 R2 = R R1 + R2

R2 q = R qmax

V1(s)

12. Potentiometer error detector bridge θ2 + V2(s)

Vbattery

θ1

Error voltage

(

)

V2 ( s ) = ks q1 ( s ) - q2 ( s ) V2 ( s ) = ks qerror( s ) ks =

Vbattery qmax

13. Tachometer, velocity sensor Shaft

+ V2(s) = Ktw(s) = Ktsq(s); Kt = constant

V2(s) θ(s), ω(s)

−

14. dc amplifier V2 ( s ) + V1(s) −

+ V2(s) −

V1 ( s )

=

ka st + 1

Ro = output resistance Co = output capacitance t = RoCo , t 1s and is often negligible for controller amplifier

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CRC Handbook of Engineering Tables

Transfer Functions of Dynamic Elements and Networks (continued) Element or System

G(s)

15. Accelerometer, acceleration sensor x o (t ) = y(t ) - x m (t );

Frame

X o (s)

xin(t)

X in ( s )

Mass M

– s2 s + (b M )s + k M 2

For low-frequency oscillations, where w < wn,

y(t) k

=

X o ( jw )

b

X in ( jw )

w2 k M

16. Thermal heating system ( s ) q( s )

ℑe ℑe

Fluid in ℑ0

ℑ0 Fluid out Heater

=

1 , where C1s + (QS + 1 R )

= o - e = temperature difference due to thermal process Ct = thermal capacitance Q = fluid flow rate = constant S = specific heat of water Rt = thermal resistance of insulation

q( s ) = rate of heat flow of heating element

17. Rack and pinion θ

r

x = rq converts radial motion to linear motion

x From Dorf, R.C. and Bishop, R.H., Mathematical models of systems, in Modern Control Systems, 9th ed., Prentice-Hall, Englewood Cliffs, NJ.

© 2004 by CRC Press LLC

1587_Book.fm Page 47 Friday, September 26, 2003 12:10 PM

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Electrical and Computer Engineering

Block Diagram Transformations Transformation

Original Diagram

Equivalent Diagram X1

1. Combining blocks in cascade

X1

X2

G1(s)

G2(s)

X3

or X1

X1 + 2. Moving a summing point behind a block

±

X3

G2G1

X1

X3

G

X3

G1G2

+

G

±

X2

X1

G

X1

X2

G

3. Moving a pickoff point ahead of a block

X1

G X2

X2

4. Moving a pickoff point behind a block

X1

5. Moving a summing point ahead of a block

+

X3

X1

±

1 G

+

G

G

X2

1 G

X2 X1

G 1 GH

X2

±

±

X3

± X2

X1 +

X2

X2

G

X1

G

X2

G

X1

X2

G

X1

6. Eliminating a feedback loop

X3

H

From Dorf, R.C. and Bishop, R.H., Mathematical Models of Systems, in Modern Control Systems, 9th ed., Prentice-Hall, Englewood Cliffs, NJ.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Functions G(s)

Polar Plot

Bode Diagram

0°

−ω

−45° 1.

K st1 + 1

−1

−90°

ω=∞

φ

ω=0

0 dB/dec M KdB

−180°

1 τ1

0 dB

+ω

−ω

2.

K (st1 + 1)(st2 + 1)

−1

φ

M

log ω −20 dB/dec

φ

0° ω=0

ω=∞

Phase margin

0 Phase margin

−20 −180° 1 0 dB 1 τ2 τ1

+ω

φ 3.

K (st1 + 1)(st2 + 1)(st3 + 1)

−1

ω=∞ ω=0 +ω

0

−20

M

−180° −270°

−40 dB/dec

φ

0°

−ω

log ω

0 dB 1 τ1

1 τ2 Phase margin

Gain margin −40 dB/dec 1 log ω τ2 −60 dB/dec

ω=0 −90° −ω 4.

K s

−1 +ω ω→0

© 2004 by CRC Press LLC

φ M ω=∞

−180°

Phase margin = 90°

90°

log ω

0 dB ω=k

−20 dB/dec

1587_Book.fm Page 49 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments jω

ω M Phase margin 0 dB −180°

−90°

φ

0°

Root locus σ

1 − τ1

Stable; gain margin = •

ω=∞ jω

Phase margin

ω

M

r1

0 dB −180°

−90°

φ

0°

−

1 τ1

−

σ

1 τ2

Elementary regulator; stable; gain margin = •

r2 ω→∞ ω

M Phase margin

jω −

Gain margin 0 dB −180°

−90°

0°

φ

1 τ1

r1 Regulator with additional energystorage component; unstable, but can be made stable by reducing gain

r3 −

1 τ3

−

1 τ2

σ r2

ω→∞ jω ω

M Phase margin 0 dB −180°

−90°

ω→∞

© 2004 by CRC Press LLC

φ

Ideal integrator; stable σ

1587_Book.fm Page 50 Sunday, August 31, 2003 9:44 PM

1-50

CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Functions (continued) G(s)

Polar Plot

ω→0 −ω

5.

K s( st1 + 1)

φ M ω=∞

−1

Bode Diagram

−20 dB/dec

−90° Phase margin

−180°

log ω

1 τ1

0 dB

+ω ω→0

−40 dB/dec

ω→0 −ω

6.

K s( st1 + 1)( st 2 + 1)

−90° φ M ω→∞

−1

−180°

Phase margin

0 dB

−270°

+ω

ω→0 −ω K ( st a + 1)

(st1 + 1)(st2 + 1)

−90°

K s2

ω=∞

−1

−180°

© 2004 by CRC Press LLC

ω→

log ω

1 τ1

−ω +ω

−20 dB/dec Phase margin

φ M

+ω ω→0

8.

−

−60 dB/dec

ω→0

7.

Gain margin 1/τ2

−20

−40 1/τ2 0 dB 1 τ1

φ log ω

1 −20 τa −40 dB/dec

φ M −1

ω=∞

−180°

−40 dB/dec

0 dB

Gain margin = 0 Phase margin = 0 φ log ω

1587_Book.fm Page 51 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments jω

Phase margin ω

M

0 dB −180°

r1

φ

−90°

−

1 τ1

σ

Elementary instrument servo; inherently stable; gain margin = •

σ

Instrument servo with field control motor or power servo with elementary WarkLeonard drive; stable as shown, but may become unstable with increased gain

r2

ω=∞

jω Phase M margin

0 dB −180°

Gain margin

ω

r1 φ

−90°

r3 −

1 τ2

−

1 τ1

r2

ω→∞ jω ω

M

r1

Phase margin 0 dB −180°

r3 φ

−90°

−

1 τ2

−

σ

1 1 − τa τ1

Elementary instrument servo with phaselead (derivative) compensator; stable

r2 ω→∞ jω

ω M

Phase margin = 0

0 dB −270° −180°

−90°

Double pole

r1 σ

φ r2

ω→∞

© 2004 by CRC Press LLC

Inherently marginally stable; must be compensated

1587_Book.fm Page 52 Sunday, August 31, 2003 9:44 PM

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CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Functions (continued) G(s)

Polar Plot

Bode Diagram

φ M 9.

K s 2 ( st1 + 1)

+ω

−1

ω=∞

−ω

−180°

−40 dB/dec Phase margin (negative) 0 dB

−270°

log ω

1 τ1

φ −60 dB/dec

K ( st a + 1) 10.

s 2 ( st1 + 1)

t a > t1

−40 dB/dec

−ω −1 +ω

ω=∞ −180°

+ω 11.

ω=∞

K s3

−1

−ω

1/τ1 0 dB

+ω K ( st a + 1) s3

ω=∞ −1 −ω

© 2004 by CRC Press LLC

φ M −180°

−270°

φ log ω

−20 dB/dec −40 dB/dec

−60 dB/dec

φ M −180°

1 τa

0 dB Phase margin = −90°

−270°

12.

Phase margin

φ M

log ω

φ

−60 dB/dec Phase margin (negative) 0 dB 1/τa

log ω −40 dB/dec

φ

1587_Book.fm Page 53 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments

jω M r1 0 dB −270° −180°

−90°

φ

r3

Phase margin (negative)

ω→∞

Inherently unstable; must be compensated σ Double pole

r2

jω M

Phase margin

r1 Double pole

0 dB −180°

−90°

φ

r3 1 − τ1

Stable for all gains σ

1 − τa r2

ω→∞

jω Phase margin

M

0 dB −270° −180°

−90°

r1 r1

φ

Inherently unstable σ

Triple pole

r2

ω→∞

jω

Phase margin

M

Triple pole

0 dB −270° −180°

ω→∞

© 2004 by CRC Press LLC

−90°

r1 Inherently unstable

φ −

1 τa

σ

r3 r2

1587_Book.fm Page 54 Sunday, August 31, 2003 9:44 PM

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CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Functions (continued) G(s)

Polar Plot

Bode Diagram −60 dB/dec −90°

+ω 13.

K ( st a + 1)( st b + 1) s

−40 dB/dec

φ M −1

3

ω=∞

−ω

−180°

0 dB 1 τa

−270°

Phase margin

14.

K ( st a + 1)( st b + 1)

−1

s( st1 + 1)( st 2 + 1)( st3 + 1)( st 4 + 1)

−90° ω=∞

+ω

−270°

φ M 15.

K ( st a + 1)

s 2 ( st1 + 1)( st 2 + 1)

−ω +ω

−1

ω=∞

−180°

−20 dB/dec

Gain margin

−40

1 1 τ3 τ4

−60 −40

φ M −180°

log ω

1 τb Gain margin

−20 −ω

φ

0 dB −20 1 1 1 −40 1 τ1 τ2 τ a τb −60 Phase margin

Phase margin −40 0 dB

1 τ1 1 τ2

1 −20 τa

log ω −40 −60

© 2004 by CRC Press LLC

log ω

Gain margin

1587_Book.fm Page 55 Friday, September 26, 2003 12:10 PM

1-55

Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments

jω N

r1

Gain margin 0 dB

Triple pole

r3

−270° −180°

−90°

Phase margin

φ

−

σ

1 1 − τb τa

Conditionally stable; becomes unstable if gain is too low

r2

ω→∞

jω M

r1

Gain margin 0 dB −270° −180°

−90° φ

r5

r4

r3

−1 −1 −1 −1 −1 −1 τ4 τ3 τb τa τ2 τ1

Phase margin

ω→∞

M

r2

Phase margin

jω r1

0 dB −270° Gain margin

−180°

−90° φ

σ

Conditionally stable; stable at low gain, becomes unstable as gain is raised, again becomes stable as gain is further increased, and becomes unstable for very high gains

r4 −

Double pole

r3 1 1 1 − − τ2 τ1 τa r2

σ

Conditionally stable; becomes unstable at high gain

ω→∞

From Dorf, R.C. and Bishop, R.H., Stability in the frequency domain, in Modern Control Systems, 9th ed., PrenticeHall, Englewood Cliffs, NJ.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Fraction of Area Occupied by the Eight Primaries of the Neugebauer Model Primary

Ink Combination

Reflectance

Fraction of Area

White

—

R 1(l)

a1 = ( 1 – c ) ( 1 – m ) ( 1 – y )

Cyan

Cyan

R 2(l)

a2 = c ( 1 – m ) ( 1 – y )

Magenta

Magenta

R 3(l)

a 3 = ( 1 – c )m ( 1 – y )

Yellow

Yellow

R 4(l)

a 4 = ( 1 – c ) ( 1 – m )y

Red

Magenta, yellow

R 5(l)

a 5 = ( 1 – c )my

Green

Cyan, yellow

R 6(l)

a 6 = c ( 1 – m )y

Blue

Cyan, magenta

R 7(l)

a 7 = cm ( 1 – y )

Black

Cyan, magenta, yellow

R 8(l)

a 8 = cmy

From Emmel, P., Physical models for color prediction, in Digital Color Imaging Handbook, Sharma, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 222.

Characterization vs. Calibration Characterization Stability

Stable with time (assumption)

Process Sensors Complexity

Detail

Time consuming Expensive colorimetry Three-dimensional or fourdimensional problem [3 ¥ 3 matrix, 3-D lookup table (LUT) with interpolation, includes black] Colorant characteristics, halftone orientation strategy Smooth functions

Method

Statistical averaging process

Required by

Calibration Short-term drifts and environmental sensitivity Real-time, repeatable Inexpensive densitometry One-dimensional problem (four LUTs)

Dot gain, electrical and mechanical drift, dmax Detailed functions (can contain kinks and flat spots) Measurement process

From Hains, C., Wang, S.-G., and Knox, K., Digital color halftones, in Digital Color Imaging Handbook, Sharma, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 431.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Memory Card Aperture & Shutter

Zoom Lens

IR blocking & anti-aliasing filter

Color LCD

PC interface

Imager

Optical Viewfinder

User controls Battery

Status LCD AC Adapter

Block diagram of the hardware components used in a typical digital camera. (From Parulski, K. and Spaulding, K., Color image processing for digital cameras, in Digital Color Imaging Handbook, Sharma, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 729.)

Some Basic DTFT Pairs Sequence 1. 2.

d[n] d[n – n0]

3.

1 (–• < n < •)

Fourier Transform 1 e –jwn0 •

Â 2pd(w + 2k)

k =-•

4.

anu[n] (|a| < 1)

1 1 - ae - jw

5.

u[n]

1 pd(w + 2pk ) + 1 - e - jw k =-•

6.

(n + 1)anu[n] (|a| < 1)

•

7.

8.

© 2004 by CRC Press LLC

Â

r 2 sin w p (n + 1) sin w p

sinw cn pn

u[n] (|r| < 1)

(

1

1 - ae - jw

)

2

1 1 - 2r cosw pe - jw + r 2e j2w Ï1, w < w c Ô Xe jw = Ì ÔÓ0, w c < w £ p

1587_Book.fm Page 58 Sunday, August 31, 2003 9:44 PM

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CRC Handbook of Engineering Tables

Some Basic DTFT Pairs (continued) Sequence

9.

Fourier Transform

[

sin w ( M + 1) 2

ÏÔ1, 0 £ n £ M x[n] - Ì ÔÓ0, otherwise

sin(w 2)

] =e

•

10.

Â 2pd(w - w

e jwn0

0

k =-•

11.

p

cos(w0n +f)

•

Â [e

k =-•

jf

- jw M 2

+ 2pk )

]

d(w - w 0 + 2pk ) + e - jf d(w + w 0 + 2pk )

From Jenkins, W.K., Fourier series, Fourier transforms, and the DFT, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 1-12. Originally from A.V. Oppenheim and R.W. Schafer, DiscreteTime Signal Processing, © 1989. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.

Properties of the DTFT Sequence x[n] y[n] 1. 2. 3.

Fourier Transform X(ejw) Y(ejw)

ax[n] + by[n] x[n – nd] (nd an integer)

aX(ejw) + bY(ejw) e–jwn d X(ejw)

(

e jw0n x[n]

X e(

4.

x[–n]

5.

nx[n]

6.

x[n] * y[n]

7.

x[n] y[n] •

Â x[n]

n=-• •

9.

)

X(e–jw) if x[n] is real X*(ejw) j

1 2p 2

=

( )

dX e jw

dw X(ejw) Y(ejw)

Parseval’s Theorem 8.

j w -w0 )

1 2p

Ú X (e )Y (e ( ) )dq x

jq

j w -q

-x

Ú X (e ) dw p

jw

2

-p

1 Â x[n]y * [n] = 2p inf X (e )Y * (e )dw

n=-•

p

jw

jw

-p

From Jenkins, W.K., Fourier series, Fourier transforms, and the DFT, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 1-13. Originally from A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, © 1989. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.

© 2004 by CRC Press LLC

1587_Book.fm Page 59 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Properties of the DFT Finite-Length Sequence (Length N)

N-Point DFT (Length N)

1. 2. 3. 4.

x[n] x1[n], x2[n] ax1[n] + bx2[n] X[n]

X[k] X1[k], X2[k] aX1[k] + bX2[k] Nx[((–k))N]

5.

x[((nm))N]

6.

WN- ln x[n]

WNkm X [k ]

7.

Â x (m)x [((n )) ]

X[((k – l))N]

N -1

1

2

m=0

8.

m

X1[k]X2[k]

N

1 N

x1[n]x2[n]

Â X (l)X [((k - l)) ] N -1

1

2

N

l =0

9. 10.

x*[n] x*[((–n))N]

11.

Re{x[n]}

x ep[k ] =

1 X (k ) 2

N

+K*

-k

N

12.

jIm{x[n]}

x op[k ] =

1 X k 2

N

-X*

-k

N

13.

x ep[n] = x op[n] =

X*[((–k))N] X*[k]

{ [(( )) ]} { [ ] [(( )) ]}

1 x[n] + x * 2

-n

N

1 x n - x * -n N 2 Properties 15–17 apply only when x[n] is real

14.

{ [( ) ] [(( )) ]} { [(( )) ] [(( )) ]}

Re{X[k]} jIm{X[k]}

[(

{ }

15.

{ }

Symmetry properties

{ [(( )) ]} { [ ] [(( )) ]}

16.

x ep[n] =

1 x[n] + x 2

-n

N

17.

x op[n] =

1 x n -x 2

-n

N

]

Ï Ô X [k ] = X * ( -k ) N Ô Ô ÔRe X [k ] = Re X ( -k ) N Ô ÔÔ ÌIm X [k ] = - Im X ( -k ) N Ô Ô Ô X [k ] = X ( -k ) N Ô Ô Ô<) X [k ] = - <) X ( -k ) N ÔÓ

{ }

[(

)

{ [( ) ]} { [( ) ]} ] { [( )

)

]}

Re{X[k]} jIm{X[k]}

From Jenkins, W.K., Fourier series, Fourier transforms, and the DFT, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 1-16. Originally from A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, © 1989. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Summary of the Four Types of Linear-Phase FIR Filters Odd Length (N)

Even Length (N)

Type I

Type II

Even symmetry 1 [ N -1] 2

1 N 2

Â a(k)cos(wk)

h(a + n) = h(a – n)

k =0

N -1 a= 2

zero at w = p

Ê N -1 ˆ a(k ) = 2hÁ - k˜ Ë 2 ¯

ÊN ˆ b(k ) = 2hÁ - k˜ Ë2 ¯ Ê1 ˆ cosÁ w˜ Ë2 ¯

Odd symmetry

Type III 1 N 2

Â c(k)sin(wk)

b=

p 2

Â bˆ(k)cos(wk) k =0

Ê

1 ˆ

Âd(k)sinÁË w ÈÍÎk - 2 ùúû˜¯

k =1

N -1 a= 2

1 N -1 2

Type IV

1 [ N -1] 2

h(a + n) = –h(a – n)

1 ˆ

k =1

Ê N - 1ˆ a(0) = hÁ ˜ Ë 2 ¯

b=0

Ê

Âb(k)cosÁË w ÈÍÎk - 2 ùúû˜¯

k =1

zeros at w = 0, p

zero at w = 0

Ê N -1 ˆ c (k ) = 2hÁ - k˜ Ë 2 ¯

ÊN ˆ d(k ) = 2hÁ - k˜ Ë2 ¯

Ê N - 1ˆ hÁ ˜ =0 Ë 2 ¯ a -1

Âcˆ(k)cos(wk)

sin(w )

k =0

Ê1 ˆ sinÁ w˜ Ë2 ¯

1 N -1 2

Â dˆ(k)cos(wk) k =0

From Karam, L.J., McClellan, J.H., and Selesnick, I.W., Digital filtering, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 11-12.

Basic Parameters for Three Classes of Acoustic Signals

Telephone speech Wideband speech Wideband audio (stereo) a

Frequency Range in Hz

Sampling Rate in kHz

PCM Bis per Sample

PCM Bit Rate in kb/s

300–3,400a 50–7,000 10–20,000

8 16 48b

8 8 2 ¥ 16

64 128 2 ¥ 768

Bandwidth in Europe; 200 to 3200 Hz in the U.S. Other sampling rates: 44.1 kHz, 32 kHz. From Noll, P., MPEG digital audio coding standards, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 40-2. b

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

CD and DAT Bit Rates Storage Device

Audio Rate (Mb/s)

Overhead (Mb/s)

Total Bit Rate (Mb/s)

1.41 1.41

2.91 1.05

4.32 2.46

Compact disc (CD) Digital audio tape (DAT)

Note: Stereophonic signals, sampled at 44.1 kHz; DAT supports also sampling rates of 32 kHz and 48 kHz. From Noll, P., MPEG digital audio coding standards, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 40-2.

Summary of the Functionalities and Characteristics of the Existing Standards ITU Attribute Applications

H.261

ISO H.263

Bit rate

Videoconferencing 64K–1M

Videophone <64 K

Material

Progressive

Progressive

Object shape

Rectangular

Arbitrary (simple)

Transform

8 ¥ 8 DCT

8 ¥ 8 DCT

Quantizer

Uniform

Uniform

Type

Block

Block

Block size

16 ¥ 16

Prediction type

Forward

Accuracy Loop filter

One pixel Yes

16 ¥ 16, 8¥8 Forward, backward Half pixel No

MPEG-1

MPEG-2

MPEG-4

CD storage

Broadcast

1.0–1.5M

2–10M

Wide range (multimedia) 5K–4M

Progressive, interlaced Rectangular

Progressive, interlaced Rectangular

Progressive, interlaced Arbitrary

8 ¥ 8 DCT

8 ¥ 8 DCT

8 ¥ 8 DCT

Weighted uniform

Weighted uniform

Weighted uniform

Block

Block

Block, sprites

16 ¥ 16

16 ¥ 16

16 ¥ 16, 8 ¥ 8

Forward backward Half pixel No

Forward, backward Half pixel No

Forward, backward Half pixel No

Yes No No No

Yes Yes Yes No

Yes Yes Yes Yes

Residual Coding

Motion Compensation

Scalability Temporal Spatial Bit rate Object

No No No No

Yes Yes Yes No

From Al-Shaykh, O., Neff, R., Taubman, D., and Zakhor, A., Video sequence compression, in The Digital Signal Processing Handbook, Madisetti, V.K. and Williams, D.B., Eds., CRC Press, Boca Raton, FL, 1998, p. 55-16.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

EV and ICEV Efficiencies from Crude Oil to Traction Effort Efficiency (%) ICEV Crude oil Refinery (petroleum) Distribution to fuel tank Engine Transmission/axle Wheels

Overall efficiency (crude oil to wheels)

Max.

Min.

90 99 22 98

85 95 20 95

19

15

Efficiency (%) EV Crude oil Refinery (fuel oil) Electricity generation Transmission to wall outlet Battery charger Battery (lead/acid) Motor/controller Transmission/axle Wheels Overall efficiency (crude oil to wheels)

Max.

Min.

97 40 92 90 75 85 98

95 33 90 85 75 80 95

20

14

From Husain, I., Inroduction to electric vehicles, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 12.

Nominal Energy Density of Sources Energy Source

Nominal Specific Energy (Wh/kg)

Gasoline Natural gas Methanol Hydrogen Coal (bituminous) Lead-acid battery Lithium-polymer battery Flywheel (carbon-fiber)

12,500 9350 6050 33,000 8200 35 200 200

From Husain, I., Energy Source: Battery, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 44.

Specific Energy of Batteries Specific Energy (Wh/kg) Battery Lead-acid Nickel-cadmium Nickel-zinc Nickel-iron Zinc-chlorine Silver-zinc Sodium-sulfur Aluminum-air

Theoretical

Practical

108

50 20–30 90 60 90 100 150–300 300

500 770

From Husain, I., Energy source: Battery, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 47.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

USABC Objectives for EV Battery Packs Parameter Specific energy (Wh/kg) (C/3 discharge rate) Energy density (Wh/liter) (C/3 discharge rate) Specific power (W/kg)(80% DoD per 30 s) Specific power (W/kg), Regen. (20% DoD per 10 s) Power density (W/liter) Recharge time, h (20% Æ 100% SoC) Fast recharge time, min Calendar life, years Life, cycles

Mid-Term

Commercialization

Long-Term

80–100 135 150–200 75 250 <6 <15 5 600 @ 80% DoD

150 230 300 150 460 4–6 <30 10 1000 @ 80% DoD 1600 @ 50% DoD 2670 @ 30% DoD 100,000 –40 to +50 <150 80

200 300 400 200 600 3–6 <15 10 1000 @ 80% DoD

Lifetime urban range, miles Operating environment, °C Cost, US$/kWh Efficiency, %

100,000 –30 to +65 <150 75

100,000 –40 to +85 <100 80

From Husain, I., Energy Source: Battery, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 68.

Properties of EV and HEV Batteries

Battery Type

Specific Energy, Wh/kg

Specific Power, W/kg

Energy Efficiency, %

Cycle Life

Estimated Cost, US$/kWh

Lead-acid Nickel-cadmium Nickel-metal-hydride Aluminum-air Zinc-air Sodium-sulfur Sodium-nickel-chloride Lithium-polymer Lithium-ion

35–50 30–50 60–80 200–300 100–220 150–240 90–120 150–200 80–130

150–400 100–150 200–300 100 30–80 230 130–160 350 200–300

80 75 70 <50 60 85 80 Not available >95

500–1000 1000–2000 1000–2000 Not available 500 1000 1000 1000 1000

100–150 250–350 200–350 Not available 90–120 200–350 250–350 150 200

From Husain, I., Energy Source: Battery, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 68.

Fuel Cell Types Fuel Cell Variety Phosphoric acid

Fuel

Alkaline

H2, reformate (LNG, methanol) H2

Proton exchange membrane Direct methanol

H2, reformate (LNG, methanol) Methanol, ethanol

Molten carbonate

H2, CO (coal gas, LNG, methanol) H2, CO (coal gas, LNG, methanol)

Solid oxide

Electrolyte Phosphoric acid Potassium hydroxide solution Polymer ion exchange film Solid polymer Carbonate Yttria-stabilized zirconia

Operating Temperature

Efficiency

~200°C

40–50%

~80°C

40–50%

~80°C

40–50%

Applications Stationary (>250 kW) Mobile

90–100°C

~30%

600–700°C

50–60%

EV and HEV, industrial up to ~80 kW EV and HEVs, small portable devices (1 W to 70 kW) Stationary (>250 kW)

~1000°C

50–65%

Stationary

From Husain, I., Alternative energy sources, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 86.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Summary of Power Devices

• •

•

•

•

• ! "# µ

*

,-

,

•

• ! "$% µ • /

• / %+# µ

• $%&'%% µ

• ( • )

•

• • .

•

• / "%+# µ •

• / %+' µ

.

/*6.

• (

L/5 • ( %+' µ

•

• %+# µ

5 ,

• ( L/5 , • %+2 µ .

•

•

• "%+3 µ

• * ≈ '+# (

• * ≈ '+# (

• / • . • /

0

• * ≈$+# ( • 1 • ( •

0

•

≈ %+$ Ω • / • ( • * ≈ 4+% ( • /*

,-

From Husain, I., Power electronics and motor drives, in Electric and Hybrid Vehicles: Design Fundamentals, CRC Press, Boca Raton, FL, 2003, p. 165.

© 2004 by CRC Press LLC

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1-65

Electrical and Computer Engineering

Wind Power Installed Capacity Canada China Denmark India Ireland Italy Germany Netherlands Portugal Spain Sweden U.K. U.S. Other Total

83 224 1450 968 63 180 2874 363 60 834 150 334 1952 304 9839

From Johnson, G.L., Wind power, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 1-2.

Comparison of Five Fuel Cell Technologies

Type Polymer Electrolyte Membrane (PEM) Alkaline (AFC)

Phosphoric Acid (PAFC) Molten Carbonate (MCFC)

Solid Oxide (SOFC)

Electrolyte

Operating Temperature (°C)

Applications

Advantages

Solid organic polymer poly-perflourosulfonic acid

60–100

Electric utility, transportation, portable power

Solid electrolyte reduces corrosion, low temperature, quick start-up

Aqueous solution of potassium hydroxide soaked in a matrix Liquid phosphoric acid soaked in a matrix

90–100

Military, space

Cathode reaction faster in alkaline electrolyte; therefore high performance Up to 85% efficiency in cogeneration of electricity

Liquid solution of lithium, sodium, and/or potassium carbonates soaked in a matrix Solid zirconium oxide to which a small amount of yttria is added

175–200

600–1000

Electric utility, transportation, and heat Electric utility

600–1000

Electric utility

Higher efficiency, fuel flexibility, inexpensive catalysts

Higher efficiency, fuel flexibility, inexpensive catalysts. Solid electrolyte advantages like PEM

From Rahman, S., Advanced energy technologies, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 1-12.

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CRC Handbook of Engineering Tables

Technology

Size

Fuel Sources

AC interface Type

Applications

Fuel Cells

.5Kw – Larger units With Stacking

Natural Gas Hydrogen Petroleum Products

Inverter type

Continuous

Microturbines

10Kw–100Kw Larger sizes

Natural Gas Petroleum Products

Inverter type

Continuous Standby

Batteries

.1Kw–2Mw+

Storage

Inverter type

PQ, Peaking

Flywheel

>.1Kw–.5Kw

Storage

Inverter type

PQ, Peaking

PV

>.1Kw–1Kw

Sunlight

Inverter type

Peaking

Gas Turbine

10Kw–5Mw+

Natural Gas Petroleum Products

Rotary type

Continuous, Peaking Standby

Distributed generation technology chart. (From Kennedy, J.R., Distributed utilities, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 2-28.)

Basic fuel cell operation. (From Kennedy, J.R., Distributed utilities, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 2-29.)

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Electrical and Computer Engineering

Usual Operating Conditions for Transformers (ANSI/IEEE, C57.12.01-1989 (R1998)) Temperature of cooling air 24hr average temperature of cooling air Minimum ambient temperature Load currenta Altitudeb Voltagec (without exceeding limiting temperature rise)

£40°C £30°C ≥–30°C Harmonic factor £0.05 per unit £3300 ft (1000 m) • Rated output KVA at 105% rated secondary voltage, power factor ≥0.80 • 110% rated secondary voltage at no load

a

Any unusual load duty should be specified to the manufacturer. At higher altitudes, the reduced air density decreases dielectric strength; it also increases temperature rise reducing capability to dissipate heat losses (ANSI/IEEE, C57.12.01-1989 (R1998)). c Operating voltage in excess of rating may cause core saturation and excessive stray losses, which could result in overheating and excessive noise levels (ANSI/IEEE, C57.94-1982 (R1987), C57.12.01-1989 (R1998)). From Payne, P.A., Dry type transformers, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 3-65. b

Resistivity and Temperature Coefficient of Some Materials Material Silver Annealed copper Hard-drawn copper Aluminum

Resistivity at 20°C (W-m)

Temperature Coefficient (°C)

1.59 ¥ 10 1.72 ¥ 10–8 1.77 ¥ 10–8 2.83 ¥ 10–8

243.0 234.5 241.5 228.1

–8

From Reta-Hernandez, M., Transmission line parameters, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 4-65.

Most Commonly Found Relays for Generator Protection Identification Number 87G 87T 87U 40 46

Function Description

32 24 59 60 81 51V

Generator phase phase windings protection Step-up transformer differential protection Combined differential transformer and generator protection Protection against the loss of field voltage or current supply Protection against current imbalance. Measurement of phase negative sequence current Anti-motoring protection Overexcitation protection Phase overvoltage protection Detection of blown voltage transformer fuses Under- and overfrequency protection Backup protection against system faults

21 78

Backup protection against system faults Protection against loss of synchronization

Relay Type Differential protection Differential protection Differential protection Offset mho relay Time-overcurrent relay Reverse-power relay Volt/Hertz relay Overvoltage relay Voltage balance relay Frequency relays Voltage controlled or voltage-restrained time overcurrent relay Distance relay Combination of offset mho and blinders

From Benmouyal, G., The protection of synchronous generators, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 9-12.

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CRC Handbook of Engineering Tables

Appliances and Sectors under Direct Utility Control, U.S. — 1983 Appliance or Sector Electric water heaters Air conditioners Irrigation pumps Space heating Swimming pool pumps Other Total Residential Commercial Industrial Agricultural

Number Controlled

Percent of Total Controlled

648,437 515,252 14,261 50,238 258,993 13,710 1,500,891 1,456,212 29,830 588 14,261

43% 34% 1% 3% 17% 1% 100% 97% 2% — 1%

From Merrill, H.M., Power system planning, in The Electric Power Engineering Handbook, Grigsby, L.L., Ed., CRC Press, Boca Raton, FL, 2001, p. 13-43. Originally from New Electric Power Technologies: Problems and Prospects for the 1990s, Washington, D.C.: U.S. Congress, Office of Technology Assessment, OTA-E-246, July 1985.

Typical Characteristics of Integrated Circuit Resistors

Resistor Type Semiconductor Diffused Bulk Pinched Ion-implanted Deposited resistors Thin-film Tantalum SnO2 Ni-Cr Cermet (Cr-SiO) Thick-film Ruthenium-silver Palladium-silver

Sheet Resistivity (per square)

Temperature Coefficient (ppm/°C)

0.8 to 260 W 0.003 to 10 kW 0.001 to 10 kW 0.5 to 20 kW

1100 to 2000 2900 to 5000 3000 to 6000 100 to 1300

0.01 to 1 kW 0.08 to 4 kW 40 to 450 W 0.03 to 2.5 kW 10 W to 10 MW 0.01 to 100 kW

m100 –1500 to 0 m100 m150 m200 –500 to 150

From Pecht, M. and Lall, P., Resistors, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 13.

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Electrical and Computer Engineering

Speech Coder Performance Comparisons Standardization

Subjective

Algorithm (acronym)

Body

Identifier

Rate kbits/s

MOS

DRT

DAM

µ-law PCM ADPCM LD-CELP RPE-LTP VSELP CELP IMBE LPC-10e

ITU-T ITU-T ITU-T GSM CTIA U.S. DoD Inmarsat U.S. DoD

G.711 G.721 G.728 GSM IS-54 FS-1016 IMBE FS-1015

64 32 16 13 8 4.8 4.1 2.4

4.3 4.1 4.0 3.5 3.5 3.13b 3.4 2.24b

95 94 94a — — 90.7b — 86.2b

73 68 70a — — 65.4b — 50.3b

a

Estimated. From results of 1996 U.S. DoD 2400 bits/s vocoder competition. From McClellan, S. and Gibson, J.D., Coding, transmission, and storage, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 345.

b

Surface Mount Substrate Material Substrate Material (Units)

Tg – Glass Transition Temperature (°C)

TCE – Thermal Coefficient of X–Y Expansion (PPM/°C)

Thermal Conductivity (W/M°C)

Moisture Absorption (%)

FR-4 Epoxy glass Polymide glass Copper-clad invar Poly Aramid fiber Alumina/ceramic

125 250 Depends on resin 250 NA

13–18 12–16 5–7 3–8 5–7

0.16 0.35 160XY — 15–20Z 0.15 20–45

0.10 0.35 NA 1.65 NA

From Blackwell, G.R., Surfact mount technology, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 692.

Emissivities of Some Common Materials Material Tungsten Nickel-chromium (80-20) Lampblack Polished silver Glass Platinum Graphite Aluminum (oxidized) Carbon filament

Temperature (∞C)

Emissivity

2000 600 20–400 200 1000 600 3600 600 1400

0.28 0.87 0.96 0.02 0.72 0.1 0.8 0.16 0.53

From Watkins, L.S., Sources and detectors, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 818.

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CRC Handbook of Engineering Tables

Thermal Conductivities of Typical Packaging Materials at Room Temperature Materials Air Mylar Silicone rubber Solder mask Epoxy (dielectric) Ablefilm 550 dielectric Nylon Polytetrafluorethylene RTV Polyimide Epoxy (conductive) Water Mica Ablefilm 550 K Thermal greases/pastes Borosilicate glass Glass epoxy Stainless steel Kovar Solder (Pb-In) Alumina Solder 80-20 Au-Sn Silicon Molybdenum Aluminum Beryllia Gold Copper Silver Diamond

Thermal Conductivity (W/m K) 0.024 0.19 0.19 0.21 0.23 0.24 0.24 0.24 0.31 0.33 0.35 0.59 0.71 0.78 1.10 1.67 1.70 15 16.60 22 25 52 118 138 156 242 298 395 419 2000

From Bar-Cohen, A., Thermal management of electronics, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 855. Originally from C.A. Harper, Electronic Packaging and Interconnection Handbook, New York: McGraw-Hill, 1991, p. 27. R.R. Tummala and E.J. Rymaszewski, Microelectronics Packaging Handbook, New York: Van Nostrand Reinhold, 1989, p. 174.

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Electrical and Computer Engineering Relative Permeability, mr , of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials mr

Material Diamagnetics Bismuth Mercury Silver Lead Copper Water Paraffin wax Paramagnetics Oxygen (s.t.p.) Air Aluminum Tungsten Platinum Manganese Ferromagnetics Purified iron: 99.96% Fe Motor-grade iron: 99.6% Fe Permalloy: 78.5% Ni, 21.5% Fe Supermalloy: 79% Ni, 15% Fe, 5% Mo, 0.5% Mn Permendur: 49% Fe, 49% Ca, 2% V Ferrimagnetics Manganese–zinc ferrite

Ms, A/m2

0.999833 0.999968 0.9999736 0.9999831 0.9999906 0.9999912 0.99999942 1.000002 1.00000037 1.000021 1.00008 1.0003 1.001 280,000 5,000 70,000

2.158 2.12 2.00

1,000,000 5,000

0.79 2.36

750 1,200 650

0.34 0.36 0.29

Nickel–zinc ferrite

From Bate, G., Magnetism, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 902. Originally from F. Brailsford, Physical Principles of Magnetism, London: Van Nostrand, 1966. With permission.

“Hard” and “Soft” Magnetic Materials

Soft Fe 80 Ni 20 Fe Mn Zn ferrite Co70Fe5Si15B10

Hard Particles -Fe2O3 CrO2 Fe BaO.6Fe2O3 Alloys SmCo5 Sm2Co17 Fe14BNd2

High Ms

Low Hc

Low Mr

High µ

1700 emu/cc 660 400 530

1 Oe 0.1 0.02 0.1

<500 <300 <200 <250

20,000 50,000 5,000 10,000

High Ms

High Hc

High Mr

Tc

400 400 870–1100 238–370

250–450 450–600 1100–1500 800–3000

200–300 300 435–550 143–260

115–126 120 768 320

875 1000 1020

40,000 17,000 12,000

690 875 980

720 920 310

From Bate, G., Magnetism, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 908.

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Standard Rectangular Waveguides Physical Dimensions EIAa Designation WRb( ) 2300 2100 1800 1500 1150 975 770 650 510 430 340 284 229 187 159 137 112 90 75 62 51 42 34 28 22 19

© 2004 by CRC Press LLC

Inside, cm (in.)

Outside, cm (in.)

Width

Height

Width

Height

58.420 (23.000) 53.340 (21.000) 45.720 (18.000) 38.100 (15.000) 29.210 (11.500) 24.765 (9.750) 19.550 (7.700) 16.510 (6.500) 12.954 (5.100) 10.922 (4.300) 8.636 (3.400) 7.214 (2.840) 5.817 (2.290) 4.755 (1.872) 4.039 (1.590) 3.485 (1.372) 2.850 (1.122) 2.286 (0.900) 1.905 (0.750) 1.580 (0.622) 1.295 (0.510) 1.067 (0.420) 0.864 (0.340) 0.711 (0.280) 0.569 (0.224) 0.478 (0.188)

29.210 (11.500) 26.670 (10.500) 22.860 (9.000) 19.050 (7.500) 14.605 (5.750) 12.383 (4.875) 9.779 (3.850) 8.255 (3.250) 6.477 (2.500) 5.461 (2.150) 4.318 (1.700) 3.404 (1.340) 2.908 (1.145) 2.215 (0.872) 2.019 (0.795) 1.580 (0.622) 1.262 (0.497) 1.016 (0.400) 0.953 (0.375) 0.790 (0.311) 0.648 (0.255) 0.432 (0.170) 0.432 (0.170) 0.356 (0.140) 0.284 (0.112) 0.239 (0.094)

59.055 (23.250) 53.973 (21.250) 46.350 (18.250) 38.735 (15.250) 29.845 (11.750) 25.400 (10.000) 20.244 (7.970) 16.916 (6.660) 13.360 (5.260) 11.328 (4.460) 9.042 (3.560) 7.620 (3.000) 6.142 (2.418) 5.080 (2.000) 4.364 (1.718) 3.810 (1.500) 3.175 (1.250) 2.540 (1.000) 2.159 (0.850) 1.783 (0.702) 1.499 (0.590) 1.270 (0.500) 1.067 (0.420) 0.914 (0.360) 0.772 (0.304) 0.681 (0.268)

29.845 (11.750) 27.305 (10.750) 23.495 (9.250) 19.685 (7.750) 15.240 (6.000) 13.018 (5.125) 10.414 (4.100) 8.661 (3.410) 6.883 (2.710) 5.867 (2.310) 4.724 (1.860) 3.810 (1.500) 3.233 (1.273) 2.540 (1.000) 2.344 (0.923) 1.905 (0.750) 1.588 (0.625) 1.270 (0.500) 1.207 (0.475) 0.993 (0.391) 0.851 (0.335) 0.635 (0.250) 0.635 (0.250) 0.559 (0.220) 0.488 (0.192) 0.442 (0.174)

Cut-off Frequency for Air-filled Waveguide, GHz

Recommended Frequency Range for TE10 Mode, GHZ

0.257

0.32–0.49

0.281

0.35–0.53

0.328

0.41–0.62

0.394

0.49–0.75

0.514

0.64–0.98

0.606

0.76–1.15

0.767

0.96–1.46

0.909

1.14–1.73

1.158

1.45–2.20

1.373

1.72–2.61

1.737

2.17–3.30

2.079

2.60–3.95

2.579

3.22–4.90

3.155

3.94–5.99

3.714

4.64–7.05

4.304

5.38–8.17

5.263

6.57–9.99

6.562

8.20–12.50

7.874

9.84–15.00

9.494

11.90–18.00

11.583

14.50–22.00

14.058

17.60–26.70

17.361

21.70–33.00

21.097

26.40–40.00

26.362

32.90–50.10

31.381

39.20–59.60

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Electrical and Computer Engineering

Standard Rectangular Waveguides (continued) Physical Dimensions EIAa Designation WRb( ) 15 12 10 8 7 5 4 3

Inside, cm (in.)

Outside, cm (in.)

Width

Height

Width

Height

0.376 (0.148) 0.310 (0.122) 0.254 (0.100) 0.203 (0.080) 0.165 (0.065) 0.130 (0.051) 0.109 (0.043) 0.086 (0.034)

0.188 (0.074) 0.155 (0.061) 0.127 (0.050) 0.102 (0.040) 0.084 (0.033) 0.066 (0.026) 0.056 (0.022) 0.043 (0.017)

0.579 (0.228) 0.513 (0.202) 0.457 (0.180) 0.406 (0.160) 0.343 (0.135) 0.257 (0.101) 0.211 (0.083) 0.163 (0.064)

0.391 (0.154) 0.358 (0.141) 0.330 (0.130) 0.305 (0.120) 0.262 (0.103) 0.193 (0.076) 0.157 (0.062) 0.119 (0.047)

Cut-off Frequency for Air-filled Waveguide, GHz

Recommended Frequency Range for TE10 Mode, GHZ

39.894

49.80–75.80

48.387

60.50–91.90

59.055

73.80–112.00

73.892

92.20–140.00

90.909

114.00–173.00

115.385

145.00–220.00

137.615

172.00–261.00

174.419

217.00–333.00

a

Electronic Industry Association. Rectangular waveguide. From Demarest, K., Waveguides, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 947. Originally from S.Y. Liao, Microwave Devices and Circuits, 3rd ed., Englewood Cliffs, NJ: Prentice-Hall, 1990, p. 118. With permission. b

Material Parameters for Several Semiconductors Semiconductor

Eg (eV)

er

k (W/cm-K) @300 K

Ec (V/cm)

tminority (s)

Si GaAs InP a-SiC b-SiC

1.12 1.42 1.34 2.86 2.2

11.9 12.5 12.4 10.0 9.7

1.5 0.54 0.67 4 4

3 ¥ 105 4 ¥ 105 4.5 ¥ 105 (1–5) ¥ 106 (1–5) ¥ 106

2.5 ¥ 10–3 10–8 10–8 (1–10) ¥ 10–9 (1–10) ¥ 10–9

From Trew, R.J., Active microwave devices, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 991.

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CRC Handbook of Engineering Tables

Absorption Loss Is a Function of Type of Material and Frequency (Loss Shown Is at 150 kHz) Metal Silver Copper—annealed Copper—hard drawn Gold Aluminum Magnesium Zinc Brass Cadmium Nickel Phosphor–bronze Iron Tin Steel, SAE1045 Beryllium Lead Hypernik Monel Mu-metal Permalloy Steel, stainless a

Relative Conductivity

Relative Permeability

Absorption Loss A, dB/mm

1.05 1.00 0.97 0.70 0.61 0.38 0.29 0.26 0.23 0.20 0.18 0.17 0.15 0.10 0.10 0.08 0.06 0.04 0.03 0.03 0.02

1 1 1 1 1 1 1 1 1 1 1 1000 1 1000 1 1 80000 1 80000 80000 1000

52 51 50 42 40 31 28 26 24 23 22 650 20 500 16 14 3500a 10 2500a 2500a 220a

Assuming that material is not saturated. From Hemmings, L.H., Grounding, shielding, and filtering, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1007.

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Electrical and Computer Engineering

1-75

Filters provide a variety of frequency characteristics. (From Hemmings, L.H., Grounding, shielding, and filtering, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1012.)

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CRC Handbook of Engineering Tables

Radar Bands Band

Frequency Range

HF VHF UHF L S

3–30 MHz 30–300 MHz 300–1000 MHz 1000–2000 MHz 2000–4000 MHz

C

4000–8000 MHz

X

8–12 GHz

Ku

12–18 GHz

Ka

27–40 GHz

V

40–75 GHz

W

75–110 GHz

Principal Applications Over-the-horizon radar Long-range search Long-range surveillance Long-range surveillance Surveillance Long-range weather characterization Terminal air traffic control Fire control Instrumentation tracking Fire control Air-to-air missile seeker Marine radar Airborne weather characterization Short-range fire control Remote sensing Remote sensing Weapon guidance Remote sensing Weapon guidance Remote sensing Weapon guidance

From Belcher, Jr., M.L. and Nessmith, J.T., Pulse radar, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1044.

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Electrical and Computer Engineering

Typical Acoustic Properties Velocity (km/s) Material

Longitudinal

Alcohol, methanol Aluminum, rolled Brass, 70% Cu, 30% Zn Cadmium sulphide Castor oil Chromium Copper, rolled Ethylene glycol Fused quartz Glass, crown Gold, hard drawn Iron, cast Lead Lithium niobate, LiNbO3

1.103 6.42 4.70 4.46 1.507 6.65 5.01 1.658 5.96 5.1 3.24 5.9 2.2 6.57

Nickel Polystyrene, styron PZT-5H Quartz

5.6 2.40 4.60 5.74

Sapphire Al2O3 Silver Steel, mild Tin Titanium Water YAG Y3Al15O12 Zinc Zinc oxide

11.1 3.6 5.9 3.3 6.1 1.48 8.57 4.2 6.37

Impedance (kg/m2 s 106) Shear 3.04 2.10 1.76 4.03 2.27 3.76 2.8 1.20 3.2 0.7 4.08 4.79 3.0 1.15 1.75 3.3 5.1 6.04 1.6 3.2 1.7 3.1 5.03 2.4 2.73

Longitudinal 0.872 17.33 40.6 21.5 1.42 46.6 44.6 1.845 13.1 11.4 63.8 46.4 24.6 30.9 49.5 2.52 34.5 15.2 44.3 38.0 46.0 24.2 27.3 1.48 39.0 29.6 36.1

Shear 8.21 18.14 8.5 28.21 20.2 8.26 6.26 23.6 24.6 7.83 19.17 22.53 26.5 1.21 13.1 8.7 13.5 25.2 16.9 24.9 12.5 13.9 22.9 16.9 15.47

Density (kg/m3103)

Comments

0.791 2.70 8.64 4.82 0.942 7.0 8.93 1.113 2.20 2.24 19.7 7.69 11.2 4.70

Liq. 25°C Isot. Isot. Piez crys Z-dir Liq. 20oC Isot. Isot. Liq. 25°C Isot. Isot. Isot. Isot. Isot. Piez crys X-dir

8.84 1.05 7.50 2.65

Isot. Isot. Piez ceram Z Piez crys X-dir

3.99 10.6 7.80 7.3 4.48 1.00 4.55 7.0 5.67

Cryst. Z-axis Isot. Isot. Isot. Isot. Liq. 20°C Cryst. Z-axis Isot. Piez crys Z-dir

From Farnell, G.W., Ultrasound, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1171.

Ferroelectric, Piezoelectric, and Electrostrictive Materials Type

Material Class

Example

Applications

Electret Electret

Organic Organic

Waxes Fluorine based

No recent Microphones

Ferroelectric Ferroelectric Ferroelectric

Organic Organic Ceramic

PVF2 Liquid crystals PZT thin film

No known Displays NV-memory

Piezoelectric Piezoelectric Piezoelectric Piezoelectric Piezoelectric

Organic Ceramic Ceramic Single crystal Single crystal

PVF2 PZT PLZT Quartz LiNbO3

Transducer Transducer Optical Freq. control SAW devices

Electrostrictive

Ceramic

PMN

Actuators

From Etzold, K.F., Ferroelectric and piezoelectric materials, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1180.

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CRC Handbook of Engineering Tables

Material Parameters for Type I Superconductors* Material

Tc (K)

o (nm)

o (nm)

o (meV)

m0Hco (mT)

Al In Sn Pb Nb

1.18 3.41 3.72 7.20 9.25

50 65 50 40 85

1600 360 230 90 40

0.18 0.54 0.59 1.35 1.50

110.5 123.0 130.5 180.0 198.0

* The penetration depth o is given at zero temperature, as are the coherence length o , the thermodynamic critical field Hco , and the energy gap o . From Delin, K.A. and Orlando, T.P., Superconductivity, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1224. Originally from R.J. Donnelly, “Cryogenics,” in Physics Vade Mecum, H.L. Anderson, Ed., New York: American Institute of Physics, 1981. With permission.

Material Parameters for Conventional Type II Superconductors* Material

Tc (K)

GL(0) (nm)

GL(0) (nm)

o (meV)

m0Hc2,o (T)

Pb-In Pb-Bi Nb-Ti Nb-N PbMo6 S8 V3Ga V3Si Nb3Sn Nb3Ge

7.0 8.3 9.5 16.0 15.0 15.0 16.0 18.0 23.0

150 200 300 200 200 90 60 65 90

30 20 4 5 2 2–3 3 3 3

1.2 1.7 1.5 2.4 2.4 2.3 2.3 3.4 3.7

0.2 0.5 13.0 15.0 60.0 23.0 20.0 23.0 38.0

* The values are only representative because the parameters for alloys and compounds depend on how the material is fabricated. The penetration depth GL(0) is given as the coefficient of the Ginzburg–Landau temperature dependence as GL( T) = lGL(0)(1 – T/Tc )–1/2; likewise for the coherence length where GL(T) = GL(0)(1 – T/Tc)–1/2. The upper critical field Hc2,o is given at zero temperature as well as the energy gap o . From Delin, K.A. and Orlando, T.P., Superconductivity, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1225. Originally from R.J. Donnelly, “Cryogenics,” in Physics Vade Mecum, H.L. Anderson, Ed., New York: American Institute of Physics, 1981. With permission.

Spontaneous Polarizations and Curie Temperatures for a Range of Ferroelectrics Material

Tc(k)

Ps(cm-2)

T(k)

KH2PO4 (KDP) Triglycine sulphate Polyvinylidene fluoride (PVDF) DOBAMBC (liquid crystal) PbTiO3 BaTiO3

123 322 > 453 359 763 393

0.053 0.028 0.060 ~3 ¥ 10–5 0.760 0.260

96 293 293 354 293 296

From Whatmore, R.W., Pyroelectric materials and devices, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1230.

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Electrical and Computer Engineering

Pyroelectric Properties of Selected Materials

Material (Temperature)

Pyroelectric Coefficient P 10–4 cm–2 K–1

TGS (35∞C) DTGS (40∞C) PVDF polymer LiTaO3 crystal Modified PZ ceramic Modified PT ceramic

5.5 5.5 0.27 2.3 3.8 3.8

Dielectric Properties (1 kHz)

tand

Volume-Specific Heat c¢ 106 Jm–3 K–1

55 43 12 47 290 220

0.025 0.020 0.015 0.005 0.003 0.011

2.6 2.4 2.43 3.2 2.5 2.5

Thermal Conductivity K 10–7 m2 s–1 3.3 3.3 0.62 13.0

Fv m2 C–1

FD 10–5 Pa–1/2

Fvid 106 sC–1

0.43 0.60 0.10 0.17 0.06 0.08

6.1 8.3 0.88 4.9 5.8 3.3

1.3 1.8 1.6 0.13

PZ = PbZrO3, PT = PbTiO3 . From Whatmore, R.W., Pyroelectric materials and devices, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1233.

Electrical Properties of a Number of Representative Insulating Liquids

Liquid Capacitor oil Pipe cable oil Self-contained cable oil Heavy cable oil Transformer oil Alkyl benzene Polybutene pipe cable oil Polybutene capacitor oil Silicone fluid Castor oil C8F16O fluorocarbon

Viscosity cSt (37.8°C)

Dielectric Constant (at 60 Hz, 25°C)

Dissipation Factor (at 60 Hz, 100°C)

Breakdown Strength, (kV cm–1)

21 170 49.7

2.2 2.15 2.3

0.001 0.001 0.001

>118 >118 >118

2.23 2.25 2.1 2.14 (at 1 MHz) 2.22 (at 1 MHz)

0.001 0.001 0.0004 0.0003

>118 >128 >138 >138

0.0005

>138

2.7 3.74

0.00015 0.06

>138 >138

2365 9.75 6.0 110 (SUS) 2200 (SUS at 100°C) 50 98 (100°C) 0.64

1.86

<0.0005

>138

From Bartnikas, R., Dielectrics and insulators, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1247. Originally from Bartnikas, R., Ed., Engineering Dielectrics, Vol. III, Electrical Insulating Liquids, Monograph 2, ASTM, Philadelphia, PA, 1994; Encyclopedia Issue, Insul. Circuits, June/July 1972.

© 2004 by CRC Press LLC

Material

Medium-density PE

High-density PE

© 2004 by CRC Press LLC

3.1–3.9 2.3–2.5 2.7–2.9 3.57 2.47 2.7–3.1

8.2 (density: 0.910–0.925 g cm3) (density: 0.926–0.940 g cm3) (density: 0.941–0.965 g cm3)

Dielectric Constant 60 Hz

20°C 1 kHz

Dissipation Factor 1 MHz

20°C 1 kHz

60 Hz

1 MHz

AC Dielectric Strength (kV cm–1)

1950 1000 1000–1100 <2800 110–460 550 <900 <1000 <1800 4700°F

8.5 8.2 5.5 9.65 6.25 6.9

8.5 8.2 5.0 9.65 6.16 6.9 3.9 12.7 28 35

8.5 8.2 5.0 9.69 6.00 5.4

1 10 1.4 103 1.3 103 <3 104 5.0 103 1.5 103

1 10 5.7 104 4.5 104 <3 104 4.2 103 2.0 104 7 104 <1 104 1 102 1 102

1 103 2 104 3.7 104 <3 104 2.7 103 3.5 104

70

2.3

2.3

2.3

2 104

2 104

2 104

181–276

70

2.3

2.3

2.3

2 104

2 104

2 104

197–295

70

2.35

2.35

2.35

2 104

2 104

2 104

177–197

3

3

98–157 94–157 200 >2000 4500 3000–8200 1000–10,000 1000–10,000

CRC Handbook of Engineering Tables

Alumina (Al2O3) Porcelain (mullite) Steatite 3MgO · 4SiO2 · H2O Magnesium oxide (MgO) Glass (soda lime) Mica (KAl2(OH)2Si3AlO10) SiO2 film Si3 N4 Ta2O5 HfO2 Low-density PE

Specific Gravity

Maximum Operating Temperature (°C)

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Electrical and Physical Properties of Some Common Solid Insulating Materials

90 300–350°F 128–186 <327 265

1.31–1.58

250

1.43–1.49

480°F

1.20 1.6–1.9

215 200 (decomposition temperature) 200 (decomposition temperature) 700°F

Epoxy (with silica filler)

1.6–2.0

Silicone rubber

1.1–1.5

2.3 2.22–2.28 2.0 5.3–7.3

2.28 3.0–3.5 2.22–2.28 2.0

2.22–2.28 2.0 5.06.4

3 104 4 103 2–3 104 <2 104 1–4 102

4 104 2.5–3.0 104 <2 104

4.6 104 <2 104 0.8–2.2 102

1.5–2.0 103

3.3–3.8 (100 Hz)

232–295 1–5 103 (100 kHz)

3.4 (100 kHz)

217 354–413 295–314 189 90.6–158

220

3.17 4.4–5.6

4.2–4.9

2.96 4.1–4.6

9 104 1.1–8.3 102

0.19–1.4 101

1 102 0.13–1.4 101

157 98.4–158

3.2–4.5

3.2–4.0

3.0–3.8

0.8–3.0 102

0.8–3.0 102

2–4 102

158–217

3.1–3.7

1.5–3.0 102

3.0–5.0 103

158–197

3.3–4.0

From Bartnikas, R., Dielectrics and insulators, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, pp. 1249–1250. Originally from Bartnikas, R. and Eichhorn, R.M., Eds., Engineering Dielectrics, Vol. IIA, Electrical Properties of Solid Insulating Materials: Molecular Structure and Electrical Behavior, STP 783, ASTM, Philadelphia, PA, 1983; Encyclopedia Issue, Insul. Circuits, June/July 1972.

1-81

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EPR Polypropylene PTFE Glass-reinforced polyester premix Thermoplastic polyester Polyimide polyester Polycarbonate Epoxy (with mineral filler)

(density: 0.92 g cm3) 0.86 0.90 2.13–2.20 1.8–2.3

Electrical and Computer Engineering

XLPE

Secondary Signal Primary Signal

Mechanical (Fluid) mechanical and acoustic effects (e.g., diaphragm, gravity balance, echo sounder)

Thermal

Thermal expansion (bimetal strip, liquid-in-glass and gas thermometers, resonant frequency) Radiometer effect (light mill) Electrokinetic and electromechanical effects (e.g., piezoelectricity, electrometer, Ampere’s law) Magnetomechanical effects (e.g., magnetorestriction, magnetometer)

Electrical

Magnetic

Friction effects (e.g., friction calorimeter) Cooling effects (e.g., thermal flow meters)

Electrical Piezoelectricity Piezoresistivity Resistive, capacitive, and inductive effects

Magnetic Magneto-mechanical effects (e.g., piezomagnetic effect)

Seebeck effect Thermoresistance Pyroelectricity Thermal (Johnson) noise

Joule (resistive) heating Peltier effect

Charge collectors Langmuir probe

Thermomagnetic effects (e.g., Righi-Leduc effect) Galvanomagnetic effects (e.g., Ettingshausen effect)

Thermomagnetic effects (e.g., EttingshausenNernst effect) Galvanomagnetic effects (e.g., Hall effect, magnetoresistance) Photoelectric effects (e.g., photovoltaic effect, photoconductive effect) Potentiometry Conductimetry Amperometry Flame ionization Volta effect Gas-sensitive field effect

Radiant

Radiation pressure

Bolometer thermopile

Chemical

Hygrometer Electrodeposition cell Photoacoustic effect

Calorimeter Thermal conductivity cell

Biot-Savart’s law

Nuclear magnetic resonance

Radiant Photoelastic systems (stress-induced birefringence) Interferometers Sagnac effect Doppler effect Thermooptical effects (e.g., in liquid crystals) Radiant emission

Chemical

Reaction activation (e.g., thermal dissociation)

Electrooptical effects (e.g., Kerr effect) Pockel’s effect Electroluminescence Magnetooptical effects (e.g., Faraday effect) Cotton-Mouton effect

Electrolysis Electromigration

Photorefractive effects Optical bistability

Photosynthesis, -dissociation

(Emission and absorption) spectroscopy Chemiluminiscence

From Smith, R.L., Sensors, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1256. Originally from T. Grandke and J. Hesse, Introduction, Vol. 1: Fundamentals and General Aspects, Sensors: A Comprehensive Survey, W. Gopel, J. Hesse, and J. H. Zemel, Eds., Weinheim, Germany: VCH, 1989. With permission.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Mechanical

Thermal

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Physical and Chemical Transduction Principles

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Electrical and Computer Engineering

Electrical Properties of Metals Used in Transmission Lines

Metal

Relative Conductivity (Copper = 100)

Electrical Resistivity at 20°C, W · m (10–8)

Temperature Coefficient of Resistance (per °C)

100 97 61 12 8

1.724 1.777 2.826 13.80 21.4

0.0039 0.0039 0.0040 0.0045 0.0040

Copper (HC, annealed) Copper (HC, hard-drawn) Aluminum (EC grade, 1/2 H-H) Mild steel Lead

From Chen, M.-S., Alternating current overhead: Line parameters, models, standard voltages, insulators, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1323.

Typical Synchronous Generator Parametersa Parameter Synchronous reactance d-axis q-axis Transient reactance d-axis q-axis Subtransient reactance d-axis q-axis Time constants Transient Stator winding open-circuited Stator winding short-circuited Subtransient Stator winding short-circuited a

Round Rotor

Salient-Pole Rotor with Damper Windings

Xd Xq

1.0–2.5 1.0–2.5

1.0–2.0 0.6–1.2

X¢d X¢q

0.2–0.35 0.5–1.0

0.2–0.45 0.25–0.8

X≤d X≤q

0.1–0.25 0.1–0.25

0.15–0.25 0.2–0.8

Tdo ¢ T¢d

4.5–13 1.0–1.5

3.0–8.0 1.5–2.0

T≤d

0.03–0.1

0.03–0.1

Symbol

Reactances are per unit, i.e., normalized quantities. Time constants are in seconds. From Liu, C.-C., Vu, K.T., and Yu, Y., Generators, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1451. Originally from M.A. Laughton and M.G. Say, eds., Electrical Engineer’s Reference Book, Stoneham, Mass.: Butterworth, 1985.

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CRC Handbook of Engineering Tables

Excitation Methods and Voltage Current Characteristics for DC Generators Excitation Methods

Characteristics

Separate

For low currents, the curve is nearly a straight line. As load current increases, the armature reaction becomes more severe and contributes to the nonlinear drop. Series

At no load, there is no field current, and voltage is due to the residual flux of the stator core. The voltage rises rapidly over the range of low currents, but the resistive drop soon becomes dominant. Shunt

Voltage buildup depends on the residual flux. The shunt field resistance must be less than a critical value. Compounded

There are two field windings. Depending on how they are set up, one may have cumulative if the two fields are additive, differential if the two fields are subtractive.

Cumulative: An increase in load current increases the resistive drop, yet creates more flux. At high currents, however, resistive drop becomes dominant. Differential: An increase in load current not only increases the resistive drop, but also reduces the net flux. Voltage drops drastically.

From Liu, C.-C., Vu, K.T., and Yu, Y., Generators, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1455. Originally from S.J. Chapman, Electric Machinery Fundamentals, New York: McGrawHill, 1991.

© 2004 by CRC Press LLC

Corresponding Quadrature Modulation

Mapping Functions g[m]

x(t)

Corresponding Amplitude and Phase Modulation y(t)

AM

1 + m(t)

1 + m(t)

0

1 + m(t)

DSB-SC

m(t)

m(t)

0

m(t)

PM

e jDp m(t)

cos[Dpm(t)]

sin[Dpm(t)]

1

È sin ÍD f Î ˆ ± m(t)

1

ˆ m(t) ± jm(t)

È cos ÍD f Î m(t)

e jDp[m(t)±j ˆm(t)]

e Dp ˆm(t )cos[D pm(t)]

e Dp ˆm(t)sin[D pm(t)]

t È ù cosÍD f m(s)d sú – • Î û [1 + m(t)] cos {lnˆ [1 + m(t)]}

t È ù sin ÍD f m(s)d sú • – Î û ±[1 + m(t)]sin{lnˆ [1 + m(t)]}

FM e SSB-AMSCa SSB-PMa SSB-FMa e a

jDf

jDf

t

Ú-• m(s )d s

t

Ú-•[m(s)± jmˆ (s )]d s

{ln[1 + m(t)]±jl ˆn[1 + m(t )]}

SSB-EV

e

SSB-SQa

e (1/2){ln[1 + m(t )]±jl ˆn[1 + m(t )]}

QM

m1(t) + jm2(t)

e

ù m(s)ds ú –• û

Ú

t

ˆ (s )d s m D f Ú–t • m

Ú

Ï1 ˆ ¸ 1 + m(t ) cosÌ ln[ 1 = m(t )]ý 2 Ó þ m1(t)

e

ù m(s)ds ú –• û

Ú

t

m D f Ú–t • mˆ (s )d s

Linearity

m (t ) > –1¸ Ï0, Ì ý Ó180∞, m (t ) < –1þ

Lb

m(t) > –1 required for envelope detection.

Ï0, m (t ) > 0 ¸ Ì ý 180 ∞ , m (t ) < 0þ Ó Dpm(t)

L

Coherent detection required.

NL

Dp is the phase deviation constant (radian/volts). Df is the frequency deviation constant (radian/volt-sec). Coherent detection required.

Df [m(t )2 + [mˆ (t )]2 e Dp ˆm(t)

Ú

Ï1 ˆ ¸ ± 1 + m(t ) sin Ì ln[ 1 + m(t )]ý 2 Ó þ m2(t)

q(t)

R(t)

e

m D f Ú–t • mˆ (s )d s

1 + m(t)

1 + m (t ) m12 (t ) + m 22 (t )

Ú

t

–•

m(s)ds

NL

ˆ (t)/m(t)] tan–1[± m

L

Dpm(t)

NL

Df

Ú

t

–•

m(s)ds

±lnˆ [1 + m(t)]

±

NL

NL

1 ˆ ln[1 + m(t )] 2

tan–1[m2(t)/m1(t)]

Remarks

NL

L

m(t) > –1 is required so that the ln will have a real value. m(t) > –1 is required so that the ln will have a real value. Used in NTSC color television: requires coherent detection.

1 1 • x (l) L = linear, NL = nonlinear, [ˆ.] is the Hilbert transform (i.e., –90° phase-shifted version) of [·]. The Hilbert transform is xˆ (t ) =D x (t )* = dl pt p -• t - l a Use upper signs for upper sideband signals and lower signs for lower sideband signals. b In the strict sense, AM signals are not linear because the carrier term does not satisfy the linearity (superposition) condition. From Dorf, R.C. and Wan, Z., Modulation and demodulation, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1505. Orignally from L. W. Couch, Digital and Analog Communication Systems, New York: Macmillan, 1990. With permission.

Ú

1-85

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Type of Modulation

Electrical and Computer Engineering

Complex Envelope Functions for Various Types of Modulation

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CRC Handbook of Engineering Tables

Protected Service Signal Intensities for Standard Broadcasting (AM)

Class of Station

Power (kW)

A

10–50

B

0.25–50

C D

0.25–1 0.25–50

Class of Channel Used Clear Clear Regional Local Clear Regional

Signal Strength Contour of Area Protected from Objectionable Interference* (µV/m)

Permissible Interfering Signal

Day†

Night

Day†

Night‡

SC 100 AC 500 500

SC 500 50% SW AC 500 GW 2000†

500 500

Not precise§ Not precise

SC 5 AC 250 25 AC 250 SC 25 SC 25 AC 250

SC 25 AC 250 25 250 Not precise Not precise

* When a station is already limited by interference from other stations to a contour of higher value than that normally protected for its class, this higher-value contour shall be the established protection standard for such station. Changes proposed by Class A and B stations shall be required to comply with the following restrictions. Those interferers that contribute to another station’s RSS using the 50% exclusion method are required to reduce their contribution to that RSS by 10%. Those lesser interferers that contribute to a station’s RSS using the 25% exclusion method but do not contribute to that station’s RSS using the 50% exclusion method may make changes not to exceed their present contribution. Interferers not included in a station’s RSS using the 25% exclusion method are permitted to increase radiation as long as the 25% exclusion threshold is not equaled or exceeded. In no case will a reduction be required that would result in a contributing value that is below the pertinent value specified in the table. † Groundwave. ‡ Skywave field strength for 10% or more of the time. For Alaska, Class SC is limited to 5 µV/m. § During nighttime hours, Class C stations in the contiguous 48 states may treat all Class B stations assigned to 1230, 1240, 1340, 1400, 1450, and 1490 kHz in Alaska, Hawaii, Puerto Rico and the U.S. Virgin Islands as if they were Class C stations. Note: SC = same channel; AC = adjacent channel; SW = skywave; GW = groundwave; RSS = root of sum squares. From Lindsey III, J.F. and Doelizsch, D.F., Radio broadcasting, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1515. Originally from FCC Rules and Regulations, Revised 1991; vol. III, pt. 73.182(a).

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Electrical and Computer Engineering

Coding Gains with BPSK or QPSK Coding Technique Used

Coding Gain (dB) at 10–5 BER

Coding Gain (dB) at 10–8 BER

11.2

13.6

6.5–7.5

8.5–9.5

Moderate

6.0–7.0 5.0–6.0 4.5–5.5 4.0–5.5

8.0–9.0 6.5–7.5 6.5–7.5 5.0–6.5

Moderate Moderate Very high High

4.0–5.0 3.0–4.0 2.0–4.0 1.5–3.0

6.0–7.0 4.5–5.5 3.5–5.5 2.5–4.0

High High High Very high

Ideal coding Concatenated Reed–Solomon and convolution (Viterbi decoding) Convolutional with sequential decoding (soft decisions) Block codes (soft decisions) Concatenated Reed–Solomon and short block Convolutional with Viterbi decoding Convolutional with sequential decoding (hard decisions) Block codes (hard decisions) Block codes with threshold decoding Convolutional with threshold decoding

Data Rate Capability

BPSK: modulation technique—binary phase-shift keying; QPSK: modulation technique—quadrature phaseshift keying; BER: bit error rate. From Dorf, R.C. and Wan, Z., Error control coding, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1554. Originally from V.K. Bhargava, “Forward error correction schemes for digital communications,” IEEE Communication Magazine, 21, 11–19, © 1983 IEEE. With permission.

Comparison of Orbit and Link Parameters for LEO, MEO, and GEO for the Particular Case of Circular Orbits (eccentricity, e, = 0) and for Elevation Angle (el = 10°) Orbit Example system Inclination, i (deg.) Altitude, h (km) Semi-major axis radius, a (km) Orbit period (minutes) (re + h)/re Earth central angle, g (deg.) Nadir angle, q (deg.) Nadir spread factor 10 log(4ph2 (dB m2)) Slant range, rs (km) One-way time delay (ms) Maximum spread factor 10 log(4prs2 (dB m2)) 20 log(rs /h (dB)) Ground coverage area (km2) Fraction of earth area

LEO

MEO/ICO

GEO

Iridium® 86.4 780 7159 100.5 1.1222 18.658 61.3

ICO-P ±45 10,400 16,778 360.5 2.6305 58.015 22

INTELSAT 0 35,786 42,164 1436.1 6.6107 71.433 8.6

128.8 2325 2.6

151.3 14,450 51.8

162.1 40,586 139.1

154.2 2.9 120.2 ¥ 106 0.235

163.2 1.1 174.2 ¥ 106 0.34

138.3 9.5 13.433 ¥ 106 0.026

Note: earth radius, re , (km) = 6378.14; earth surface area, ae , (km2) = 511.2 ¥ 106; elevation angle, el (degrees) = 10. From DiFonzo, D.F., Satellites and aerospace, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1701.

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CRC Handbook of Engineering Tables

Partial List of Satellite Frequency Allocations Band VHF VHF L-Band

Uplink

Downlink

Satellite Service

0.3120–0.315

0.137–0.138 0.387–0.390 1.492–1.525

Mobile Mobile Mobile Mobile, radio astronomy Mobile LEO Mobile Global positioning system GPS MSS (available Jan. 1, 2000) (proposed for U.S. in 2000) Deep-space research Mobile Fixed (FSS) FSS FSS FSS Direct Broadcast (BSS) (U.S.) FSS (BSS in U.S.) 22.55–23.55 Intersatellite 24.45–24.75 Intersatellite 25.25–27.5 Intersatellite FSS FSS, MSS Fixed Broadcast Satellite Intersatellite Intersatellite

1.610–1.6138 1.613.8–1.6265 1.6265–1.6605

S-Band

1.980–2.010 1.980–1.990 2.110–2.120

C-Band

5.85–7.075 7.250–7.300 7.9–8.4 12.75–13.25 14.0–14.8

X-Band Ku-Band Ka-Band

Q

27–31 42.5–43.5, 47.2–50.2 50.4–51.4

1.6138–1.6265 1.525–1.545 1.575 1.227 2.170–2.200 2.165–2.200 2.290–2.300 2.4835–2.500 3.4–4.2 4.5–4.8 7.25–7.75 10.7–12.2 12.2–12.7 17.3–17.7

17–21 37.5–40.5 40.5–42.5

V

54.24–58.2– 59–64

Note: Frequencies in GHz. Allocations are not always global and may differ from region to region in all or subsets of the allocated bands. From DiFonzo, D.F., Satellites and aerospace, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1703. Originally from Final Acts of the World Administrative Radio Conference (WARC-92), MalagaTorremolinos, 1992; 1995 World Radiocommunication Conference (WRC-95).

Specifications of TDMA and CDMA Systems TDMA

CDMA

Bandwidth per channel Time slots

30 kHz 3

Bandwidth per channel Speech coder

Modulation Speech coder

p/4-DQPSK 8 kbps—VSELP code (vector sum excited LPC*) Rate 1/2 convolutional (13 kbps) 48 kbps per channel Up to 40 ms

Forward radio channels

Channel coding Total transmit rate Equalizer

Reverse radio channels Power control Diversity

1.23 MHz 8 kbps(max.)—a variable rate vocoder Pilot (1) sync (1), paging (7), traffic channels (55), total 64 channels Access (9), traffic channels (55) Forward, reverse Rake receiver

* LPC = linear predictive code. From Lee, W.C.Y., Mobile radio and cellular communications, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1710.

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Electrical and Computer Engineering

Switching Algebra Summary (P1) XY = YX (P2) X(YZ) = (XY)Z (P3) XX = X (P4) X(X + Y) = X (P5) X(Y + Z) = XY + XZ (P6) XX = 0

(S1) X + Y = Y + X (S2) X + (Y + Z) = (X + Y) + Z (S3) X + X = X (S4) X + XY = X (S5) X + YZ = (X + Y)(X + Z) (S6) X + X = 1 (C1) X = X

(P7) XY = X + Y (P8) X( X + Y) = XY

(S7) X + Y = XY (S8) X + XY = X + Y

(B1) 1 = 0 (P10) X · 0 = 0 (P11) X · 1 = X (P13) (X + Y)(Y + Z)( X + Z) = (X + Y)( X + Z)

(S10) X + 1 = 1 (S11) X + 0 = X (S13) XY + YZ + X Z = XY + X Z

Commutativity Associativity Idempotency Absorption Distributivity Complementarity Involution De Morgan’s

Consensus

From Preparata, F.P., Combinational networks and switching algebra, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1858.

Binary-to-Decimal Conversion Two-Bit Binary

Decimal Value

Three-Bit Binary

Decimal Value

Four-Bit Binary

Decimal Value

Five-Bit Binary

Decimal Value

Six-Bit Binary

Decimal Value

00 01 10 11

0 1 2 3

000 001 010 011 100 101 110 111

0 1 2 3 4 5 6 7

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

100000 100001 100010 100011 100100 100101 100110 100111 101000 101001 101010 101011 101100 101101 101110 101111

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

From Tinder, R.F., Number systems, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 1993.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

DFs of Single-Valued Nonlinearities a< d1 dM+1 > a > dM

Np = 0 M

(

N p = 4 a 2p

)Âh (a

)

- n 2d 2

)

m=1

a
Np = 0

(2M + 1)d > a > (2M – 1)d

N p = 4h a2 p

n = (2m – 1)/2 ad

- d m2

2

m

M

(

)Â (a

2

n=1

12

12

Np = 0 Np = 4h(a2 – d2)1/2/a2p

Np = 4h/ap

Np = (4h/ap) + m

a < d1 dM+1 > a > dM

Np = (4h/ap) + m1 Np = (4h/ap) + mM+1 M

+

Â (m - m ) N (d a) j

i =1

NP = mNs(d/a)

Np = m[1 – Ns(d/a)

© 2004 by CRC Press LLC

j +1

i

j

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Electrical and Computer Engineering

DFs of Single-Valued Nonlinearities (continued) Np = (m1 – m2)Ns(d/a) + m2

Np = m[Ns(d2 /a) – Ns(d1/a)]

Np = –m1Ns(d1 /a) + (m1 – m2)Ns(d2 /a) + m2

ad

Np = 0 Np = 4h(a2 – d2)1/2/a2p + m – mNs(d/a)

ad

Np = m1 Np = (m1 – m2)Ns(d/a) + m2 + 4h(a2 – d2)1/2/a2 p

ad

Np = 4h/ap Np = 4h/[a – (a2 – d2)1/2]/a2 p

Np = (m1 + m2)Ns(d/a) – m2Ns[(m1 + m2)d/m2a]

ad

m > –2 G is the gamma function

Np = m 1 Np = m1Ns(d/a) – 4m1d(a2 – d2)1/2 /a2p

Np =

=

G(m + 1)am-1

[ ][ 2 G[(m + 2) 2]a p G[(m + 3) 2]

2m-1 G (3 + m) 2 G (1 + m) 2

]

m-1

From Atherton, D.P., Nonlinear control systems, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2318–2319.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Illuminance Categories and Illuminance Values for Generic Types of Activities in Interiors Ranges of Illuminances

Illuminance Category

Lux

Footcandles

Public spaces with dark surroundings Simple orientation for short temporary visits Working spaces where visual tasks are only occasionally performed

A

20–30–50

2–3–5

B

50–75–100

5–7.5–10

C

100–150–200

10–15–20

Performance of visual tasks of high contrast or large size Performance of visual tasks of medium contrast or small size Performance of visual tasks of low contrast or very small size

D

200–300–500

20–30–50

E

500–750–1,000

50–75–100

F

1,000–1,500–2,000

100–150–200

Performance of visual tasks of low contrast and very small size over a prolonged period Performance of very prolonged and exacting visual tasks Performance of very special visual tasks of extremely low contrast and small size

G

2,000–3,000–5,000

200–300–500

H

5,000–7,500–10,000

500–750–1,000

I

10,000–15,000–20,000

1,000–1,500–2,000

Type of Activity

Reference WorkPlane

General lighting throughout spaces

Illuminance on task

Illuminance on task, obtained by a combi- nation of general and local (supplementary lighting)

From Chen, K., Industrial illuminating systems, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 2449. Originally from IES Lighting Handbook, Application Volume.

Representative Transducers Measurand Displacement (Length) Force Temperature Pressure Flow

Transducer Resistive Capacitive Inductive Strain gage Thermistor Thermocouple Diaphragm Differential pressure Turbine

Operating Principles Change in resistance, capacitance, or inductance caused by linear or angular displacement of transducer element Resistance, piezoresistivity Resistance Peltier, seebeck effect Diaphragm motion sensed by a displacement technique. Pressure drop across restriction Angular velocity proportional to flow rate

From Schmalzel, J.L., Instruments, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 2470.

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Electrical and Computer Engineering

Worldwide Radio Navigation Aids Frequency System

Hz

Omega Loran-C/Chaika Decca Beacons* Instrument Landing System (ILS)* VOR* SARSAT/COSPAS Transit PLRS JTIDS DME* Tacan* Secondary Surveillance Radar (SSR)* Identification Friend or Foe (IFF) GPS-GLONASS Satellite Control Network (SCN) Spaceflight Tracking and Data Network (STDN) Radar Altimeter MLS* FPQ-6, FPQ-16 radar Weather/map radar Shuttle rendezvous radar Airborne Doppler radar SPN-41 carrier-landing monitor SPN-42/46 carrier-landing radar

10–13 kHz 100 kHz 70–130 kHz 200–1600 kHz 108–112 MHz 329–335 MHz 108–118 MHz 121.5 MHz 243,406 MHz 150, 400 MHz 420–450 MHz 960–1213 MHz 962–1213 MHz 962–1213 MHz 1030, 1090 MHz

VLF LF LF MF VHF UHF VHF VHF UHF VHF UHF L L L L

1227, 1575 MHz 1760–1850 MHz 2200–2300 MHz 2025–2150 MHz 2200–2300 MHz

L S S S

4200 MHz 5031–5091 MHz 5.4–5.9 GHz 10 GHz 13.9 GHz 13–16 GHz 15 GHz 33 GHz

C C C X Ku Ku Ku Ka

{

{

{ {

Band

Number of Stations

Number of Users in 1996 Air

Marine

Space

Land

8 50 150 4000 1500

15,000 120,000 2,000 130,000 150,000

10,000 550,000 20,000 500,000 0

0 0 0 0 0

0 25,000 0 0 0

1500 5 satellites

180,000 200,000

0 200,000

0 0

0 100,000

7 satellites None None 1500 850 800

0 0 500 90,000 15,000 250,000

0 0 0 0 0 0

0 0 0 4 4 0

0 2,000 0 0 0 0

24 + 24 satellites 10

120,000 0

275,000 0

4 200

125,000 0

3 satellites 10 ground

0

0

50

0

None 30 10 None None None 25 25

20,000 100 0 10,000 0 20,000 1600 1600

0 0 0 0 0 0 0 0

0 0 0 0 4 0 0 0

0 0 0 0 0 0 0 0

* Standardized by International Civil Aviation Organization. From Kayton, M., Navigation systems, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 2482.

Classifications of Chemical Biomedical Sensors 1. Electrochemical a. Amperometric b. Potentiometric c. Coulometric 2. Optical a. Colorimetric b. Emission and absorption spectroscopy c. Fluorescence d. Chemiluminescence 3. Thermal methods a. Calorimetry b. Thermoconductivity 4. Nuclear magnetic resonance From Neuman, M., Biomedical sensors, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 2587.

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CRC Handbook of Engineering Tables

Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristic Impedance for Water and Selected Tissues at 3.5 MHz Tissue

Attenuation Coefficient (m–1)

Water Amniotic fluid Blood Liver Muscle Bone Lung

0.2 0.7 7 35 50 800 1000

Speed (m/s)

Characteristic Impedance (106 Pa s/m)

1520 1510 1550 1580 1560 3360 340

1.50 1.51 1.60 1.74 1.72 5.70 0.25

From Frizzell, L.A., Ultrasound, in The Electrical Engineering Handbook, 2nd ed., Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1998, p. 2623.

Parasitics in Various Electronic Packages Package Type

Parasitic Capacitance, pF

Flip chip Chip on board/wire bond Pin grid array Quad flat pack Through-hole DIP

Parasitic Inductance, nH

0.1 0.5 1 1 3

0.01 1–2 2 1–6 8–20

From Blackwell, G.R., Direct chip attach, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 4-5.

Wiring Board Material Properties CTE (¥ 10–6/°C) Material FR-4 epoxy-glass Polyimide-glass Teflon® Benzocyclobutene High-temperature one-component epoxy-glass Cyanate ester-glass Ceramic Copper Copper/invar/copper

e¢r

e r≤ §er¢

x, y

z

Tg, °C

4.0–5.0 3.9–4.5 2.1 2.6 4.45–4.45

0.02–0.03 0.005–0.02 0.0004–0.0005 0.0004 0.02–0.022

16–20 12–14 70–120 35–60

60–90 60

125–135 >260 — >350 170–180

3.5–3.9 ~10.0 — —

0.003–0.007 0.0005 — —

6–7 17 3–6

240–250 — — —

From Blackwell, G.R., Circuit boards, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 5-3.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Interconnect Models

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Interconnect Models (continued)

From Blackwell, G.R., Circuit boards, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 5-13 to 5-14.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Dielectric Constants and Wave Velocities within Various PCB Materials Material Air PTFE/glass (Teflon™) RO 2800 CE/custom ply (Canide ester) BT/custom ply (Beta-triazine) CE/glass Silicon dioxide BT/glass Polyimide/glass FR–4 glass Glass cloth Alumina

er (at 30 MHz)

Velocity (in/ns)

Velocity (ps/in)

1.0 2.2 2.9 3.0 3.3 3.7 3.9 4.0 4.1 4.5 6.0 9.0

11.76 7.95 6.95 6.86 6.50 6.12 5.97 5.88 5.82 5.87 4.70 3.90

85.0 125.8 143.9 145.8 153.8 163.4 167.5 170.1 171.8 170.4 212.8 256.4

Note: Values measured at TDR frequencies using velocity techniques. Values were not measured at 1 MHz, which provides faster velocity values. Units for velocity differ due to scaling and are presented in this format for ease of presentation. From Montrose, M.I., EMC and printed circuit board design, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 6-40. Originally from IPC–2141, Controlled Impedance Circuit Boards and High Speed Logic Design, Institute for Interconnecting and Packaging Electronics Circuits. ” 1996. Reprinted with permission.

Wire Ampacity and Size

AWG wire size

Resistance, W per 1000 ft

Ampacity for low-temperature insulation

Ampacity for high-temperature insulation

Bare wire diameter mm (in)

30 28 26 24 22 20 18

100 60 40 25 14 10 6

2 3 4 6 8 10 15

4 6 7 10 13 17 24

0.254 (0.0100) 0.320 (0.0126) 0.404 (0.0159) 0.511 (0.0201) 0.643 (0.0253) 0.810 (0.0319) 1.024 (0.0403)

Note: W/1000 ft is approximate. Exact value depends on whether the conductor is solid or stranded, and if stranded, the type of stranding. Consult the manufacturers’ data sheets for exact values. From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-4.

Parameters for Multimode and Single-Mode Fiber Parameter

Multimode (62.5/125 µm)

Dispersion-Unshifted Single-Mode

Core size Mode field diameter Numerical aperture Cladding diameter Attenuation

62.5 ± 3.0 µm — 0.275 ± 0.015 125.0 ± 2.0 µm £3.5 dB/km at 850 nm £1.5 dB/km at 1300 nm ≥160 MHz·km at 850 nm ≥500 MHz·km at 1300 nm —

8.3 µm (typical) 8.8–9.3 µm (typical) 0.13 (typical) 125.0 ± 1.0 µm £0.5 dB/km at 1310 nm £0.4 dB/km at 1550 nm —

Bandwidth Dispersion

£3.5 ps/nm·km for 1285–1330 nm

From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-24.

© 2004 by CRC Press LLC

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Standard Optical Cable Color Coding Unit or Fiber

Color

Unit or Fiber

Color

1 2 3 4 5 6

Blue Orange Green Brown Slate White

7 8 9 10 11 12

Red Black Yellow Violet Rose Aqua

From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-30.

Common Tests for Optical Fiber Test

FOTP

Core diameter

FOTP–43 and –58

Mode field diameter

FOTP–167

Cladding diameter

FOTP–176

Core–clad concentricity Core noncircularity

FOTP–176

Cladding noncircularity Fiber cutoff wavelength Cable cutoff wavelength

FOTP–176 FOTP–176 FOTP–80 FOTP–170

Curl

FOTP–111 (underdevelopment)

Coating diameter

FOTP–173

Numerical aperture

FOTP–47 and –177

Proof test

FOTP–31

Attenuation coefficient Bandwidth

FOTP–61 and –78 FOTP–30 and –5

Purpose Determine the size of the core in a multimode fiber to ensure compatibility with other fibers of the same core size as well as with end equipment. Measure of the spot size of light propagating in a single-mode fiber to ensure compatibility with other fibers of similar core size as well as with end equipment. Differences in mode field diameters of two fibers being spliced together can affect splice loss. Determine the size of the cladding. The consistency of cladding diameter can affect connector and mechanical splice performance. Distance between the center of the core and the center of the cladding. High values can affect splice and connector losses. Measures the roundness of multimode cores. High values can have a slight effect on splice and connector losses. Measures the roundness of the cladding. High values can have a slight effect on splice and connector losses. Measures the minimum wavelength at which a single-mode fiber will support the propagation of only one mode. If the system wavelength is below the cutoff wavelength, multimode operation may occur introducing modal dispersion and higher attenuation. The difference in fiber and cable cutoff wavelength is due to the deployment of fiber during the test. Cabling can shift the cutoff wavelength to a lower value. Measures the curvature of a short length of fiber in an unsupported condition. Excessive curl can affect splice loss in passive alignment fusion splicers such as mass fusion splicers. Measures the outside diameter of a coated fiber. Out of spec values can affect cable manufacturing and potentially cable performance. Measures the numerical aperture of a fiber. Ensures compatibility with other fibers as well as end equipment. Ensures the minimum strength of a fiber. Every fiber is normally subjected to the proof test. Measured by the fiber and cable manufacturers and reported to the customer in units of dB/km. Measured by the fiber manufacturer and reported to the customer by the cable manufacturer in units of MHz·km.

From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-47.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Common Tests for Optical Cable Design Test

FOTP

Temperature cycling

FOTP–3

Impact

FOTP–25

Tensile

FOTP–33

Compressive load

FOTP–41

Cable twist

FOTP–85

Cycle flex or bend

FOTP–104

Water penetration

FOTP–82

Filling and flooding compound flow

FOTP–81

Purpose Simulates environmental conditions once the cable is deployed. Simulates an object being dropped on the cable for a sudden and brief impact. Measures the performance of the cable at its rated tensile load simulating installation by pulling. Measures cable performance while under a compressive or crushing force. Measures the ability of the cable to perform when under a twist condition. Measures the ability of the cable to perform even when subjected to a bend, and withstand repeated bending during installation. Measures the ability of an outdoor cable to prevent the ingress of water along the length of the cable. Measures the resistance to flow of compound flow filling and flooding compounds at elevated temperatures.

From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-47.

Cable Interconnects

Cable Designation

Nominal Z0

Vp

Diameter, in

RG-8A/U RG-8/X RG-213/U RG-58/U RG-58A/U RG-58C/U RG-11A/U RG-59B/U RG-62B/U RG-71/U RG-141A/U RG-178B/U RG6A/U

52 50 50 53.5 50 50 75 75 93 93 50 50 75

0.66 0.78 0.66 0.66 0.66 0.66 0.66 0.66 0.84 0.84 0.695 0.695 0.66

0.405 0.242 0.405 0.195 0.195 0.195 0.405 0.242 0.242 0.245 0.190 0.70 0.332

Nominal Atten. at 50 MHz, dB/100 ft

Nominal Atten. at 200 MHz, dB/100 ft

Nominal Atten. at 700 MHz, dB/100 ft

Max. Op. Voltage, RMS

1.6 2.5 1.6 3.1 3.3 3.3 1.3 2.4 2.0 1.9 2.7 10.5 1.9

3.2 5.4 3.2 6.8 7.3 7.3 2.9 4.9 4.2 3.8 5.6 19.0 4.1

6.5 11.1 6.5 14.0 17.0 17.0 5.8 9.3 8.6 7.3 11.0 37.0 8.1

4000 600 5000 1900 1900 1900 5000 2300 750 750 1400 1000 2700

From Blackwell, G.R., Interconnects, in The Electronic Packaging Handbook, Blackwell, G.R., Ed., CRC Press, Boca Raton, FL, 2000, p. 8-53.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

© 2004 by CRC Press LLC

1587_Book.fm Page 100 Friday, September 26, 2003 12:10 PM

1-100

(From Norgard, J., Electromagnetic spectrum, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 4.)

Maximum Relative Permeability, mmax/m0

Coercive Force He, A/m (Oe)

250 10,000 1500 7500 — 20,000 8000 100,000 800 1500 2500

9000 200,000 7000 55,000 116,000 100,000 100,000 1,000,000 5000 2500 5000

ª80 (1) 4 (0.05) 20 (0.25) 8 (0.1) 4.8 (0.06) 4 (0.05) 4 (0.05) 0.16 (0.002) 160 (2) 16 (0.2) 8 (0.1)

Residual Field Br, Wb/m2(G)

Saturation Field Bs, Wb/m2(G)

Electrical Resistivity r ¥ 10–8 W · m

0.77 (7700) — 0.5 (5000) 0.95 (9500) 1.22 (12,200) 0.23 (2300) 0.6 (6000) 0.5 (5000) 1.4 (14,000) — —

2.15 (21,500) 2.15 (21,500) 1.95 (19,500) 2 (20,000) 2 (20,100) 0.65 (6500) 1.08 (10,800) 0.79 (7900) 2.45 (24,500) 0.34 (3400) 0.32 (3200)

10 10 60 50 50 62 16 60 7 20 ¥ 106 1011

Uses

Soft Commercial iron (0.2 imp.) Purified iron (0.05 imp.) Silicon-iron (4 Si) Silicon-iron (3 Si) Silicon-iron (3 Si) Mu metal (5 Cu, 2 Cr, 77 Ni) 78 Permalloy (78.5 Ni) Supermalloy (79 Ni, 5 Mo) Permendur (50 Cs) Mn-Zn ferrite Ni-Zn ferrite

Relays Transformers Transformers Transformers Transformers Sensitive relays Transformers Electromagnets Core material for coils

From Parker, M.R. and Webb, W.E., Magnetic materials for inductive processes, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 151. Originally after Plonus, M.A., 1978, Applied Electromagnetics, McGraw-Hill, New York.

1-101

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Material (Composition)

Initial Relative Permeability, mi/m0

Electrical and Computer Engineering

Properties of Magnetic Materials and Magnetic Alloys

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CRC Handbook of Engineering Tables

Units Quantity Magnetic flux density Magnetic field intensity Magnetic flux Magnetic flux linkage Self, mutual inductance Magnetic permeability

Symbol

Unit (S.I.)

B H f¢ L L, M m

T (or Wb/m2) A/m Wb Wb-turns H H/m

From Parker, M.R. and Webb, W.E., Magnetic materials for inductive processes, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 154.

CAPACITOR SYMBOL C STATE VARIABLE: VOLTAGE

ANALYTICAL DESCRIPTION i (t ) = C du dt

PROPERTY C IS A POSITIVE REAL CONSTANT

TRANSIENT REGIME

SINUSOIDAL REGIME: 1 f ( j ω) V ( j ω) = j ωC

I(s ) = sCV (s ) Z (s ) =

STATIONARY REGIME:

i=0

1 sC

XC (ω) = 1 ωC Z ( jω) = −jXc (ω)

Y (s ) = sC (SEE ALSO EQUIVALENT CIRCUITS)

V

I

ENERGY RELATIONSHIPS I2 2 SINUSOIDAL REGIME: P = 0, Q = −VI = −ω CV = − ωC 1 d 2 TRANSIENT REGIME: p (t ) = dt 2 Cv (t )

[

]

TIME DOMAIN DIAGRAMS FOR SINUSOIDAL REGIME v (t ) i (t )

t

p (t )

Summary of capacitor properties. (From Filanovsky, I.M., Capacitance and capacitors, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 168.)

© 2004 by CRC Press LLC

1587_Book.fm Page 103 Sunday, August 31, 2003 9:44 PM

1-103

Electrical and Computer Engineering

Frequency Response Magnitude Functions for Butterworth LP Prototype Filters V2 (w )

Order n

V1 (w ) 1

2

1+ w4 1

3

1 + w6 1

4

1 + w8

From Harrison, C., Passive filters, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 282.

Frequency Response Magnitude Functions for Chebyshev LP Prototype Filters

Order n 2

Chebyshev Polynomial Tn(w) 2w2 – 1

3

4w3 – 3w

4

8w4 – 8w2 + 1

V2 (w ) V1 (w )

1

(

)

4 e 2w 4 - 4 e 2w 2 + e 2 + 1 1

16e 2w 6 - 24e 2w 4 + 9e 2w 2 + 1 1

(

)

64e 2w 8 - 128e 2w 6 + 80e 2w 4 - 16e 2w 2 + e 2 + 1

From Harrison, C., Passive filters, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 283.

© 2004 by CRC Press LLC

No.

Type of Circuit

Circuit Gain or Variable of Interest

Schematic

Input Resistance or Input Currents or Voltages

Special Requirements or Remarks

R 1.

R

Noninverting amplifier

− +

−+

vi

− 2.

Buffer

+

−+

∞

∞

vo + −

vo +

−

vi

uO R =1+ 2 ui R1

Rin = • (ideally)

uO =1 ui

Rin = • (ideally)

R

Difference amplifier

v

−+

−

i

+

i v

4.

Adder

© 2004 by CRC Press LLC

u1 - u2 ∞ vo

−+

Ra

v

−+

v

−+

vn

−+

Rb

R

i

R

i Rn in

uO =

+ −

Rf − +

∞

R2 (u - u1 ) R1 2

R Ï R uO = - Ìu1 f + u2 f R2 ÔÓ R1

vo + −

+ L + un

Rf ¸ ý Rn Ôþ

i1 =

a

R1

i2 =

u2 Ra + Rb

i1 =

u1 R1

i2 =

u2 R2

M in =

(R

un Rn

Rb + Rb )

R1 Ra = R2 Rb

CRC Handbook of Engineering Tables

3.

R

Special case of circuit 1

1587_Book.fm Page 104 Sunday, August 31, 2003 9:44 PM

1-104

Op–amp Circuits

Variable gain circuit

R

R/(K−1)

−

vi

+

xR!

∞ vo

+ −

uO = (2 Kx – K ) ui

i=

0 £ x £ 1, K > 1

ui Kui (1 - x ) + R3 R

Potentionmeter R3 adjusts the gain over the range –K to +K

R!

RL

i 6.

Voltage-to-current converter

−+

i 7.

vi

R + −

Current-to-voltage converter

ii

+

v

−

+

∞

Ri

vo +

i=

ui R1

i=

ui R

The current through RL is independent of RL

−

R ∞

vo + −

R

R

ii 8.

+

−

R L is

Voltage-to-current converter with grounded load

−

R

vi

is =

ui Ê RL ˆ Á1 - ˜ RË R¯

n0 = ni(2RL/R) The current i is independent of RL Circuit has wide band-width for RL R

R − +

∞

RL

vo + −

n0 = –Rii

n=0

The voltage n0 is independent of RL and Ri

1-105

© 2004 by CRC Press LLC

1587_Book.fm Page 105 Sunday, August 31, 2003 9:44 PM

5.

+ −

Electrical and Computer Engineering

R/K

i

No.

Type of Circuit

Schematic

Current-to-voltage converter

v

−

R

R

vi

© 2004 by CRC Press LLC

vi

∞

−

R4 R3

n=0

R"

vo +

−

uO = 7.5 - ui

R2 R1

R = 3.9 kW

R2 +5

∞

+

10 uF

100 k +15 R

+ 1 uF −

uO = -2iR1

R2 +15

− + + −

+ −

0.1 uF

10 uF − + R1

Noninverting amplifier with single supply

R!

+

R

11.

vo

R

−

R

+ −

+

R"

∞

R

vo +

−

Ê R ˆ uO = 7.5 + ui Á1 + 2 ˜ Ë R1 ¯

R = 3.9 kW

CRC Handbook of Engineering Tables

Inverting amplifier with single supply

Special Requirements or Remarks

∞

+

10 uF +15

10.

R!

−

− + R1

−

∞

+

+

i

Input Resistance or Input Currents or Voltages

R

− 9.

Circuit Gain or Variable of Interest

1587_Book.fm Page 106 Sunday, August 31, 2003 9:44 PM

1-106

Op–amp Circuits (continued)

12.

Integrator + −

Vi

+

R

13.

De Boo integrator

−

R

i + −

vi

+

Vo + −

i=

ui R

Negative feedback is required at DC. A large value of RC can be used or a feedback path can be established through an external circuit.

Ú u (t )dt

i=

ui uO R 2R

One end of capacitor is physically grounded.

dui dt

Differentiators are usually avoided in the design of circuits because they accentuate noise.

Ú

R

∞

vo +

−

+

C

−

∞

1 t u (t )dt RC 0 i V (0) is the initial voltage across the capacitor, RC is very large. uO = -V (0) -

uO = 2V (0) +

R

v

2 RC

t

0

i

−

C

i

14.

Differentiator

vi

−

+ −

+

R

∞

vo +

uO = RC

−

dui dt

i =C

∞ + − 15.

Generalized impedance converter (GIC)

Z1 Zin

Z2

Z3 − + ∞

Z4

Z in =

Z 1Z 3 Z 5 Z 2Z 4

Zs

From Aronhime, P., Operational amplifiers, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, pp. 554–556.

1-107

© 2004 by CRC Press LLC

1587_Book.fm Page 107 Sunday, August 31, 2003 9:44 PM

i

Electrical and Computer Engineering

RC C R + V −

1587_Book.fm Page 108 Sunday, August 31, 2003 9:44 PM

1-108

CRC Handbook of Engineering Tables

Operating Characteristics of Common Battery Types

Energy density, Wh/kg Cycle lifea (typical) Fast-charge time,b h Self-dischargec Cell voltage,e (nominal) V Load current,f Exercise requirementg Battery costh (estimated, ref. only) Cost per cyclei ($) In commercial use since a

NiCd

NiMH

SLA

Li-ion

Lipolymer

Reusable Alkaline

50 1500 1 1/2 Moderated 1.25 Very high /30 days Low (50,000) 0.04 1950

75 500 2–3 High 1.25 Moderate /90 days Moderate (80.00) 0.16 1970

30 200–300 8–15 Low 2 Low /180 days Very low (25.00) 0.10 1970

100 300–500 3–6 Low 3.6 High N/A Very high (100.00) 0.25 1990

175 150 8–15 Very low 2.7 Low N/A High (90.00) 0.60 (1997)

80 (initial) 10 (to 65%) 3–4 Very low 1.5 Very low N/A Very low (5.00) 0.50 1990

Cycle life indicates the typical number of charge–discharge cycles before the capacity decreases from the nominal 100% to 80% (65% for the reusable alkaline). b Fast-charge time is the time required to fully charge an empty battery. c Self-discharge indicates the self-discharge rate when the battery is not in use. d Moderate refers to 1–2% capacity-loss per day. e Cell voltage multiplied by the number of cells provides the battery terminal voltage. f Load current is the maximum recommended current the battery can provide. High refers to a discharge rate of 1C; very high is a current higher than 1 C. C rate is a unit by which charge and discharge times are scaled. If discharged at 1, a 1000 mAh battery provides a current of 1000 mA; if discharged at 0.5C, the current is 500 mA. g Exercise requirement indicates the frequency the battery needs exercising to achieve maximum service life. h Battery cost is the estimated commercial price of a commonly available battery. i Cost-per-cycle indicates the operating cost derived by taking the average price of a commercial battery and dividing it by the cycle count. From Buchmann, I., Batteries, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, pp. 1056.

© 2004 by CRC Press LLC

1587_Book.fm Page 109 Friday, September 26, 2003 12:10 PM

1-109

Electrical and Computer Engineering

Example Fourier Transform Pairs x(t)

x(t)

1 t

X(W)

|X (W)| 1

d(t)

1

1

2pd(W)

Ω 2π

1

Ω

t 1

u(t)

pd(W) +

e–atu(t), a > 0

1 a + jW

t 1 t

t

te–atu(t), a > 0

1 t

e–at cos(W0t)u(t), a > 0

t

cos(W0t)

1 jW

Ω 1 a2

2

Ω

a + jW

(a + jW)

2

+ W20

1

1, t < t 2 0, t > t 2 1 −τ

τ

t

Ω0/π t

1 – |t|/t, |t| < t 0,|t| > t

sin(W0 t 2) pt

Ω

1 a

1

(a + jW)

π

p[d(W – W0) + d(W + W0)]

−Ω0

Ω0

π Ω

Ω0

−Ω0 τ

sin(W t 2) W2

Ω

2 1 sin (W t 2) t ( W 2 )2

τ Ω 1

1, W < W0 0, W > W 0

Ω

−Ω0

Ω0

Ω

From Hamann, J.C. and Pierre, J.W., Fourier waveform analysis, in The Electronics Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 1997, pp. 2119.

© 2004 by CRC Press LLC

1587_Book.fm Page 110 Sunday, August 31, 2003 9:44 PM

1-110

CRC Handbook of Engineering Tables

Advantages and Disadvantages of Satellites Advantages

Disadvantages

Wide-area coverage Easy access to remote sites Costs independent of distance Low error rates Adaptable to changing network patterns No right-of-way necessary; earth stations located at premises

Propagation delay Dependency on a remote facility Less control over transmission Attenuation due to atmospheric particles (e.g., rain) severe at high frequencies Continual time-of-use charges Reduced transmission during solar equinox

From Sadiku, M.N.O., Satellite communications, in The Handbook of Ad Hoc Wireless Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 8-2. Originally from D.J. Marihart, IEEE Transactions on Power Delivery, 16, 181–188, 2001.

Satellite Frequency Allocations Frequency Band

Range (GHz)

L S C X Ku K Ka

1–2 2–4 4–8 8–12 12–18 18–27 27–40

From Sadiku, M.N.O., Satellite communications, in The Handbook of Ad Hoc Wireless Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 8-5.

Typical Uplink and Downlink Satellite Frequencies (GHz) Uplink Frequencies

Downlink Frequencies

5.925–6.425 7.900–8.400 14.00–14.50 27.50–30.00

3.700–4.200 7.250–7.750 11.70–12.20 17.70–20.20

From Sadiku, M.N.O., Satellite communications, in The Handbook of Ad Hoc Wireless Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 8-5.

Frequency Allocations for FSS (Below ~30 GHz) Downlinks (in GHz) 3.4–4.2 and 4.5–4.8 7.25–7.75 10.7–11.7 11.7–12.2 (Region 2 only) 12.5–12.75 (Region 1 only) 17.7–21.2

Uplinks (in GHz) 5.725–7.075 7.9–8.4 12.75 13.25 and 14.0–14.5 27.5–31.0

From Sadiku, M.N.O., Satellite communications, in The Handbook of Ad Hoc Wireless Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 8-13.

© 2004 by CRC Press LLC

1587_Book.fm Page 111 Sunday, August 31, 2003 9:44 PM

1-111

Electrical and Computer Engineering

Characteristics of Satellite PCS Systems Parameter

Iridium

Globalstar

ICO

Company

Motorola

Loral/Qualcomm

ICO-Global

No. of satellites No. of orbit planes Altitude (km) Weight (lb) Bandwidth (MHz) Frequency up/down (GHz) Spot beams/satellite Carrier bit rate (k/sec) Multiple access Cost to build ($billion) Service start date

66 6 780 1100 5.15 30/20 48 50 TDMA/FDMA 4.7 1998

48 8 1414 704 11.35 5.1/6.9 16 2.4 CDMA/FDMA 2.5 1999

10 2 10,355 6050 30 14/12 163 36 TDMA/FDMA 4.6 2003

From Sadiku, M.N.O., Satellite communications, in The Handbook of Ad Hoc Wireless Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 8-20.

Table of Laplace Operations F(s) •

1.

Úe

- st

f (t )dt

f s(t)

f(t)

0

2. 3. 4. 5. 6.

AF(s) + BG(s) sF(s) – f(+0) snF(s) – sn–1 f(+0) – sn–2 f (1t) (+0)–L–f (n–l) (+0)

Af(t) + Bg(t) f ¢(t) f (n)(t)

1 F(s) s

Ú f (t)dt

1 F(s) s2

Ú Ú f (l)dl dt

t

0

t

0

t

0

Ú f (t - t) f (t)dt = f * f t

7.

F1(s)F2(s)

8. 9.

–F¢(s) (–1)nF (n)(s)

0

•

10.

Ú F(x)dx s

1

2

F(s – a) e–bs F(s)

13.

F(cs)

1 Êtˆ fÁ ˜ c Ëc¯

14.

F(cs – b)

1 (bt ) c Ê t ˆ e fÁ ˜ Ëc¯ c

15.

16.

Úe

a

0

a

17.

0

- st

f (t )dt

1 - e - as - st

f (t )dt

1 + e - as

F(s)

1 - e - as

© 2004 by CRC Press LLC

2

1 f (t ) t

11. 12.

Úe

1

tf (t) t n f (t)

eatf(t) f(t – b), where f(t) = 0; t < 0

f(t + a) = f(t) periodic signal

f(t + a) = –f(t) f1(t), the half-wave rectification of f(t) in No. 16.

1587_Book.fm Page 112 Friday, September 26, 2003 12:10 PM

1-112

CRC Handbook of Engineering Tables

Table of Laplace Operations (continued) F(s) F ( s ) coth

18.

p( s )

19.

q( s )

p( s )

20.

q( s )

f s(t)

as 2

f2(f), the full-wave rectification of f(t) in No. 16.

=

f( s )

( s - a)

p(an )

m

Â q ¢( a )e

, q( s ) = ( s - a1 )( s - a2 )L( s - am )

r

e at

r

ant

n

1

r -n f( ) (a) t n-1

Â (r - n)! (n - 1)! + L n=1

From Poularikas, A., Laplace transforms, in The Handbook of Formulas and Tables for Signal Processing, CRC Press, Boca Raton, FL, 1999, p. 2-6.

Table of Laplace Transforms F(s) 1.

sn

2.

s

3.

1

f (t) d(n)(t) nth derivative of the delta function dd(t )

dt d(t)

4.

1 s

1

5.

1 s2

t

6.

1 (n = 1,2,L) sn

7.

1

1

s

pt 2

8.

s –3/2

9.

s –[n+(1/2)] (n = 1,2,L)

10.

G(k ) sk

(k ≥ 0)

11.

1 s-a

12.

( s - a)

13.

14.

15.

t n-1 (n - 1)!

t p n- 1 2 2n t ( )

1 ◊ 3 ◊ 5L(2n - 1) p t k–1 e at

1

2

1 n = 1, 2,L) n ( ( s - a) G(k ) k ≥ 0) k ( ( s - a) 1

(s - a)(s - b)

© 2004 by CRC Press LLC

te at 1

(n - 1)!

t n-1e at

t k–1 e at

(a - b ) ( 1

e at - e bt

)

1587_Book.fm Page 113 Sunday, August 31, 2003 9:44 PM

1-113

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s) s

16.

(s - a)(s - b)

17.

(s - a)(s - b)(s - c )

18.

( s + a)

1

1

f (t)

) (a - b ) ( (b - c )e at + (c - a)e bt + (a - b)e ct (a - b)(b - c )(c - a) 1

ae at - be bt

e –at valid for complex a

(

)

19.

1 s ( s + a)

1 1 - e - at a

20.

1 s 2 ( s + a)

1 - at e + at - 1 a2

21.

1 s ( s + a)

1 a2

(

3

)

È1 at 2 1 - at ù - e ú Í -t + 2 a Îa û

(s + a)(s + b)

(b - a) (

1 s( s + a)( s + b)

1 È 1 be - at - ae - bt Í1 + ab ÍÎ (a - b)

24.

1 s 2 ( s + a)( s + b)

È 1 ù a2e - bt - b2e - at + abt - a - bú Í úû (ab) ÍÎ (a - b)

25.

1 s3 ( s + a)( s + b)

(ab) ÍÎ (ab)2 (a - b)

22.

23.

26.

1

1

1

e - at - e - bt

)

(

(

1

2

1 ÈÍ

a3 - b3

1

ù

)úú û

)

(a + b) t + 1 Ê b e -at - a e -bt ˆ ùú 1 + t2 ˜ ¯ú 2 ab b2 (a - b) ÁË a2 û

e - at +

1

1

(a - c )(b - c )

e - ct

(b - a)(c - a)

27.

1 s( s + a)( s + b)( s + c )

1 1 1 1 e - at e - bt e - ct abc a(b - a)(c - a) b(a - b)(c - b) c (a - c )(b - c )

28.

1 s 2 ( s + a)( s + b)( s + c )

29.

1 s3 ( s + a)( s + b)( s + c )

2 ab + ac + bc 1 2 Ï 1 ab + ac + bc ) - abc (a + b + c ) t+ t 3 ( 2 Ô abc 2 (abc ) Ô (abc ) Ì 1 1 1 Ô - at - bt - ct Ô - a3 c - a c - a e - b3 a - b c - b e - c 3 a - c b - c e ( ) ( ) ( ) ( ) ( ) ( ) Ó

30.

1 s 2 + a2

1 sin at a

31.

s s 2 + a2

© 2004 by CRC Press LLC

(a - b)(c - b)

e - bt +

(s + a)(s + b)(s + c )

Ï ab(ct - 1) - ac - bc 1 + 2 e - at Ô 2 a (b - a)(c - a) ÔÔ (abc ) Ì Ô 1 1 e - bt + 2 e - ct Ô + 2 b (a - b)(c - b) c (a - c )(b - c ) ÔÓ

[

cos at

]

1587_Book.fm Page 114 Sunday, August 31, 2003 9:44 PM

1-114

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s) 32.

1 s 2 - a2

33.

s s 2 - a2

34.

s s 2 + a2

1 sinh at a

35.

s 2 s 2 + a2

36.

(s

2

37.

(s

2

38.

(s

2

cosh at

1

(

(

1

1 + a2 1 + a2 s2 + a2

) ) )

1 (1 - cos at ) a2

)

1 (at - sin at ) a3

)

2

1 (sin at - at cos at ) 2a3

2

1 sin at 2a

2

1 (sin at + at cos at ) 2a

s 2 - a2

39.

(s

40.

(

41.

( s - a)

42.

( s - a) + b 2

43.

44.

f (t)

2

+ a2

)

t cos at

2

s

)(

s 2 + a2 s 2 + b2 1 2

s-a

[

(s + s) + b

2

]

s

[(s + a) b ] 2 2

)

cos at - cos bt b2 - a2

e at cos bt

2

2

a2 π b2

1 at e sin bt b

+ b2

1

)(

n

n

-e - at 4n-1b2n

n

r Ê 2n - r - 1ˆ r -1 (-2t ) dtd r cos(bt ) n - 1 ˜¯

Â ÁË r =1

Â

[

Â

[

Ê at 3 at 3 ˆ at 2 e - at - e ( ) Á cos - 3 sin 2 2 ˜¯ Ë

3a2 s3 + a3

46.

4a3 s + 4a 4

47.

s s 4 + 4a 4

1 (sin at ◊ sinh at ) 2a 2

48.

1 s 4 - a4

1 (sinh at - sin at ) 2a3

49.

s s 4 - a4

1 (cosh at - cos at ) 2a 2

© 2004 by CRC Press LLC

]

n r Ï e - at Ê 2n - r - 1ˆ r -1 d Ô n-1 2n -2t ) a cos(bt ) + b sin(bt ) ( Á ˜ dt r Ô 4 b r =1 Ë n - 1 ¯ Ô Ì n-1 r ¸Ô Ô Ê 2n - r - 2ˆ r -1 d -2t ) sin(bt ) ý ( Ô - 2b r Á ˜ r dt Ë n -1 ¯ Ôþ ÔÓ r =1

45.

4

[

sin at cosh at – cos at sinh at

]

]

1587_Book.fm Page 115 Sunday, August 31, 2003 9:44 PM

1-115

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

50.

51.

52.

(s

8a3 s 2 2

)

1 Ê s - 1ˆ Á ˜ sË s ¯

n

( s + a)

(

)

e t d n n -t t e n! dt n [Ln(t) is the Laguerre polynomial of degree n] Ln (t ) =

n-1 t ( )e - at where n is a positive integer (n - 1)!

1

n

[

1

1 1 - e - at - ate - at a2

53.

s ( s + a)

54.

s 2 ( s + a)

55.

s ( s + a)

56.

(1 + a2t 2) sin at – cos at

3

+ a2

f (t)

2

]

[

1

1 at - 2 + ate - at + 2e - at a3

2

]

1 È Ê1 2 2 ˆ - at ù Í1 - Á a t + at + 1˜¯ e ú a3 Î Ë 2 û

1

3

1

(s + a)(s + b)

1

(a - b )

2

s( s + a)( s + b)

58.

s 2 ( s + a)( s + b)

- bt

È 1 a - 2b ùú - bt 1 1 e - at - Í t+ e 2 2 2 2 ab Í b(a - b) a(a - b) b (a - b) úû Î

1

57.

{e + [(a - b)t - 1]e } - at

2

2

1

1

a (a - b )

2

2

1

59.

(s + a)(s + b)(s + c )

60.

(s + a)(s 2 + w 2 )

61.

s ( s + a) s 2 + w 2

62.

s 2 ( s + a) s 2 + w 2

1

1

(

1

e - at +

2(a - b) - b ù - bt 1 Ê 1 2 ˆ ÈÍ 1 úe t+ Át - - ˜ + 2 ab2 Ë a b ¯ Í b2 (a - b) b3 (a - b) úû Î

ÏÈ 1 2c - a - b ùú - ct ÔÍ i+ e ÔÍ (c - b)(c - a) (c - a)2 (c - b)2 ú ÔÎ û Ì Ô 1 1 e - at + e - bt Ô + 2 2 ÔÓ (b - a)(c - a) (a - b)(c - b) 1 1 Ê wˆ e - at + sin(wt - f); f = tan -1 Á ˜ Ë a¯ a2 + w 2 w a2 + w 2

1

(

2

2

1 1 Ê1 1 - at ˆ a Á sin wt + 2 cos wt + e ˜ ¯ a aw 2 a2 + w 2 Ë w w

) )

1 1 Ï 1 e - at Ô aw 2 t - a2w 2 + 2 2 2 a a + w ÔÔ Ì Ô 1 Ê aˆ cos(wt + f); f = tan -1 Á ˜ Ô + 3 2 2 Ë w¯ ÔÓ w a +w

(

[(s + a) + w ]

1 - at e [sin wt - wt cos wt ] 2w3

64.

1 s 2 - a2

1 sinh at a

65.

s 2 s 2 - a2

63.

2

(

1

2

)

© 2004 by CRC Press LLC

2

1 1 sinh at - 2 t a3 a

)

1587_Book.fm Page 116 Sunday, August 31, 2003 9:44 PM

1-116

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

(

1

f (t) 1 (cosh at - 1) - 21a2 t 2 a4

)

66.

s3 s 2 - a2

67.

1 s3 + a3

a Ê t 1 È - at 3 3 ˆù Íe - e 2 Á cos at - 3 sin at ˜ ú 2 2 3a2 Í Ë ¯ úû Î

68.

1 s 4 + 4a 4

1 (sin at cosh at - cos at sinh at ) 4a3

69.

1 s 4 - a4

1 (sinh at - sin at ) 2a3

70.

71.

72.

73.

74.

1

[

( s + a)

2

- w2

]

s+a

[

s ( s + b) + w 2 2

[

1 - at e sinh wt w 2 Ï 2 Ô a - 1 + (a - b) + w e - bt sin wt + f ; ( ) 2 2 2 2 ÔÔ b + w w b +w Ì Ô -1 Ê w ˆ -1 Ê w ˆ Ô f = tan Á ˜ + tan Á ˜ Ëb¯ Ë a -b¯ ÔÓ

]

s+a

s 2 ( s + b) + w 2 2

]

s+a

[

2 Ï (a - b) + w 2 -bt 2ab Ô 1 + e sin(wt + f) 2 Ô b2 + w 2 [1 + at ] - 2 w b2 + w 2 Ô b + w2 Ì Ô Ô f = tan -1 Ê w ˆ + 2 tan -1 Ê w ˆ Á ˜ Á ˜ ÔÓ Ë a -b¯ Ëb¯

(

+ w2

]

s( s + c ) ( s + b) + w

2

( s + c ) ( s + b)

2

s+a

[

2

s+a

(

)

)

2 Ï 2 a-c 1 (a - b) + w - bt - ct Ô + e e sin(wt + f) Ô c - b 2 + w2 w (c - b)2 + w 2 Ô( ) Ì Ô Ô f = tan -1 ÊÁ w ˆ˜ - tan -1 ÊÁ w ˆ˜ Ë a -b¯ Ë c -b¯ ÔÓ

]

Ï (c - a) e -ct a + Ô 2 2 2 Ôc b + w c (b - c ) + w 2 Ô Ô 2 ÔÔ (a - b) + w 2 e -bt sin wt + f 1 ( ) Ì 2 2 w b2 + w 2 (b - c ) + w Ô Ô Ô Ê wˆ Ê w ˆ -1 Ê w ˆ Ô f = tan -1 Á ˜ + tan -1 Á ˜ - tan Á ˜ Ë ¯ Ë ¯ Ë c -b¯ b a b Ô ÔÓ

(

)

[

]

a b - 3a È 3a - b a - b 2 2a - b ù - bt + 4 + Í 4 + 2 t + 3 t úe b3 b 2b b Î b û

75.

s 2 ( s + b)

76.

(s + c )(s + b)

È a-b c -a a - c ùú - bt e - ct + Í t2 + t+ e 2 2 c b Í ( ) (c - b) (c - b)3 úû (b - c ) Î

s2 s a s + ( )( + b)(s + c )

a2 b2 c2 e - at + e - bt + e - ct (b - a)(c - a) (a - b)(c - b) (a - c )(b - c )

77.

3

s+a

3

© 2004 by CRC Press LLC

a-c

3

1587_Book.fm Page 117 Sunday, August 31, 2003 9:44 PM

1-117

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

78.

79.

80.

81.

82.

83.

84.

85.

86.

f (t) È b2 b2 - 2ab ùú - bt e - at + Í t+ e 2 Í (a - b ) (b - a) (a - b) úû Î

s2

(s + a)(s + b)

a2

2

2

È a2 2 ù - at Í2 - 2at + t úe 2 û Î

s2

( s + a)

3

s2

(s + a)(s

+w

2

2

)

(

s2 2 2 ( s + a) s + w 2

(

s2

(

(s + a)(s + b) s 2 + w 2

(

s2

s +a

(s

2

2

)(

s2 2

+ w2

)

s3 + w 2

)

[

)

w

Ê wˆ sin(wt + f); f tan -1 Á ˜ Ë a¯ a +w

e - at -

2

2

ÏÈ 2 2aw 2 ÔÍ a ÔÍ a 2 + w 2 t - 2 a + w2 ÔÍ ÌÎ Ô Ô f = -2 tan -1 Ê w ˆ Á ˜ Ô Ë a¯ Ó

(

) (

)

ù w úe - at sin(wt + f); 2ú a2 + w 2 úû

(

2

+w

2

Ï a2 b2 e - at + e - bt Ô 2 2 b a a a b + w ) ( ) b2 + w 2 Ô( Ô Ì È w Ê wˆ Ê wˆù Ô sin(wt + f); f = - Ítan -1 Á ˜ + tan -1 Á ˜ ú Ô Ë ¯ Ë b ¯û 2 2 2 2 a Î a +w b +w ÔÓ

(w

(

)

(

)(

a 2

- a2

)

sin(at ) -

(

)

)

(a

w

2

- w2

)

sin(wt )

( s + a) ( s + b)

2

+w

2 Ï 2 2 2 2 Ô a2 1 b - w + 4b w - bt - at + e e sin(wt + f) Ô 2 2 2 2 w Ô (a - b ) + w a - b) + w ( Ì Ô Ô f = tan -1 Ê - sbw ˆ - tan -1 Ê w ˆ Á 2 ˜ Á ˜ ÔÓ Ë b - w2 ¯ Ë a -b¯

(

]

s2 2

]

[

)

]

Ï È ù 2 2 2 Ô Í a (b - a) + w + a (b - a) ú - at a2 - at te - 2 Í Ô úe 2 2 2 Ô (a - b ) + w 2 Í ú (b - a) + w 2 Ô ÍÎ úû Ô Ô 2 b2 - w 2 + 4b2w 2 ÔÔ e - bt sin(wt + f) Ì + 2 w (a - b ) + w 2 Ô Ô Ô Ô f = tan -1 ÊÁ -2bw ˆ˜ - 2 tan -1 ÊÁ w ˆ˜ Ô Ë b2 - w 2 ¯ Ë a -b¯ Ô Ô ÔÓ

(

[

)

[

]

87.

s2 + a s 2 ( s + b)

b2 + a - bt a a e + t- 2 b b2 b

88.

s2 + a s 3 ( s + b)

a 2 a 1 t - 2 t + 3 b2 + a - a + b2 e - bt 2b b b

© 2004 by CRC Press LLC

)

1 (sin wt + wt cos wt ) 2w

2

( s + a) ( s + b)

2

)

a + w2

-

s2

[

)

a2 2

[

(

)

]

]

1587_Book.fm Page 118 Sunday, August 31, 2003 9:44 PM

1-118

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s) 89.

s2 + a s( s + b)( s + c )

90.

s2 + a s ( s + b)( s + c )

91.

f (t)

(

)

(

)

b2 + a - bt c 2 + a - ct a + e e bc b(b - c ) c (b - c )

a(b + c ) b2 - a - bt c 2 + a - ct a e + 2 e + t- 2 2 2 bc b (c - b) c (b - c ) bc

2

s2 + a

b2 + a

e - bt +

c2 + a

d2 + a

92.

s2 + a s( s + b)( s + c )( s + d )

a b2 + a c 2a d2 + a + e - bt + e - ct e - dt bcd b(b - c )(d - b) c (b - c )(c - d ) d(b - d )(d - c )

93.

s2 + a s ( s + b)( s + c )( s + d )

Ï a a b2 + a t - 2 2 2 (bc + cd + db) + 2 e - bt Ô bcd b (b - c )(b - d ) Ô bcd Ì Ô c2 + a d2 + a - ct - dt Ô + c2 c - b c - d e + d2 d - b d - c e ( ) ( ) ( )( ) Ó

94.

95.

96.

97.

98.

(s

s2 + a 2

+ w2

)

(

(

2

+ w2

)

s2 + a

s s +w 2

2

)

t cos wt

2

)

(

1 1 a + w 2 sin wt - 2 a - w 2 t cos wt 2w3 2w

2

s2 - w2

(s

)

(b - d )(c - d )

e - dt

(c - b)(d - b)

2

(b - c )(d - c )

e - ct +

(s + b)(s + c )(s + d )

(

s ( s + a)

(s + b)(s + c )

)

a - w2 a a t sin wt - 4 cos wt 4 w w 2w3

2

È c 2 - ac c 2 - 2bc + ab ùú - ct e - bt + Í t+ e 2 b c Í (c - b) (b - c ) úû Î b2 - ab

2

s ( s + a)

(s + b)(s + c )(s + d )

2

2

Ï b2 - ab c 2 - ac d 2 - ad e - bt + e - ct + te - dt Ô 2 2 (b - d )(c - d ) b - c )(d - c ) ( Ô (c - b)(d - b) Ô Ì a bc - d 2 + d(db + dc - 2bc ) - dt Ô e Ô + 2 2 ÔÓ (b - d ) (c - d )

(

)

99.

s 2 + a1s + ao s 2 ( s + b)

b2 - a1b + ao - bt ao ab-a e + t+ 1 2 o b b2 b

100.

s 2 + a1s + ao s 3 ( s + b)

a1b - b2 - ao - bt ao 2 a1b - ao b2 - a1b + ao e + t + t+ 3 2 2b b b b3

101.

s 2 + a1s + ao s( s + b)( s + c )

ao b2 - a1b + ao - bt c 2 - a1c + ao - ct + e + e bc b(b - c ) c (c - b)

102.

s 2 + a1s + ao s 2 ( s + b)( s + c )

a bc - ao (b + c ) b2 - a1b + ao - bt c 2 - a1c + ao - ct ao + 2 t+ 1 e + 2 e bc b2c 2 b (c - b) c (b - c )

103.

s 2 + a1s + ao (s + b)(s + c )(s + d )

b2 - a1b + ao - bt c 2 - a1c + ao - ct d 2 - a1d + ao - dt e + e + e (c - b)(d - b) (b - c )(d - c ) (b - d )(c - d )

104.

s 2 + a1s + ao s( s + b)( s + c )( s + d )

ao b2 - a1b + ao - bt c 2 - a1c + ao - ct d 2 - a1d + ao - dt e e e bcd b(c - b)(d - b) c (b - c )(d - c ) d(b - d )(c - d )

© 2004 by CRC Press LLC

1587_Book.fm Page 119 Sunday, August 31, 2003 9:44 PM

1-119

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

105.

s 2 + a1s + ao s( s + b)

ao b2 - a1b + ao - bt b1 - ao - bt te + e b b2 b2

2

106.

s 2 + a1s + ao

107.

s 2 + a1s + ao

108.

109.

f (t)

s ( s + b) 2

ao a b - 2a b2 - a1b + ao - bt 2ao - a1b - bt t+ 1 3 o + te + e 2 b b b2 b3

2

(s + b)(s + c )

b2 - a1b + ao

(c - b)

2

e - bt +

c 2 - a1c + ao - ct c 2 - 2bc + a1b - ao - ct e te + 2 (b - c ) (b - c )

Ï b3 c3 d3 e - bt + e - ct + te - dt Ô 2 2 d b ( )(c - d ) c - b)(d - c ) ( Ô (b - c )(d - b) Ô Ì d 2 d 2 - 2d(b + c ) + 3bc - dt Ô e Ô + 2 2 ÔÓ (b - d ) (c - d )

s2

(s + b)(s + c )(s + d )

2

2

[

s3

(s + b)(s + c )(s + d )(s + f )

2

]

Ï b3 c3 e - bt + e - ct Ô 2 2 (c - b)(d - c )( f - c ) Ô (b - c )(d - b)( f - b) Ô Ô d2 f3 e - dt + te - ft Ô + 2 f b c f )(d - f ) ( ) ( (d - b)(c - d )( f - d ) Ô Ô Ì 3f 2 Ô +È Í Ô b f c )( - f )(d - f ) ÍÎ ( Ô Ô Ô f 3 (b - f )(c - f ) + (b - f )(d - f ) + (c - f )(d - f ) ù - dt úe Ô + 2 2 2 ú Ô (b - f ) (c - f ) (d - f ) û Ó

[

110.

111.

112.

s3

( s + b) ( s + c ) 2

-

2

s3

(s + d )(s + b) (s + c ) 2

2

s3

(s + b)(s + c )(s

© 2004 by CRC Press LLC

2

+w

2

)

b3

(c - b)

2

]

te - bt +

b2 (3c - b)

(c - b)

3

e - bt -

c3

(b - c )

2

te - ct +

c 2 (3b - c )

(b - c )

3

e - ct

Ï d3 b3 Ôe - dt + te - bt 3 Ô b-d 2 c -d 2 c - b) (b - d ) ( ) ( ) ( Ô Ô È ÔÔ b3 (c + 2d - 3b) ù - bt 3b2 c3 úe + + te - ct Ì +Í 2 3 2 2 Í ú (b - c ) (c - d ) Ô Î (c - b) (d - b) (c - b) (d - b) û Ô Ô È c 3 (b + 2d - 3c ) ù - ct 3c 2 Ô +Í úe + 2 Ô Í (b - c ) (d - c ) (b - c )3 (d - c )2 ú ÔÓ Î û Ï b3 c3 Ô e - bt + e - ct 2 2 Ô (b - c ) b + w c - b) c 2 + w 2 ( Ô Ô w2 Ô sin(wt + f) Ì Ô b2 + w 2 c 2 + w 2 Ô Ô Ô f = tan -1 ÊÁ c ˆ˜ - tan -1 ÊÁ w ˆ˜ ÔÓ Ë w¯ Ëb¯

(

)

(

)(

(

)

)

1587_Book.fm Page 120 Sunday, August 31, 2003 9:44 PM

1-120

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s) 113.

f (t)

s3

(s + b)(s + c )(s + d )(s

2

+w

2

)

Ï b3 c3 e - bt + e - ct Ô 2 2 (c - d )(d - c ) c 2 + w 2 Ô (b - c )(d - b) b + w Ô Ô d3 e - dt Ô + (d - b)(c - d ) d 2 + w 2 ÔÔ Ì Ô w2 cos(wt - f) Ô 2 2 2 b + w c + w2 d2 + w2 Ô Ô Ô Ô f = tan -1 ÊÁ w ˆ˜ + tan -1 ÊÁ w ˆ˜ + tan -1 ÊÁ w ˆ˜ Ëc¯ Ëb¯ Ëd¯ ÔÓ

(

)

(

(

(

114.

s3

( s + b) ( s 2

2

+w

2

)

)

)

)(

)(

(

)

)

Ï 3 b2 b2 + 3w 2 - bt w2 Ô- b sin(wt + f) te - bt + e - 2 2 2 2 2 2 ÔÔ b + w b + w2 b +w Ì Ô Ô f = tan -1 ÊÁ b ˆ˜ - tan -1 ÊÁ w ˆ˜ Ë w¯ Ëb¯ ÔÓ

(

)

(

)

115.

s2 s + 4w 4

116.

s3 s4 - w4

117.

s3 + a2 s 2 + a1s + ao s 2 ( s + b)( s + c )

Ï ao ao (b + c ) - a1bc -b3 + a2b2 - a1b + ao - bt + e Ô tb2c 2 b2 (c - b) ÔÔ bc Ì Ô -c 3 + a2c 2 - a1c + ao - ct e Ô + c 2 (b - c ) ÔÓ

118.

s3 + a2 s 2 + a1s + ao s( s + b)( s + c )( s + d )

Ï ao -b3 + a2b2 - a1b + ao - bt -c 3 + a2c 2 - a1c + ao - ct e e Ô b(c - b)(d - b) c (b - c )(d - c ) Ô bcd Ì Ô -d 3 + a2d 2 - a1d + ao - dt e Ô d(b - d )(c - d ) Ó

119.

s3 + a2 s 2 + a1s + ao s ( s + b)( s + c )( s + d )

Ïa È a a (bc + bd + cd ) ù -b3 + a2b2 - a1b + ao - bt Ô o t+Í 1 - o e ú+ bcd bcd b2c 2d 2 b2 (c - b)(d - b) ÔÔ ÍÎ úû Ì Ô -c 3 + a2c 2 - a1c + ao - ct -d 3 + a2d 2 - a1d + ao - dt e e + Ô + c 2 (b - c )(d - c ) d 2 (b - d )(c - d ) ÔÓ

120.

s3 + a2 s 2 + a1s + ao s + ( b)(s + c )(s + d )(s + f )

Ï -b3 + a2b2 - a1b + ao - bt -c 3 + a2c 2 - a1c + ao - ct e + e Ô (b - c )(d - c )( f - c ) Ô (c - b)(d - b)( f - b) Ì Ô -d 3 + a2d 2 - a1d + ao - dt - f 3 + a2 f 2 - a1 f + ao - ft Ô + b-d c -d f -d e + b- f c - f d - f e ( )( )( ) ( )( )( ) Ó

121.

s3 + a2 s 2 + a1s + ao s( s + b)( s + c )( s + d )( s + f )

Ï ao -b3 + a2b2 - a1b + ao - bt -c 3 + a2c 2 - a1c + ao - ct e e Ô bcdf b c (b - c )(d - c )( f - c ) (c - b)(d - b)( f - b) Ô Ì Ô d 3 + a2d 2 - a1d + ao - dt - f 3 + a2 f 2 - a1 f + ao - ft Ô - d b-d c -d f -d e - f b- f c - f d - f e ( )( )( ) ( )( )( ) Ó

4

2

© 2004 by CRC Press LLC

cos(wt) cosh(wt)

[

]

1 cosh(wt ) + cos(wt ) 2

1587_Book.fm Page 121 Sunday, August 31, 2003 9:44 PM

1-121

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s) 122.

123.

f (t)

s3 + a2 s 2 + a1s + ao (s + b)(s + c )(s + d )(s + f )(s + g )

Ï 3 2 3 2 Ô -b + a2b - a1b + ao e - bt + -c + a2c - a1c + ao e - ct 2 Ô (c - b)(d - b)2 (b - c )(d - c ) Ô Ô -d 3 + a2d 2 - a1d + ao - dt Ô te Ì + (b - d )(c - d ) Ô Ô 2 Ô a (2d - b - c ) + a1 (bc - d ) + a2d(db + dc - 2bc bc ) + d 2 d 2 - 2db - 2dc + 3bc - dt Ô + o e 2 2 Ô (b - d ) (c - d ) Ó

s3 + a2 s 2 + a1s + ao

(s + b)(s + c )(s + d )

Ï -b3 + a2b2 - a1b + ao -c 3 + a2c 2 - a1c + ao e - bt + e - ct Ô (b - c )(d - c )( f - c )( g - c ) Ô (c - b)(d - b)( f - b)( g - b) Ô Ô -d 3 + a2d 2 - a1d + ao - f 3 + a2 f 2 - a1 f + ao e - ft e - dt + Ì + b b d c d f d g d ( )( )( )( ) ( f )(c - f )(d - f )( g - f ) Ô Ô - g 3 + a2 g 2 - a1 g + ao Ô - gt Ô + b-c c - g d - g f - g e ( ) ( ) ( ) ( ) Ó

2

(

124.

Ï 3 2 3 2 Ô ao - -b + a2b - a1b + ao e - bt - -c + a2c - a1c + ao e - ct 2 2 Ô bcd 2 c (b - c )(d - c ) b(c - b)(d - b) Ô Ô -d 3 + a2d 2 - a1d + ao - dt 3d 2 - 2a2d + a1 - dt Ô te e z Ì d(b - d )(c - d ) d(b - d )(c - d ) Ô Ô Ô d 3 + a2d 2 - a1d + ao (b - d )(c - d ) - d(b - d ) - d(c - d ) - dt Ô e 2 2 Ô d 2 (b - d ) (c - d ) Ó

s3 + a2 s 2 + a1s + ao

s( s + b)( s + c )( s + d )

2

)[

(

125.

s3 + a2 s 2 + a1s + ao

(s + b)(s + c )(s + d )(s + f )

2

127. 128.

s

( s - a)

32

s -a - s -b 1 s +a

1 pt

)[

e at (1 + 2at )

1 2 pt 3 1 pt

129.

s s - a2

1

130.

s s + a2

1

© 2004 by CRC Press LLC

]

Ï -b3 + a2b2 - a1b + ao - bt -c 3 + a2c 2 - a1c + ao - ct e e + Ô 2 2 (b - c )(d - c )( f - c ) Ô (c - b)(d - b)( f - b) Ô Ô -d 3 + a2d 2 - a1d + ao - dt - f 3 + a2 f 2 - a1 f + ao - ft e + te Ô + 2 (b - f )(c - f )(d - f ) Ô (b - d )(c - d )( f - d ) Ô Ì 3 f 2 - 2a2 f + a1 Ô - ft Ô + b- f c- f d- f e ( )( )( ) Ô Ô - f 3 + a2 f 2 - a1 f + ao (b - f )(c - f ) + (b - f )(d - f ) + (c - f )(d - f ) - ft Ô e Ô 2 2 2 ÔÓ (b - f ) (c - f ) (d - f )

(

126.

)

pt

pt

(e

- e at

bt

)

( )

2

- ae a t erfc a t 2

( )

+ ae a t erf a t

-

2a p

2

e -a t

Ú

a t

0

2

e l dl

]

1587_Book.fm Page 122 Sunday, August 31, 2003 9:44 PM

1-122

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

(

1

131.

s s - a2

132.

s s + a2

133.

(

(

2

)

)(

s

1

(

s +a

)

(1 - s) s

a t

0

2

e l dp

( )

( )

2

e a t erfc a t 1

s +b

s s - a2

Ú

( )

)

e - at erf

b-a

b2 - a2

(

e -a t

2 2 e a t Èb - a erf a t ù - be b t erfc b t úû ÎÍ

1

( s + a)

2

a p

s - a2 b + s

136.

137.

( )

1 a 2t e erf a t a

)

b2 - a2

134.

135.

1

f (t)

)(

s +b

(

b-a t

)

( )

( )

2 Èb 2 ù e a t Í erf a t - 1ú + e b t erfc b t Îa û

)

( )

n

n! Ï H 2n t Ô 2 n Ô ( )! nt Ì n 2 ù ÔÈ x2 d e-x ú ÔÍ H n (t ) = Hermite polynomial = e dx n ÔÓÎ û

n+ (1 2)

( )

138.

(1 - s) s

n

-

n+ (3 2)

s + 2a

139.

[

s +a s +b G(k )

(k ≥ 0)

141.

( s + a) ( s + b)

142.

( s + a) ( s + b)

k

32

s + 2a - s

144.

(a - b )

146.

[

]

k

s +a + s +b

s s+a

k - (1 2)

Ê a-b ˆ - 1 2 a +b t e ( )( ) I k -(1 2) Á t˜ Ë 2 ¯

1 - at e I1 (at ) t

s + 2a + s

s+a + s

Ê t ˆ pÁ ˜ Ë a -b¯

Ê a -b ˆù - 1 2 a +b t È Ê a = b ˆ te ( )( ) Í I o Á t ˜ + I1 Á t˜ Ë ¯ Ë 2 ¯ úû 2 Î

1

143.

145.

k

12

( (

( t)

- 1 2 a +b t Ê a - b ˆ e ( )( ) I o Á t˜ Ë 2 ¯

1

140.

H 2n+1

Ïae - at I (at ) + I (at ) 1 o Ô Ì Ô I n (t ) = j - n J n ( jt ) where J n is Bessel's function of the first kind Ó

-1

s

n!

p (2n + 1)!

)

1 s 2 + a2

© 2004 by CRC Press LLC

-2v

)

2k

(k > 0)

k - (1 2)(a +b)t Ê a - b ˆ e Ik Á t˜ Ë 2 ¯ t 1 - (1 2)(at ) Ê 1 ˆ e I v Á at ˜ Ë2 ¯ av Jo (at)

]

1587_Book.fm Page 123 Sunday, August 31, 2003 9:44 PM

1-123

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

147.

Ê s 2 + a 2 - sˆ Ë ¯ s +a 2

1

149.

Ê s 2 + a3 - sˆ Ë ¯

150.

+a

)

k

s -a 151.

152. 153.

k

Ê s - s 2 - a2 ˆ Ë ¯ 2

(s

1 -a

2

2

)

k

(v > -1)

(k > 0)

(s

2

v

2

148.

2

f (t)

p Ê t ˆ Á ˜ G(k ) Ë 2a ¯

(k > 0)

155.

156.

157.

(v > -1)

2

(k > 0)

158.

159.

a v Iv (at)

erf

s s +1 1

k - (1 2)

( t );erf ( y)

D

I k -(1 2) (at ) the error function =

2 p

Úe y

-u 2

du

o

Ja(at); Bessel function of 1st kind, zero order

s 2 + a2

J1 (at )

s 2 + a2 + s

at

N

1 s È s 2 + a2 + s ù úû ÎÍ

N aN

N

1 s + a È s 2 + a2 + s ù ÍÎ úû 1 s - a2 2

Ú

t

o

J N (au) u

N

1 J (at ) ; N = 1,2,3,L, JN is the Bessel function of lst kind, Nth order aN N

Io(at); Io is the modified Bessel function of 1st kind, zero order

160.

e - ks s

Ï0 Sk (t ) = Ì Ó1

161.

e - ks s2

Ï0 Ì Ót - k

162.

e - ks sm

163.

1 - e - ks s

( m > 0)

© 2004 by CRC Press LLC

du ; N = 1,2,3,L, JN is the Bessel function of 1st kind, Nth order

1 J (at ) ; J1 is the Bessel function of lst kind, lst order a 1

1 s + a Ê s 2 + a 2 + sˆ Ë ¯ 2

2

; J1 is the Bessel function of 1st kind, 1st order

N J N (at ) ; N = 1,2,3,L, JN is the Bessel function of 1st kind, Nth order t aN

1 È s 2 + a2 + s ù ÍÎ úû

2

J k -(1 2) (at )

kak J (at ) t k

p Ê t ˆ Á ˜ G(k ) Ë 2a ¯

1

2

k - (1 2)

v

1 154.

a vJv (at)

when 0 < t < k when t > k

Ï0 Ô t - k m -1 ) Ì( Ô G (m ) Ó Ï1 Ì Ó0

when 0 < t < k when t > k

when 0 < t < k when t > k

when 0 < t < k when t > k

1587_Book.fm Page 124 Sunday, August 31, 2003 9:44 PM

1-124

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

164.

1

(

s 1- e

165.

166.

167.

- ks

)

1

(

s e + ks - a

=

1 1 + coth ks 2 2s

(

s 1 + e - ks

ÔÏn S(k , t ) = Ì ÔÓ

when

(n - 1)k < t < n k(n = 1,2,L)

Ï0 when 0 < t < k Ô Ô Sk (t ) = Ì1 + a + a2 + L + an-1 Ô ÔÓwhen nk < t < (n + k )k(n = 1, 2,L)

)

ÏM (2k , t ) = ( -1)n-1 Ô Ô when 2k(n - 1) < t < 2nk Ì Ô Ô (n = 1,2,L) Ó

1 tanh ks s

1

f (t)

n Ï1 1 – (1 - 1) ÔÔ M (k , t ) + 1 = 2 2 Ì2 Ô when (n - 1)k < t < nk ÔÓ

)

[H(2k,t ) = k + (r - k)(-1)

168.

1 tanh ks s2

ÏH 2k , t ) Ô ( Ì ÔÓ

169.

1 s sinh ks

Ï2S( sk, t + k ) - 2 = 2(n - 1) Ô Ì when (2n - 3)k < t < (2n - 1)k(t > 0) ÔÓ

170.

1 s cosh ks

ÏM (2k , t + 3k ) + 1 = 1 + ( -1)n Ô Ì Ô when (2n - 3)k < t < (2n - 1)k(t > 0) Ó

171.

1 coth ks s

Ï2S(2k , t ) - 1 = 2n - 1 Ô Ì when 2k(n + 1) < t < 2kn ÔÓ

172.

k ps coth 2k s2 + k2 1

173.

(

174.

1 -k s e s

175.

176.

)(

s 2 + 1 1 - e -ps

1 s 1 s

]

)

when (2n - 2)p < t < (2n - 1)p when (2n - 1)p < t < 2np

ÏÔsint Ì ÔÓ0

( )

J o 2 kt 1

ek s

1

pt pt

177.

1 -k s e s3 2

1

178.

1 ks e s3 2

1

pk pk

where t = 2kn + r ;

0 £ r £ 2k ; n = 0,1, 2,L

|sin kt|

e -k s

© 2004 by CRC Press LLC

n

cos 2 kt

cosh 2 kt

sin 2 kt sinh 2 kt

1587_Book.fm Page 125 Sunday, August 31, 2003 9:44 PM

1-125

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

179.

1 -k s e sm

180.

1 ks e sm

181.

e -k

182.

1 -k e s

183.

184.

185.

(k ≥ 0)

s -3 2e - k

s

(k ≥ 0)

ae - k

187.

188.

189.

190.

s

(

e -k

s

(

s a+ s e

(s

e

2

-a

2

192.

Ê 2 k ˆ e ake a t erfc Á a t + ˜ Ë 2 t¯

(k ≥ 0)

when t > k

) )

ÏÔ0 ÌI Ê a t 2 - k 2 ˆ o ¯ ÓÔ Ë

when 0 < t < k when t > k

)

(k ≥ 0)

J o Ê a t 2 + 2kt ˆ Ë ¯

s 2 +a 2

s 2 + a 2 - e - ks

2

when 0 < t < k

when 0 < t < k when t > k

a ve - k

(s

ˆ Ê k ˆ ˜ + erfc Á ˜ ¯ Ë2 t ¯

ÔÏ0 Ì J Ê a t 2 - k2 ˆ o ¯ ÓÔ Ë

s 2 + a2

e -k

Ê k ˆ Ê k2 ˆ 1 expÁ - ˜ - k erfc Á ˜ 4 p t Ë ¯ Ë2 t ¯

Ï0 Ô Ìe - (1 2)at I ÊÁ 1 a t 2 - k 2 ˆ˜ o ÔÓ Ë2 ¯

Ê ˆ - k Á s 2 +a 2 -s ˜ Ë ¯

(

( )

I m -1 2 kt

Ê 2 k -e ake a t erfc Á a t + Ë 2 t

s 2 -a 2

e -k

(s

+a

2

e - ks - e - k

194.

2

s 2 +a 2

2

2

Ê k2 ˆ expÁ - ˜ Ë 4t ¯ pt

s ( s + a) e -k

( m -1)

1

- k s (s +a )

191.

193.

)

J m -1 2 kt

Ê k ˆ erfc Á ˜ Ë2 t ¯

(k ≥ 0)

)

s a+ s

( )

2

Ê k2 ˆ expÁ - ˜ Ë 4t ¯ 2 pt 3

(k ≥ 0)

s

( m -1)

k

s

186.

Êtˆ Á ˜ Ë k¯

( m > 0)

e -k

s

Êtˆ Á ˜ Ë k¯

( m > 0)

(k > 0)

s

1

f (t)

)

s 2 -a 2

+ a2 Ê s 2 + a2 + s ˆ Ë ¯

1 log s s

© 2004 by CRC Press LLC

v

(v > -1)

Ï0 Ô ak Ì J1 Ê a t 2 - k 2 ˆ ¯ ÔÓ t 2 - k 2 Ë

when 0 < t < k

Ï0 Ô ak Ì I1 Ê a t 2 - k 2 ˆ ¯ ÔÓ t 2 - k 2 Ë

when 0 < t < k

when t > k

when t > k

Ï0 Ô (1 2)v ÌÊ t - k ˆ Jv Ê a t 2 - k2 ˆ Á ˜ ÔË t + k ¯ Ë ¯ Ó G¢(l) – logt [G¢(1) = –0.5772]

when 0 < t < k when t > k

1587_Book.fm Page 126 Sunday, August 31, 2003 9:44 PM

1-126

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

f (t) Ï ¸ Ô G ¢(k ) log t Ô t k -1 Ì ý 2 Ô G(k ) G(k ) Ô Ó þ

(k > 0)

195.

1 log s sk

196.

log s s-a

197.

log s s2 + 1

cos t Si(t) – sin t Ci(t)

198.

s log s s +1

–sin t Si(t) – cost t Ci(t)

199.

1 log(1 + ks ) s

200.

log

201.

1 log 1 + k 2 s 2 s

202.

1 log s 2 + a2 s

203.

1 log s 2 + a2 s2

204.

log

s 2 + a2 s2

2 (1 - cos at ) t

205.

log

s 2 - a2 s2

2 (1 - cosh at ) t

206.

arctan

207.

1 k arctan s s

208.

e k s erfc (ks )

209.

1 k 2s 2 e erfc (ks ) s

210.

e kserfc

211.

212.

213.

214.

( a > 0)

1 bt at e -e t

1

)

(

) ( a > 0)

s

) ( a > 0)

k s

s

[

]

2 at log a + sin at - at Ci (at ) a

Si(kt)

(k > 0) (k > 0) (k > 0)

( ks ) ( ks )

Ê k ˆ erf Á ˜ Ë s¯ 1

2 log a – 2Ci(at)

1 sin kt t

( ks )

e kserfc

)

Êtˆ -2Ci Á ˜ Ë k¯

(

erfc

Ê tˆ -Ei Á - ˜ Ë k¯

(

s-a s -b

2 2

s

e at[log a – Ei(–at)]

(k > 0)

(

1

[ ]

Ê k ˆ 2 e k serfc Á ˜ Ë s¯

© 2004 by CRC Press LLC

Ê t2 ˆ exp Á - 2 ˜ Ë 4k ¯ k p 1

Ê t ˆ erf Á ˜ Ë 2k ¯ k p t (t + k ) when 0 < t < k when t > k

ÔÏ0 -1 2 Ì ÔÓ( pt )

(k > 0)

1 p(t + k )

( )

1 sin 2k t pt 1 pt

e -2k

t

1587_Book.fm Page 127 Sunday, August 31, 2003 9:44 PM

1-127

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s) 215.

–e asEi(–as)

216.

1 + se as Ei( -as ) a

217.

Èp ù Í 2 - Si( s )ú cos s + Ci( s ) sin s Î û

218.

f (t)

( a > 0)

1 ; t +a 1

(t + a)

2

1 t 2 +1 Ï0 Ô Ì 2 2 ÔÓ t - k

Ko(ks)

( a > 0)

;

(

)

219.

Ko k s

( )

Ê k2 ˆ 1 expÁ - ˜ 2t Ë 4t ¯

220.

1 ks e K 1 (ks ) s

1 t (t + 2k ) k

221.

222.

1 s 1 s

( )

K1 k s

[K (t ) is Bessel function of the

when 0 < t < k -1 2

n

second kind of imaginary argument]

when t > k

Ê k2 ˆ 1 expÁ - ˜ k Ë 4t ¯

Ê kˆ ek s K o Á ˜ Ë s¯

(

2

K o 2 2kt

pt

[

]

223.

pe–ksIo(ks)

ÏÔ t 2k - t ( ) Ì ÔÓ0

224.

e–ksI1(ks)

k -t Ï Ô Ì pk t (2k - t ) Ô0 Ó 2

-1 2

) when 0 < t < 2k when t > 2k when 0 < t < 2k when t > 2k

∑ u [t − (2k+1)a]

k=0 225.

1 s sinh(as )

8 6 4 2 0

2

f(t)

0

∑

a

3a

5a

7a

t

7

t

(−1)k u (t − 2k − 1)

k=0

226.

1 s cosh s

f(t) 2 0

© 2004 by CRC Press LLC

0

1

2

3

4

5

6

1587_Book.fm Page 128 Sunday, August 31, 2003 9:44 PM

1-128

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

f (t)

u(t) + 2

∑ (−1) u (t − ak) k

k=1

227.

1 Ê as ˆ tanhÁ ˜ Ë2¯ s

square wave f(t)

1 0

a

2a

3a

4a

5a

t

−1

∑ u(t − ak) k=0

228.

stepped function

1Ê as ˆ Á1 + coth ˜ 2s Ë 2¯

4 f(t) 3 2 1 0 0

mt − ma

a

2a

3a

4a

t

u(t − ka) ∑ k =1

229.

saw − tooth function

m ma Ê as ˆ Á coth - 1˜ ¯ 2 s 2 2s Ë

f(t)

0

SLOPE = m

0

1 a

a

t+2

2a

3a

t

(−1) (t − ka) . u(t − ka) ∑ k k

=1

230.

triangular wave

1 Ê as ˆ tanhÁ ˜ Ë2¯ s2

f(t) 1 0

© 2004 by CRC Press LLC

0

a

2a

3a

4a

5a

6a

t

1587_Book.fm Page 129 Sunday, August 31, 2003 9:44 PM

1-129

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

f (t)

∑ (−1) u (t − k) k

k=0 231.

1

(

s 1 + e -s

f(t)

)

1 0

0

1

∑ k

2

3

sin a t − k

=0

232.

(s

+a

2

π a

5

6

.u t−k

7

t

π a

half − wave rectification of sine wave

a

2

4

)(1 - e ) p - s a

f(t) 1 0

π a

0

2π a

[sin (at)] . u (t) + 2

3π a

∑

4π a

t

sin a t − k

k=1

233.

È Í a Í s 2 + a2 Î

(

)

ù ú cothÊÁ ps ˆ˜ Ë 2a ¯ ú û

π a

.u t−kπ a

full − wave rectification of sine wave f(t) 1 0 0

π a

2π a

3π a

4π a

t

u (t − a) f(t)

234.

1 - as e s

∞

1 0

0

t

a

u (t − a) − u (t − b) 235.

(

1 - as - bs e -e s

)

f(t)

1 0

© 2004 by CRC Press LLC

0

a

b

t

1587_Book.fm Page 130 Sunday, August 31, 2003 9:44 PM

1-130

CRC Handbook of Engineering Tables

Table of Laplace Transforms (continued) F(s)

f (t)

m . (t − a) . u (t − a) 236.

m - as e s2

f(t) 1 SLOPE = m 0

0

t

a

mt . u(t − a) or

237.

È ma m ù - as Í s + s 2 úe Î û

[ma + m (t − a)] . u(t − a) f(t) 1

SLOPE = m

0

0

t

a

(t − a)2 . u(t − a) 238.

f(t)

2 - as e s3 0

0

t

a

t2 . u(t − a) 239.

È 2 2a a2 ù - as Í 3 + 2 + úe s û s Îs

f(t)

−t2

a2 0

0

t

a

mt . u(t) − m(t − a) . u(t − a) f(t) 240.

m m - as - e s2 s2

ma SLOPE = m 0

© 2004 by CRC Press LLC

0

a

t

1587_Book.fm Page 131 Friday, September 26, 2003 12:10 PM

1-131

Electrical and Computer Engineering

Table of Laplace Transforms (continued) F(s)

f (t)

mt − 2m(t − a) . u(t − a) + m(t − 2a) . u(t − 2a) 241.

m 2m - as m -2as e + 2e s2 s2 s

f(t) ma SLOPE =m 0

SLOPE = −m

0

a

t

2a

mt − [ma + m(t − a)] . u(t − a) 242.

m Ê ma m ˆ - as -Á + 2 ˜e s2 Ë s s ¯

f(t) ma 0

SLOPE = m 0

243.

(1 - e ) -s

s

2

3

≤J

− J −

≤J

≤J

t

a

0.5t2 for 0 ≤ t < 1 0.75 − (t − 1.5)2 for 1 ≤ t < 2

244.

(

È 1 - e -s Í Í s Î

) ùú

0.5(t − 3)2 for 2 ≤ t < 3

3

0 for 3 < t

ú û

1 f(t)

0

245.

(

0

1

t

3

ebt − . ut − ebt − . ut − a + Ke−b t−a . ut − a

)

b + e ba - 1 s( s - b)

b ù È s + ba Í 1 - 1 úe - as e Í + s b s s b ( ) úú Í ÍÎ úû

2

K eba −

From Poularikas, A., Laplace transforms, in The Handbook of Formulas and Tables for Signal Processing, CRC Press, Boca Raton, FL, 1999, pp. 2-7 to 2-23.

© 2004 by CRC Press LLC

1587_Book.fm Page 132 Friday, September 26, 2003 12:10 PM

1-132

CRC Handbook of Engineering Tables

Properties of Fourier Transform Operation

f(t)

F(w) •

1.

Transform-direct

Ú f (t )e

f(t)

- jwt

dt

-•

2.

Inverse transform

1 2p

•

Ú F(w)e

jwt

dw

F(w)

-•

3. 4.

Linearity Symmetry

af1(t) + bf2(t) F(t)

aF1(w) + bF2(w) 2pf(–w)

5.

Time shifting

f(t ± to)

e ± jwt o F (w )

6.

Scaling

f(at)

1 Ê wˆ FÁ ˜ a Ë a¯

7.

Frequency shifting

e ± jwot f (t )

8.

Modulation

Ï f (t ) cos w ot Ô Ì ÔÓ f (t ) sin w ot

9.

Time differentiation

dn f (t ) dt n

Time convolution

f (t ) * h(t ) =

10.

11.

12.

Frequency convolution

Autocorrelation

Parseval’s formula

E=

Ú

Moments formula

mn =

Ú

Frequency differentiation

16. 17.

Time reversal Conjugate function

18.

Integral (F(0) = 0)

Ú f (t )dt

-• t

Integral (F(0) π 0)

Ú f (t)h(t - t)dt

Ú f (t )dt

-•

F(w) H(w)

-•

1 1 F (w ) * H (w ) = 2p 2p

Ï( - jt ) f (t ) Ô Ì n Ô( - jt ) f (t ) Ó

t

19.

•

•

Ú F(t)H(w - t)dt

-•

•

Ú f (t)f * (t - t )dt

F(w) F*(w) = |F(w)|2

-•

t n f (t )dt =

f(–t) f *(t)

]

(jw)n F(w)

2

-•

15.

[

f (t ) dt

•

]

1 F (w - w o ) - F (w + w o ) 2j

f (t ) f * (t ) =

-•

14.

[

1 F (w + w o ) + F (w - w o ) 2

f(t) h(t)

•

13.

F(w m wo )

E=

() n (- j )

n F( ) 0

where

1 2p

•

Ú F(w) dw 2

-•

d n F (w ) n F ( ) (0) = dw n

, n = 0,1, 2L w =0

dF (w ) dw

d F (w ) n

dw n F(–w) F*(–w)

1 F (w ) jw 1 F (w ) + pF (0)d(w ) jw

From Poularikas, A., Fourier transformation, in The Handbook of Formulas and Tables for Signal Processing, CRC Press, Boca Raton, FL, 1999, pp. 3-3.

© 2004 by CRC Press LLC

Ú

+•

-•

F (y) ù F ( y ) e + lxydy ú û

1/a

È ÍF( y ) = Î

A

Ú

+•

-•

ù f ( x ) e -txydx ú û

A√x a

2a

(

A exp -a2 x 2

[Gaussian]

)

(

A p exp - y 2 4a2 a

[Gaussian] a

1/a

2A a

A

(

A exp -a x

)

2 A a2 a a2 + y 2

[Lorentzian] a

a

1/a A

A/a

A exp( -ax ) 0

)

[ x > 0] [ x < 0]

A/2a

Ï a - iy ¸ AÌ 2 2ý Óa + y þ

1-133

© 2004 by CRC Press LLC

1587_Section_1c.fm Page 133 Saturday, September 27, 2003 12:45 PM

f (x ) È Í f ( x ) = (1 2p) Î

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w)

F (y ) a 1/a

A

A/a

A exp( -ax )

(

- A exp -a x 2π/yo

[ x > 0]

) [ x < 0]

-2iA

y a2 + y 2

2π/yo A

a A

2A/a

yo

(

A exp iy0 x - a x

2A a2 a a 2 + ( y - y )2 0

)

a

~ A/a

A

yo

(

A cos y0 x exp -a x

)

Ï ¸ AÔ a2 a2 Ô + Ì 2 ý 2 2 2 a Ô a + (y - y ) a + ( y + y0 ) þÔ 0 Ó =

© 2004 by CRC Press LLC

(

)

2 2 2 2 Ï ¸ A Ô 2a a + y 0 + y Ô Ì ý a Ô a 2 + y 2 - y 2 2 + 4a 2 y 2 Ô 0 Ó þ

(

)

CRC Handbook of Engineering Tables

2π/yo

1587_Section_1c.fm Page 134 Wednesday, October 8, 2003 4:09 PM

f (x )

1-134

Table of Fourier Transforms (x = t, y = w) (continued)

F (y )

2π/yo ~ A/a

Ï ¸ iA Ô a2 a2 Ô Ì ý a Ô a 2 + ( y + y )2 a 2 + ( y - y )2 Ô 0 0 Ó þ

A

(

A sin y0 x exp -a x

)

=

A

a

¸ Ï -4a2 yy0 iA Ô Ô ý Ì 2 a Ô a 2 + y 2 - y 2 + 4a 2 y 2 Ô 0 þ Ó

(

)

2π/yo

2π/yo

yo

a

a

A

A/2a

A/a

Electrical and Computer Engineering

f (x )

yo yo A exp(iy0 x - ax ) 0

Ï a + i ( y - y) ¸ ÏÔ ¸Ô 1 Ô Ô 0 =AÌ AÌ ý 2ý 2 ÔÓ a + i ( y - y0 ) Ôþ ÔÓ a + ( y0 - y ) Ôþ

[ x > 0] [ x < 0] 2π/yo

A

a a a

A/4a

A/2a

yo yo

A cos y0 x exp( -ax ) 0

(

) ( )

Ï a a2 + y 2 + y 2 - iy a2 + y 2 - y 2 0 0 Ô = AÌ 2 2 2 2 2 2 a + y 0 - y + 4a y Ô Ó

(

) ¸Ôý Ô þ

1-135

© 2004 by CRC Press LLC

[ x > 0] [ x < 0]

ÈÏ ¸ Ï ¸ù y0 - y y0 + y A ÍÔ a a Ô Ô Ôú +iÌ + Ì ý ýú 2 2 2 2 2 2 2 2 ÍÔ a 2 + ( y + y ) + + + + a y y a y y a y y Ô Ô Ôþúû ( ) ( ) ( ) 0 0 0 0 ÍÎÓ þ Ó

1587_Section_1c.fm Page 135 Wednesday, October 8, 2003 4:09 PM

Table of Fourier Transforms (x = t, y = w) (continued)

1-136

f (x )

F (y ) a

2π/yo

~ A/2a

A

yo

~ A/4a

a

yo a

A sin y0 x exp( -ax ) 0

y0 - y y0 + y ¸Ô ÏÔ A ÈÏÔ a a ¸Ôù +i + Í ú 2 ÍÌÔ a2 + ( y - y )2 a2 + ( y + y )2 ýÔ ÌÔ a2 + ( y + y )2 a2 + ( y - y )2 ýÔú 0 0 0 0 þ Ó þû ÎÓ

[ x > 0] [ x < 0]

1 Ï Ô¸ = Ay0 ÔÌ 2 ý 2 2 ÔÓ a + y0 - y + i2ay Ôþ

(

)

2AL

A A L

0

L

[ x < L] [ x > L]

2A 2π/L

2π/L

sin Ly y

a

2AL

2π/S

2π/S

2AL

A L

2π/L

2π/L

L

S A 0

© 2004 by CRC Press LLC

[a < x < b] [ x < a; x > b ]

2A

È (sin by - sin ay ) - i(cos ay - cos by ) ù sin Ly exp( -iSy ) = A Í ú y y ÍÎ úû

È (sin Ly cos Sy ) - i(sin Ly sin Sy ) ù iA exp( -iby ) - exp( -iay ) = 2 AÍ ú= y ÍÎ úû y

[

]

CRC Handbook of Engineering Tables

b

1587_Section_1c.fm Page 136 Saturday, September 27, 2003 12:45 PM

Table of Fourier Transforms (x = t, y = w) (continued)

F (y )

S

S 2π/S

4AL A

2L

2L A 0

L

[

2π/L

]

(S - L ) < x < (S + L )

[otherwise]

4A

L

L

L

A

yo

2AL

A

A exp(iy0 x ) 2π/yo

cos Sy sin Ly y

0

L

[ x < L] [ x > L]

2π/L 2π/L 2A

2π/yo

yo

L

{

}

sin L( y0 - y )

(y

0 - y)

yo

AL

A

A cos y0 x

© 2004 by CRC Press LLC

0

2π/L È sin L( y - y0 ) sin L( y + y0 ) ù AÍ + ú ( y + y0 ) úû ÍÎ ( y - y0 )

1-137

2π/yo

[ x < L] [ x > L]

1587_Section_1c.fm Page 137 Saturday, September 27, 2003 12:45 PM

f (x )

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) L

L

y0 2π/L A

~ AL

2π/y0

A sin y0 x 0

[ x < L] [ x > L]

2A/y0

A

A cos y0 x 0

[ x < (p 2 y )] [ x > (p 2 y )]

6y0

Ê y ˆ Ê py ˆ 2 AÁ 2 0 2 ˜ cos Á ˜ Ë 2 y0 ¯ Ë y0 - y ¯

4y0

0 0

A AL

L

© 2004 by CRC Press LLC

L

Ê xˆ AÁ1 - ˜ L¯ Ë 0

[ x < L] [ x > L]

4π/L

2π/L

Ê sin( Ly 2) ˆ ALÁ ˜ Ë ( Ly 2) ¯

2

CRC Handbook of Engineering Tables

π/y0

ÏÔ sin L( y + y0 ) sin L( y - y0 ) ¸Ô iAÌ ( y - y0 ) ýþÔ ÓÔ ( y + y0 )

y0

1587_Section_1c.fm Page 138 Saturday, September 27, 2003 12:45 PM

1-138

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x)

L

A L 2π/L

[ x < L] [ x > L]

Ax L 0

sin Ly ˆ 2iA Ê Á cos Ly ˜ y Ë Ly ¯

AL

A

L

L 2π/L

[ x < L] [ x > L]

Ax L 0

2π/y0

2 Ï ¸ Ô sin Ly Ê sin( Ly 2) ˆ Ô 2 AL Ì - 2Á ý ˜ Ly ¯ Ô Ë ÔÓ Ly þ

2π/y0 2πA A

y0

© 2004 by CRC Press LLC

2 xAd( y - y0 )

1-139

A exp(iy0 x )

1587_Section_1c.fm Page 139 Saturday, September 27, 2003 12:45 PM

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

1-140

F(y)

f (x) 2π/y0

πA A y0

y0

{

}

xA d( y - y0 ) + d( y + y0 )

A cos y0 x 2π/y0

y0

πA A πA y0

{

}

piA d( y + y0 ) - d( y - y0 )

A sin y0 x 2π/y0

πA 2y0

A sin 2 y0 x

2y0

{

}

pA - 12 d( y + 2 y0 ) + d( y ) + 12 d( y - 2 y0 )

2π/y0 πA

πA/2 2y0 A sin 2 y0 x

© 2004 by CRC Press LLC

{

2y0

}

pA - 12 d( y + 2 y0 ) + d( y ) - 12 d( y - 2 y0 )

CRC Handbook of Engineering Tables

πA/2

A

1587_Section_1c.fm Page 140 Saturday, September 27, 2003 12:45 PM

Table of Fourier Transforms (x = t, y = w) (continued)

A

npy +•

Ê

Â 4 AÁË y

2π/y0

npy -•

A cos y0 x

Ê xy ˆ y02 ˆ cos Á ˜ d( y - 2py0 ) - y 2 ˜¯ Ë 2 y0 ¯

2 0

[n = 0, ± 1, ± 2, º]

2y0

A

npy +•

[

A sin y0 x

npy -•

]

2π/yt

Ê

Â (-1) 4 AÁË y

2π/y0

a

2 0

Ê xy ˆ y02 ˆ cos Á ˜ d( y - 2py0 ) - y 2 ˜¯ Ë 2 y0 ¯

[n = 0, ± 1, ± 2, º]

2y0

πA

2a

(1) A πa/2

(2)

(3)

2π/y0

© 2004 by CRC Press LLC

0

1

0

1

0

1

(4)

y0

y1

1-141

[ ] cos y x [ A + a sin y x ] º (2) sin y x [ A + a cos y x ] º (3) sin y x [ A + a sin y x ] º (4) cos y0 x A + a cos y1x º (1)

F ( y ) consists of delta functions as shown

1587_Section_1c.fm Page 141 Wednesday, October 8, 2003 4:09 PM

F(y)

f (x)

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

1-142

F(y)

f (x)

2πA πA a Ï 2p Ì Ad( y - y0 ) + d( y - y0 + y1 ) 2 Ó

exp (iy0 x) (A + a cos y1x)

+

a ¸ d( y - y0 - y1 )ý 2 þ

y0

yt

2πA

exp (iy0 x) (A + a sin y1x)

y0 ia ia ¸ Ï 2p Ì Ad( y - y0 ) + d( y - y0 + y1 ) - d( y - y0 - y1 )ý 2 2 þ Ó

yt

A Aδ(x)

A A Ad( x - x 0 )

© 2004 by CRC Press LLC

2π/y0

A exp( -ix0 y )

CRC Handbook of Engineering Tables

A A

x0

πA

1587_Section_1c.fm Page 142 Saturday, September 27, 2003 12:45 PM

Table of Fourier Transforms (x = t, y = w) (continued)

Electrical and Computer Engineering

F(y)

f (x)

2A A

x0

x0

{

}

A d( x - x 0 ) + d( x + x 0 ) (N − 3)

n= 0 1 2

(N − 2)

2 A cos x 0 y

2π/x0 2π/x0

(N − 1)

[N odd]

A

x0

4π/Nx0

S N -1

Ï

Â AdÔÌÔÓx - nx - S + 0

(N - 1)x0 Ô¸

n=0

2

[N even]

ý Ôþ

Set of N delta functions symmetrically placed about x = S.

A

sin( Nyx0 2) sin( yx 0 2)

[

exp( -iSy ) Drawn for S = 0; N = 7 and N = 8

x0

2π/x0

2πA/x0

A etc

Â

n x 0 -•

© 2004 by CRC Press LLC

etc +•

Ad( x - nx 0 )

Â

n x 0 -•

2pA Ê 2p ˆ d y -n ˜ x 0 ÁË x0 ¯

1-143

+•

]

1587_Section_1c.fm Page 143 Wednesday, October 8, 2003 4:09 PM

Table of Fourier Transforms (x = t, y = w) (continued)

1-144

F(y)

f (x) x0

2πA/x0 A +•

Â (-1)

+•

x Ê ˆ AdÁ x - 0 - nx 0 ˜ Ë ¯ 2 x 0 -•

Â

n

n x 0 -•

n

2pA Ê 2x ˆ d y -n ˜ x 0 ÁË x0 ¯

4x/x0

2π/x0

2π/y0

2πA/x0

2a

πa/x0 (1) y0

A

y0

x0

0

0

0

[n = 0,

0

]

± 1, ± 2, º

ˆ a Ê ˆ ¸Ô 2p ÏÔ Ê 2p ˆ a Ê 2p 2p + y 0 ˜ + dÁ y - y0 ˜ ý Ì AdÁ y - n ˜ + dÁ y - n x0 ¯ 2 Ë x0 x0 ¯ 2 Ë ¯ þÔ Ô Ë 0 Ó

Âx n

ˆ ¸Ô ˆ ia Ê 2p ÏÔ Ê 2p ˆ ia Ê 2p 2p - y0 ˜ ý + y 0 ˜ - dÁ y - n Ì AdÁ y - n ˜ + dÁ y - n x0 ¯ 2 Ë x0 x0 ¯ Ôþ ¯ 2 Ë 0 Ô Ó Ë n = 0, ±1, ± 2, º

Âx n

[

]

A

2πA

A 2πAδ(y)

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Â d(x - nx ){A + a cos y x} (1) Â d(x - nx ){A + a sin y x} (2)

(2)

1587_Section_1c.fm Page 144 Wednesday, October 8, 2003 4:09 PM

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x)

A

A

[x > 0] f (x ) = A sgn(x ) ] [ x < 0] [

+A -A

-2iA

1 y

πA A

[x > 0] f (x ) = AU (x ) ] [ x < 0] [

A 0

Ï AÌpd( y ) Ó

1/a

i¸ ý yþ

πA

A A/a a

{

} [ x > 0]

A 1 - exp( -ax )

[ x < 0]

Ï a2 Ô a pAd( y ) - AÌ 2 +i 2 2 a + y y a + y2 ÔÓ

(

)

¸ Ô ý Ôþ

1-145

© 2004 by CRC Press LLC

0

1587_Section_1c.fm Page 145 Saturday, September 27, 2003 12:45 PM

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) 2π/L

2πA

A 2π/L L A 0

2AL

L

[ x > L] [ x < L]

2pAd( y ) - 2 A

sin Ly y

y0

A exp{i(a cos y0 x + bx)} b +•

Â (i) J (a)d( y - b - ny ) n

n

n

0

m -•

b

A exp{i(a sin y0 x + bx)} y0

2pA

+•

Â J (a)d( y - b - ny ) n

n m -•

Note: Jn(-a) = J–n(a) = (–1)nJn(a).

© 2004 by CRC Press LLC

0

CRC Handbook of Engineering Tables

2pA

1587_Section_1c.fm Page 146 Saturday, September 27, 2003 12:45 PM

1-146

Table of Fourier Transforms (x = t, y = w) (continued)

Electrical and Computer Engineering

F(y)

f (x) ~2π/b

b

2π/y0 y0

A cos(a sin y0 x + bx ) pA

+•

Â {J (a)d( y - b - ny ) + J (a)d( y + b + ny )} n

0

n

0

n m -•

A cos (a cos y0 x + bx)

pA

Â {(+i) J (a)d( y - b - ny ) + (-i) J (a)d( y + b + ny )} +•

n

n

n

n

n

0

0

m -•

A sin (a sin y0 x + bx)

+•

Â {- J (a)d( y - b - ny ) + J (a)d( y + b + ny )} n

n m -•

© 2004 by CRC Press LLC

0

n

0

1-147

i pA

1587_Section_1c.fm Page 147 Wednesday, October 8, 2003 4:09 PM

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x)

A sin (a cos y0 x + bx) b

ipA

Â {(-i) J (a)d( y - b - ny ) + (-i) J (a)d( y + b + ny )} +•

n

n

n

n

n

0

0

m -•

2π/y0

y0

A ea

A exp( -a cos y0 x )

+•

Â (-1) I (a)d( y - ny ) n

n

0

n m -•

2π/y0 y0 A ea

A exp( -a sin y0 x )

© 2004 by CRC Press LLC

2pA

+•

Â (i) I (a)d( y - ny ) n

n

n m -•

0

CRC Handbook of Engineering Tables

2pA

1587_Section_1c.fm Page 148 Saturday, September 27, 2003 12:45 PM

1-148

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x)

Re f(x) Re F(y)

Im F(y)

Im f(x)

(

A exp ±ia2 x 2

Ê x ˆ 2 A(1 — i) exp m iy 2 4a2 Á ˜ Ë 2¯ a

)

1

x0

m=0 m = −1

(

m=1 m=2

m = −2 m = −1 y0

m = −2

) m=0 m=1 m=2

2π/y0 f (x ) = A

Â d(x - nx + a sin y x) 0

0

n=0

n

n = −3

n = −1

n=1

n=3 2π/x0

F( y ) =

2 xA x0

ÂJ m, n

m

Ê 2pa ˆ Án x ˜ Ë 0 ¯

Ê ˆ 2p dÁ y - n - my0 ˜ x0 Ë ¯

© 2004 by CRC Press LLC

1-149

(m = 0, ± 1, ± 2, ± 3, º) (n = 0, ± 1, ± 2, ± 3, º)

1587_Section_1c.fm Page 149 Wednesday, October 8, 2003 4:09 PM

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) g(x)

H(y)

G(y)/x0

h(x)

x0 f ( x ) = h( x )

+•

Â g (x - nx )

n

f (x ) =

2π/x0

0

m -•

+•

Â h(nx )g (x - nx ) 0

n

0

m -•

Ï Ê n2p ˆ Ê n2p ˆ Ô¸ ˜ HÁy - x ˜ý ¯ Ë 0 0 ¯Ô þ n m -• +•

Â ÔÌÔÓGÁË x

F( y ) =

1 x0

F( y ) =

1 G( y ) x0

+•

Ê

Â H ÁË y -

n m -•

n2p ˆ x 0 ˜¯

2

1.5 1

1

0.5 0

0

−0.5

−1.5 −4

−2

0 x

2

4

A -A

s-a < x <s+a -s - a < x < -s + a

−2 −5

1.5

3

1

2

0.5

1

0

0

−0.5

−1

−1 −1.5 −1.5 −1

© 2004 by CRC Press LLC

0

5

y

-2Aj

sin ay sin ys y

−2 −0.5

0 x

0.5

1

1.5

A -A

0 < x < 2a -2a < x < 0

−3 −5

y

-4jA sin ay 5

sin ay y

CRC Handbook of Engineering Tables

−1

−1

1587_Section_1c.fm Page 150 Saturday, September 27, 2003 12:45 PM

1-150

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) 7

1

6

0.5

5 4

0

3

−0.5 −20

−10

0 x

10

25

2 −1

J0 (x )

−0.5

0

0.5

1

2

y

1 - y2

0.3

1

0.25

0.8

0.2 0.15

0.6

0.1

0.4

0.05 0.2

0

−0.05 −20

−10

0 x

10

20

0 −1

JI (x )

−0.5

0 y

0.5

1 - y2

2x

4

1

1.5 1

2 0.5 0

0

−0.5

−2

© 2004 by CRC Press LLC

−1

0 x

1

2

1 px

−1.5

−2

−1

0 y

1

2

Ï1 Ô sqn y = Ì 0 Ô-1 Ó

y >0 y =0 y <0

1-151

−4 −2

−1

1587_Section_1c.fm Page 151 Saturday, September 27, 2003 12:45 PM

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) 0.3

0.2

0.2 0.1

0.1 0

0

−0.1 −0.2

−0.1

−0.3 −0.4 −2

−1

0 x

1

−0.2 −5

2

xe

0 y

-px 2

5

-j

y2

y - 4p e 2p

2

1.5 1

1 0.5 0

0 −0.5

−1

−1 −1

0 x

1

2

d( x + a ) - d( x - a )

1

10

0.5

5

0

−1 −2

−5

0 y

5

10

2 j sin

y 2

0

−0.5

© 2004 by CRC Press LLC

−2 −10

−1 −1

0 x

1

2

tanh px

−10 −2

−1

0 y

1

2

-j cos ech

y 2

CRC Handbook of Engineering Tables

−1.5 −2

1587_Section_1c.fm Page 152 Saturday, September 27, 2003 12:45 PM

1-152

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) 2

1.2 1

1.5

0.8 0.6

1

0.4 0.2

0.5

0 −0.2 −4

−2

0 x

2

4

e

-x

sin x x

1

0 −10

−5

0 y

5

10

tan -1

2 y2

1.2 1

0.8

0.8 0.6

0.6

0.4

0.4 0.2

0.2

0 0 −40

−20

20

0

40

x

p( x ) * p( x ) * p( x )

−0.2 −5

0 y

5

Ê sin y ˆ Á ˜ Ë y ¯

1.5

Pa ( x )

3

1.5

1 0.8

1

0.6 0.4

0.5

0.2 0

0

−0.2 −0.4 −10

0 x

5

10

sin ax px

−0.5 −1.5

−1

−0.5

0 y

0.5

1

1-153

© 2004 by CRC Press LLC

−5

1587_Section_1c.fm Page 153 Saturday, September 27, 2003 12:45 PM

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

0.4

1

0.3

0.5

0.2

0

0.1

−0.5

1

2

3

x

4

5

xe

- ax

1

a>0 x ≥0

−1 −5

5

0 y

a2 - y2

(a

2

+y

2

)

2

-j

(a

2ay 2

+ y2

)

2

3.5 3

0.8

2.5 0.6

2

0.4

1.5 1

0.2

0.5 5

1 a2 + x2

0 −5

1

2

0.5

1.5

0

1

−0.5

0.5

−1 −5

© 2004 by CRC Press LLC

0 y

0 x

5

cos bx a2 + x2

0 −10

0 y

−5

0 y

5

5

p -a y d a

10

p - a y -b - a y +b +e e 2a

[

]

CRC Handbook of Engineering Tables

0 −5

1587_Section_1c.fm Page 154 Wednesday, October 8, 2003 4:09 PM

F(y)

f (x)

0 0

1-154

Table of Fourier Transforms (x = t, y = w) (continued)

1

2

0.5

1

0

0

−0.5

−1

−1 −5

0 x

5

sin bx a2 + x2

−2 −10

4

4

2

2

0

0

−2

−2

−4 −4

−2

0 x

2

4

dd( x )

−4 −4

−5

0 y

5

10

−2

0 jy

2

4

4

2

2

0

0

−2

−2

−4 −4

0 x

2

4

−4 −4

0 y

2

−2

4

2pj

dd( y ) dy

1-155

© 2004 by CRC Press LLC

−2

]

jy

dx

4

[

p - a y -b - a y +b -e e 2aj

1587_Section_1c.fm Page 155 Wednesday, October 8, 2003 4:09 PM

F(y)

f (x)

Electrical and Computer Engineering

Table of Fourier Transforms (x = t, y = w) (continued)

F(y)

f (x) 1

3 2

0.5 1 0

0 −1

−0.5

−2

−1 0

2

x

4

6

sin w 0 x 0

x ≥0 x <0

1

−3 −6

−4

−2

0 y

2

4

6

w0 p -j d( y - w 0 ) - d( y + w 0 ) 2 w 02 - y 2

−4

−2

0 y

2

4

6

jy p + d( y - w 0 ) - d( y + w 0 ) w 02 - y 2 2

−2

−1

0 y

1

2

3

[

]

3 2

0.5

1 0

0 −1

−0.5

−2 2

4

6

x

cos w 0 x 0

3.5

x ≥0 x <0

−3 −6

[

5

3 2.5 2 1.5

0

1 0.5 0 −0.5 0

1

x

2

3

x 0

x ≥0 x <0

−5 −3

jp

dd( y ) dy

-

1 y2

From Poularikas, A., Fourier transformation, in The Handbook of Formulas and Tables for Signal Processing, CRC Press, Boca Raton, FL, 1999, pp. 3-4 to 3-27.

© 2004 by CRC Press LLC

]

CRC Handbook of Engineering Tables

−1 0

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Table of Fourier Transforms (x = t, y = w) (continued)

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1 Inverse

Log

Display Brightness

0.8

Identity 0.6

Squared 0.4 Square Root

Exponential

0.2 Inverse Log

0

0

64

128

192

256

Stored Pixel Value Examples of display transfer functions. (From Russ, J.C., Image enhancement: Processing in the spatial domain, in The Image Processing Handbook, 3rd ed., CRC Press, Boca Raton, FL, 1999, p. 232.)

Common Fourier Transforms x(t)

X(jw)

d(t) 1

1 2pd(w)

u(t)

pd(w ) +

e –atu(t), a > 0

1 a + jw

te –atu(t), a > 0 sin(wot) cos(wot)

1 jw

1

(a + jw)

2

jp[d(w + wo) – d(w – wo)] p[d(w + wo) + d(w – wo)]

From Heinen, J.A. and Niederjohn, R.J., Signal processing, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 77.

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Common Laplace Transforms x(t)

X(s)

d(t)

1

u(t)

1 , Re{s} > 0 s

e –atu(t)

1 , Re{s} > -a s+a

te –atu(t)

1

( s + a)

2

, Re{s} > -a

sin(wot)u(t)

wo , Re{s} > 0 s 2 + w 2o

cos(wot)u(t)

s , Re{s} > 0 s 2 + w 2o

From Heinen, J.A. and Niederjohn, R.J., Signal processing, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 78.

Important Properties of Laplace Transforms Signals

Laplace Transforms

Ax1(t) + Bx2(t)

AX1(s) + BX2(s)

x(t – to), to ≥ 0

X ( s )e - st o

x(at), a > 0

1 Ê sˆ XÁ ˜ a Ë a¯

dx (t )

sX(s) – x(0–)

dt

Ú

t

-•

x ( t)dt

x1(t)*x2(t)

X (s)

s X1(s)X2(s)

Note: x(t), x1(t), x2(t) are arbitrary signals with Laplace transforms X(s), X1(s), X2(s), respectively. A, B, a, to are arbitrary constants. From Heinen, J.A. and Niederjohn, R.J., Signal processing, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 79.

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Representative Values of Absolute Seebeck Thermoelectric Coefficients of Some Materials Used in Industrial Electronic Circuits Seebeck Coefficient, mV/˚C 20˚C 100˚C

0˚C Lead Tin Copper Silver Gold Tungsten Chromium Nickel Platinum Brass Kovar Manganin Nichrome Silicon Germanium CuO Cu2O Mn2O3

0.03 ¥ 10 0.03 ¥ 10–3 1.72 1.42 2.3 1.9 13.2 –7.0 –4.2 0.7 0.20 1.37 20.84 –408 –303 –696 –474 – 1150 –385 –3

0.05 ¥ 10 0.06 ¥ 10–3 1.82 1.50 2.12 4.1 14.4 –9.7 –7.2 0.82 0.20 1.39 20.24 417 –3

400˚C

0.08 ¥ 10 0.09 ¥ 10–3 2.23 1.84 2.0 6.7 15.3 –12.4 –9.7 1.33 0.19 1.45 17.85 –455

0.11 ¥ 10–3 0.12 ¥ 10–3 3.85 4.07 2.3 12.1 17.3 –15.0 –13.1 1.95 0.02 1.95 11.89 –502

–3

Note: Values reported in the literature are for nominal materials that may not be well documented as to composition and state. They are presented only to allow estimates of plausible Seebeck emf contributions. Specific values should be determined for critical applications. From Reed, R.P., Measurement system architecture — Thermal effects in industrial electronic circuits, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 153. Data originally from Reed, R.P. 1992. Absolute Seebeck thermoelectric characteristics—principles, significance, and applications, Temperature, Its Measurement and Control in Science and Industry, American Institute of Physics, 6(2):503–508. Reed, R.P. 1993. Manual on the Use of Thermocouples in Temperature Measurement, MNL-12, 4th edition, Ch. 2, Park, R.W., ed., American Society for Testing and Materials, Philadelphia, PA. Wang, T.P. 1992. Absolute Seebeck coefficients of metallic elements, Temperature, Its Measurement and Control in Science and Industry, American Institute of Physics, 6(2):509–514. Kinzie, P.A. 1973. Thermocouple Temperature Measurement, Wiley-Interscience.

Power Definitions (Single-Phase Circuits) Quantity (and Synonyms) Active power (real power, average power)

Symbol P

Relationships P = Vrms I rms cos(f) = Vrms I rms pf

Units Watt (W)

= S 2 - Q2 Q = Vrms I rms sin(f) = Vrms I rms rpf

Reactive power

Q

VAr

Power factor

pf

= S2 - P 2 cos(f)

Reactive power factor Complex power

rpf S

sin(f) S = VI*

None, often represented as a percentage None Voltamperes (VA)

Apparent power

|S|

S = Vrms I rms = P 2 + Q2

Voltamperes (VA)

From Heydt, G., Main disturbances — Reactive power and harmonics compensation, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 357.

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Power Definitions (Three-Phase Circuits) Quantity

Symbol

Active power (real power)

P

Relationships P = 3Vln I phase cos(f)

Units Watt (W)

= 3Vln I phase pf = 3 Vll I line pf = S 2 - Q2 Reactive power

Q

Q = 3Vln I phase sin(f)

VAr

= 3Vrubln I phase rpf = 3 Vll I line rpf = S 2 - p2 Power factor Reactive power factor

pf rpf

cos(f) sin(f)

Often represented as a percentage None

Complex power

S

* S = 3Vln I phase

Voltamperes (VA)

* = 3 - 30∞Vline I line

Apparent power

|S|

S = 3Vln I phase

Voltamperes (VA)

= 3Vll I line = P 2 + Q2 From Heydt, G., Main disturbances — Reactive power and harmonics compensation, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 357.

Summary of Describing Differential Equations for Ideal Elements Type of Element

Inductive storage

© 2004 by CRC Press LLC

Physical Elements

Describing Equation

Energy E or Power P

Symbol L

di dt

E=

1 2 Li 2

v2

1 dF K dt

E=

1 F2 2 K

v2

Electrical inductance

v21 = L

Translational spring

v21 =

K

w 21 =

1 dT K dt

E=

1T 2 K

ω2

Fluid inertia

P21 = I

dQ dt

E=

1 2 IQ 2

P2

Electrical capacitance

i =C

1 2 E = Cv21 2

v2

Translational mass

F=M

dv2 dt

E=

1 Mv22 2

v1

K

2

Rotational spring

dv21 dt

i v 1

ω1

l

F

l

Q C

v2 M

F T P1 v1

v1 = constant

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Summary of Describing Differential Equations for Ideal Elements (continued) Type of Element

Physical Elements

Capacitive storage

Energy dissipators

Describing Equation dw 2 dt

Energy E or Power P 1 2 Jw 2 2

T

Rotational mass

T=J

Fluid capacitance

Q = Cf

Thermal capacitance

q = Ct

Electrical resistance

i=

Translational damper

F = fv21

2 P = fv21

F

Rotational damper

T = fw21

P = fw 221

T

Fluid resistance

Q=

1 P R f 21

P=

1 2 P R f 21

Thermal resistance

q=

1 T Rt 21

P=

1 T Rt 21

dP21 dt dt 2 dt

1 v R 21

E=

Symbol

1 E = C f P212 2

Q

ω2

P2

J

ω1 = constant

Cf

P1

E = Ctt2 P=

1 2 v R 21

R

v2

2

i

v2

f

ω2

f

4B 3

v1 v1 ω1

2

Nomenclature • Through-variable: F = force, T = torque, i = current, Q = fluid volumetric flow rate, q = heat flow rate. • Across-variable: v = translational velocity, w = angular velocity, v = voltage, P = pressure, T = temperature. • Inductive storage: L = inductance, l/k = reciprocal translational or rotational stiffness, I = fluid inertance. • Capacitive storage: C = capacitance, M = mass, J = moment of inertia, Cf = fluid capacitance, Ct = thermal capacitance. • Energy dissipators: R = resistance, f = viscous friction, Rf = fluid resistance, Rt = thermal resistance. From Boye, A.J. and Brogan, W.L., Modeling for system control, in The Industrial Electronics Handbook, Irwin, J.O., Ed., CRC Press, Boca Raton, FL, 1997, p. 449. Originally from Dorf, R. and Bishop, R. 1995. Modern Control Systems, 7th ed. © 1995 by Addison-Wesley Publishing Company. Reprinted by permission.

Properties of the Wave Types for Time-of-Flight Measuring Principle

Wave Velocity

Avg. Carrier Frequency

Wavelength

Avg. Burst Time

Ultrasonic Radar Laser

340 m s–1 300,000 km s–1 300,000 km s–1

50 kHz 10 GHz 300 THz

7 mm 3 cm 1 mm

1 ms 1 ns 1 ns

From Brumbi, D., Level measurement, in The Measurement, Instrumentation and Sensors Handbook, Webster, J.G., Ed., CRC Press, Boca Raton, FL, 1999, p. 11-8.

© 2004 by CRC Press LLC

Description

Longitudinal strain sensitivity

Transverse strain sensitivity

Temperature sensitivity

Strain resolution

Piezoresistive constantan foil

DR/R/DeL = 2.1

DR/R/Det = <0.02

DR/R/DT = 2 ¥ 10–6/°C

<1 µstraina

Annealed constantan foild Piezoresistive semiconductor Piezoelectric PVDF Piezoelectric quartz

DR/R/DeL = 2.1 DR/R/DeL = 150 DQ/A/DeL = 120 nC/m2/µe DQ/A/DeL = 150 nC/m2/µe bonded to steel 2 to 1000 µstrain/volt Ke = 0.15–0.002 1 fringe order/417 nm displ.

DR/R/Det = <0.02 DR/R/Det = ??? DQ/A/Det = 60 nC/m2/µe

DR/R/DT = 2 ¥ 10–6/°C DR/R/DT = 1.7 ¥ 10–3/°C DQ/A/DT = –27 µC/m2/°C DQ/A/DT = 0

<11 µstrain <0.1 µstrain 1–10 µstrain <0.01 µstrain 20 mm gage <1 µstrain

Fiber optic Fabry-Perot Birefringent Film Moiré

b c d e f g

1 fringe order/417 nm displ.

Not defined

41.7 µe over 10 mm

5–100 mmb 5–100 mm 1–15 mm Gage size Gage size 2–10 mm 0.5 mmf full fieldg

Time resolution <1 µsc

0–3%

<1 µs <1 µs <1 µs <10 µs

0–10% 0–0.1% 0–30% 0–0.1%

<20 µs <5 µs Limited by signal conditining

With good signal conditioning. Equal to grid area. Gage response is within 100 ns. Most signal conditioning limits response time to far less than this. Annealed foil has a low yield stress and a large strain to failure. It also has hysteresis in the unload and a zero shift under cyclic load. This technique measures a difference in principal strains. e2 – e1 = Nl/2tK Approximately the film thickness. The spatial strain resolution depends on the strain level. This is a displacement measurement technique. From Lynch, C.S., Strain measurement, in The Measurement, Instrumentation, and Sensors Handbook, Webster, J.G., Ed., CRC Press, Boca Raton, FL, 1999, p. 22-5.

© 2004 by CRC Press LLC

Measurable strain range

0.05–5% 0.005–5%

CRC Handbook of Engineering Tables

a

Near zero

Spatial resolution

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Comparison of Strain Sensors

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Motion Pressure

Motion

Motion Pressure

(a)

Pressure

(b)

(c)

Motion Motion Motion

Pressure

Pressure

Pressure (d)

(e)

Motion

(f)

Motion

Motion

Pressure

Pressure (g)

(h)

Pressure (i)

Pressure-sensing elements: (a) flat diaphragm; (b) corrugated diaphragm; (c) capsule; (d) bellows; (e) straight tube; (f) Cshaped Bourdon tube; (g) twisted Bourdon tube; (h) helical Bourdon tube; (i) spiral Bourdon tube. (From Norton, H.N., Handbook of Transducers, Englewood Cliffs, NJ: Prentice-Hall, 1989, 294–330. Reprinted with permission.) Previously published in Chau, K.H.L., Pressure and sound measurement, in The Measurement, Instrumentation, and Sensors Handbook, Webster, J.G., Ed., CRC Press, Boca Raton, FL, 1999, p. 26-3.)

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Permittivity (Dielectric Constants of Materials Used in Capacitors) Material

Permittivity

Vacuum Air Teflon Polyethylene, etc. Impregnated paper Glass and mica Ceramic (low K) Ceramic (medium K) Ceramic (high K)

1.0 1.0006 2.1 2.0–3.0 4.0–6.0 4.0–7.0 £20.0 80.0–100.0 ≥1000,0

From Eren, H. and Goh, J., Capacitance and capacitance measurements, in The Measurement, Instrumentation, and Sensors Handbook, Webster, J.G., Ed., CRC Press, Boca Raton, FL, 1999, p. 45-5.

MECHANICS OF SOLIDS TRANSLATIONAL AND ROTATIONAL SYSTEMS FLUID SYSTEMS ELECTRICAL SYSTEMS THERMAL SYSTEMS MICRO- AND NANO-SYSTEMS ROTATIONAL ELECTROMAGNETIC MEMS PHYSICAL SYSTEM ANALOGIES FUNDAMENTALS OF TIME AND FREQUENCY SENSOR AND ACTUATOR CHARACTERISTICS SENSORS Linear and rotational sensors Acceleration sensors Force, torque, and pressure sensors Flow sensors Temperature measurements Ranging and proximity sensing Light detection, image, and vision systems Fiber optic devices Micro- and nanosensors ACTUATORS Electro-mechanical actuators Motors: DC motors, AC motors, and stepper motors Piezoelectric actuators Pneumatic and hydraulic actuators Micro- and nanoactuators

Physical System Modeling

MECHATRONICS MODELING SIGNALS AND SYSTEMS IN MECHATRONICS RESPONSE OF DYNAMIC SYSTEMS ROOT LOCUS METHODS FREQUENCY RESPONSE METHODS STATE VARIABLE METHODS STABILITY, CONTROLLABILITY, AND OBSERVABILITY OBSERVERS AND KALMAN FILTERS DESIGN OF DIGITAL FILTERS OPTIMAL CONTROL DESIGN ADAPTIVE AND NONLINEAR CONTROL DESIGN NEURAL NETWORKS AND FUZZY SYSTEMS INTELLIGENT CONTROL FOR MECHATRONICS IDENTIFICATION AND DESIGN OPTIMIZATION

Sensors and Actuators MECHATRONICS

Software and Data Acquisition

DATA ACQUISITION SYSTEMS TRANSDUCERS AND MEASUREMENT SYSTEMS A/D AND D/A CONVERSION AMPLIFIERS AND SIGNAL CONDITIONING COMPUTER-BASED INSTRUMENTATION SYSTEMS SOFTWARE ENGINEERING DATA RECORDING

Signals and Systems

Computers and Logic Systems

DIGITAL LOGIC COMMUNICATION SYSTEMS FAULT DETECTION LOGIC SYSTEM DESIGN ASYNCHRONOUS AND SYNCHRONOUS SEQUENTIAL LOGIC COMPUTER ARCHITECTURES AND MICROPROCESSORS SYSTEM INTERFACES PROGRAMMABLE LOGIC CONTROLLERS EMBEDDED CONTROL COMPUTERS

The key elements of mechatronics. (From Bishop, R.H., What is mechatronics? in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-3.)

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Mechanical process and information processing develop towards mechatronic systems. (From Iserman, R., Mechatronic design approach, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 2-3.)

Generalized Through and Across Variables for Processes with Energy Flow System

Through Variables

Electrical Magnetic Mechanical • translation • rotation Hydraulic Thermodynamic

Across Variables

Electric current Magnetic Flow

I F

Electric voltage Magnetic force

U Q

Force Torque Volume flow Entropy flow

F M V˙

Velocity Rotational speed Pressure Temperature

w w p T

From Iserman, R., Mechatronic design approach, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 2-12.

Power and Energy Variables for Mechanical Systems Energy Domain General Translational Rotational Electrical Hydraulic

Effort, e

Flow, f

Power, P

e Force, F [N] Torque, T or t [N m] Voltage, v [V] Pressure, P [Pa]

f Velocity, V [m/sec] Angular velocity, w [rad/sec] Current, i [A] Volumetric flowrate, Q [m3/sec]

e · f [W] F · V [N m/sec, W] T · w [N m/sec, W] v · i [W] P · Q [W]

From Longoria, R.G., Modeling of mechanical systems for mechatronics applications, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca

Raton, FL, 2002, p. 9-3.

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Mechanical Dissipative Elements Physical System

Fundamental Relations Dissipation: e ◊ f = Â ei f i = T ◊ f s

Generalized Dissipative Element

Resistive law: e = F R ( f ) Conductive law: f = F R (e ) -1

R

Co-content: Pe = Ú f ◊ de

Mechanical Translation

Constitutive: F = F(V )

damping, b

F1

F2 V2

damping, b

F1 = F2 = F V1 - V2 = V

Co-energy: PF = Ú V ◊ dF

Constitutive: T = F(w )

damping, B

T2 w1

Content: PV = Ú F ◊ dV

Dissipation: Pd = PV + PF

Mechanical Rotation T1

e1

w2

T1 = T2 = T

w 1 - w2 = w Torsional damper damping, B

Content: Pw = Ú T ◊ d w

Co-energy: PT = Ú w ◊ dT

Dissipation: Pd = Pw + PT

en fn

e2 f2

R ...

Content: Pf = Ú e ◊ df

Resistive element Resistance, R

Damper

f1

i

e f

V1

Bond Graph

e3

f3

Generalized multiport R-element

F V

R :b

Linear: F = b ◊ V Dissipation: Pd = bV 2

T

w

R :B

Linear: T = B ◊ w Dissipation: Pd = Bw

2

From Longoria, R.G., Modeling of mechanical systems for mechatronics applications, in The Mechantronics Hand-

book, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 9-11.

Typical Coefficient of Friction Values Contacting Surfaces Steel on steel (dry) Steel on steel (greasy) Teflon on steel Teflon on teflon Brass on steel (dry) Brake lining on cast iron Rubber on asphalt Rubber on concrete Rubber tires on smooth pavement (dry) Wire rope on iron pulley (dry) Hemp rope on metal Metal on ice

Static, ms

Sliding or Kinetic, mk

0.6 0.1 0.04 0.04 0.5 0.4 — — 0.9 0.2 0.3 —

0.4 0.05 0.04 — 0.4 0.3 0.5 0.6 0.8 0.15 0.2 0.02

Note: Actual values will vary significantly depending on conditions. From Longoria, R.G., Modeling of mechanical systems for mechatronics applications, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press,

Boca Raton, FL, 2002, p. 9-11.

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Mechanical Potential Energy Storage Elements (Integral Form) Physical System

Fundamental Relations

Generalized Potential Energy Storage Element

State: q = displacement Rate: q = f Constitutive: e = Φ(q )

C

e f

Energy: U q = ∫ e ⋅ dq Co-energy: U e = ∫ q ⋅ de

Capacitive element Capacitance, C

Mechanical Translation stiffness, k = 1/C

F1

F2

V1 spring

V2 F1 = F2 = F V1 − V2 = V

stiffness, k, compliance, C

Mechanical Rotation stiffness, K= 1/C T1 ω1

T2

T1 = T2 = T ω1 − ω 2 = ω Torsional spring stiffness, K, compliance, C

e1

f1 = q1

en f n = qn

e2

C ...

f2 = q2

e3

f3 = q3

Generalized multiport C-element

State: x = displacement

F

Rate: x = V Constitutive: F = F ( x)

x =V

Linear: F = k ⋅ x

Energy: U x = ∫ F ⋅ dx

Energy: U x = 12 kx 2

Co-energy: U F = ∫ x ⋅ dF

Co-energy: U F = F

State: θ = angle

T C : 1/C=K θ =ω Linear: T = K ⋅ θ

Rate: θ = ω Constitutive: T = T (θ )

ω2

Bond Graph

Energy: Uθ = ∫ T ⋅ dθ Co-energy: U T = ∫ θ ⋅ dT

C :1/C=k

2

2k

Energy: Uθ = 12 kθ 2 Co-energy: U T = T

2

2K

From Longoria, R.G., Modeling of mechanical systems for mechatronics applications, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 9-13.

Mechanical Kinetic Energy Storage Elements (Integral Form) Physical System

Fundamental Relations

Generalized Kinetic Energy Storage Element e f

State: p = momentum Rate: p = e Constitutive: f = F(p )

Inertive element Inertance, I

Co-energy: Tf = Ú p ◊ df

I

Mechanical Translation mass, M

F1 V1 Mass

mass, m

Energy: Tp = Ú f ◊ dp

State: p = momentum Rate: p = F Constitutive: V = V ( p )

F2

Energy: Tp = Ú f ◊ dp

V2 F1 - F2 = F V1 = V2 = V

Co-energy: TV = Ú p ◊ dV

Mechanical Rotation

State: h = angular momentum

inertia, J

Rate: h = T

w2

w1

T

T2 T1 - T2 = T

1 w1 = w 2 = w Rotational inertia mass moment of inertia, J

Constitutive: w = w (h) Energy: Th = Ú w ◊ dh

Co-energy: Tw = Ú h ◊ dw

Bond Graph en = pn

e1 = p1 f1 e2 = p2 f2 e3 = p3

fn

I ... f3

Generalized multiport I-element

p=F

I: M

V Linear: V = p

M 2 p Energy: Tp =

2M Co-energy: TV = 12 MV 2 h =T I: J w Linear: w = h J 2 h Energy: Th = 2J Co-energy: Tw = 12 J w 2

From Longoria, R.G., Modeling of mechanical systems for mechatronics applications, in The Mechantronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 9-14.

© 2004 by CRC Press LLC

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Resistance of Copper Wire AWG Size

Number of Strands

Diameter per Strand

Resistance per 1000 ft (W)

24 24 22 22 20 20 18 18 16 16

Solid 7 Solid 7 Solid 7 Solid 7 Solid 19

0.0201 0.0080 0.0254 0.0100 0.0320 0.0126 0.0403 0.0159 0.0508 0.0113

28.4 28.4 18.0 19.0 11.3 11.9 7.2 7.5 4.5 4.7

From Rizzoni, G., Electrical engineering, in The Mechatronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, p. 11-9.

Type of Sensors for Various Measurement Objectives Sensor

Features Linear/Rotational sensors

Linear/Rotational variable differential transducer (LVDT/RVDT) Optical encoder Electrical tachometer Hall effect sensor Capacitive transducer

Strain gauge elements Interferometer Magnetic pickup Gyroscope Inductosyn

High resolution with wide range capability Very stable in static and quasi-static applications Simple, reliable, and low-cost solution Good for both absolute and incremental measurements Resolution depends on type such as generator or magnetic pickups High accuracy over a small to medium range Very high resolution with high sensitivity Low power requirements Good for high frequency dynamic measurements Very high accuracy in small ranges Provides high resolution at low noise levels Laser systems provide extremely high resolution in large ranges Very reliable and expensive Output is sinusoidal Very high resolution over small ranges Acceleration sensors

Seismic accelerometer Piezoelectric accelerometer

Good for measuring frequencies up to 40% of its natural frequency High sensitivity, compact, and rugged Very high natural frequency (100 kHz typical) Force, torque, and pressure sensors

Strain gauge Dynamometers/load cells Piezoelectric load cells Tactile sensor Ultrasonic stress sensor

Good for both static and dynamic measurements They are also available as micro- and nanosensors Good for high precision dynamic force measurements Compact, has wide dynamic range, and high Good for small force measurements

Pitot tube Orifice plate Flow nozzle, venturi tubes

Widely used as a flow rate sensor to determine speed in aircrafts Least expensive with limited range Accurate on wide range of flow More complex and expensive

Flow sensors

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Type of Sensors for Various Measurement Objectives (continued) Sensor Rotameter Ultrasonic type Turbine flow meter Electromagnetic flow meter

Features Good for upstream flow measurements Used in conjunction with variable inductance sensor Good for very high flow rates Can be used for both upstream and downstream flow measurements Not suited for fluids containing abrasive particles Relationship between flow rate and angular velocity is linear Least intrusive as it is noncontact type Can be used with fluids that are corrosive, contaminated, etc. The fluid has to be electrically conductive Temperature sensors

Thermocouples Thermistors Thermodiodes, thermo transistors RTD—resistance temperature detector Infrared type Infrared thermography

This is the cheapest and the most versatile sensor Applicable over wide temperature ranges (-200∞C to 1200∞C typical) Very high sensitivity in medium ranges (up to 100∞C typical) Compact but nonlinear in nature Ideally suited for chip temperature measurements Minimized self-heating More stable over a long period of time compared to thermocouple Linear over a wide range Noncontact point sensor with resolution limited by wavelength Measures whole-field temperature distribution Proximity sensors

Inductance, eddy current, hall effect, photoelectric, capacitance, etc.

Robust noncontact switching action The digital outputs are often directly fed to the digital controller Light sensors

Photoresistors, photodiodes, photo transistors, photo conductors, etc. Charge-coupled diode

Measure light intensity with high sensitivity Inexpensive, reliable, and noncontact sensor Captures digital image of a field of vision Smart material sensors

Optical fiber As strain sensor As level sensor As force sensor As temperature sensor Piezoelectric As strain sensor As force sensor As accelerometer Magnetostrictive As force sensors As torque sensor

Alternate to strain gages with very high accuracy and bandwidth Sensitive to the reflecting surface’s orientation and status Reliable and accurate High resolution in wide ranges High resolution and range (up to 2000∞C) Distributed sensing with high resolution and bandwidth Most suitable for dynamic applications Least hysteresis and good setpoint accuracy Compact force sensor with high resolution and bandwidth Good for distributed and noncontact sensing applications Accurate, high bandwidth, and noncontact sensor Micro- and nanosensors

Micro CCD image sensor Fiberscope Micro-ultrasonic sensor Micro-tactile sensor

Small size, full field image sensor Small (0.2 mm diameter) field vision scope using SMA coil actuators Detects flaws in small pipes Detects proximity between the end of catheter and blood vessels

From Anjanappa, M., Datta, K., and Song, T., Introduction to sensors and actuators, in The Mechatronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, pp. 16-2 to 16-3.

© 2004 by CRC Press LLC

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Type of Actuators and Their Features Actuator

Features Electrical

Diodes, thyristor, bipolar transistor, triacs, diacs, power MOSFET, solid state relay, etc.

Electronic type Very high frequency response Low power consumption

Electromechanical DC motor

Wound field

Separately excited Shunt Series Compound

Permanent magnet

Conventional PM motor Moving-coil PM motor Torque motor

Electronic commutation (brushless motor)

AC motor

AC induction motor AC synchronous motor

Universal motor

Stepper motor

Hybrid Variable reluctance

Speed can be controlled either by the voltage across the armature winding or by varying the field current Constant-speed application High starting torque, high acceleration torque, high speed with light load Low starting torque, good speed regulation Instability at heavy loads High efficiency, high peak power, and fast response Higher efficiency and lower inductance than conventional DC motor Designed to run for long periods in a stalled or a low rpm condition Fast response High efficiency, often exceeding 75% Long life, high reliability, no maintenance needed Low radio frequency interference and noise production The most commonly used motor in industry Simple, rugged, and inexpensive Rotor rotates at synchronous speed Very high efficiency over a wide range of speeds and loads Need an additional system to start Can operate in DC or AC Very high horsepower per pound ratio Relatively short operating life Change electrical pulses into mechanical movement Provide accurate positioning without feedback Low maintenance

Electromagnetic Solenoid type devices Electromagnets, relay

Large force, short duration On/off control Hydraulic and Pneumatic

Cylinder Hydraulic motor

Air motor Valves

© 2004 by CRC Press LLC

Gear type Vane type Piston type Rotary type Reciprocating Directional control valves Pressure control valves Process control valves

Suitable for liner movement Wide speed range High horsepower output High degree of reliability No electric shock hazard Low maintenance

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Electrical and Computer Engineering

Type of Actuators and Their Features (continued) Actuator

Features Smart Material actuators

Piezoelectric & Electrostrictive

High frequency with small motion High voltage with low current excitation High resolution High frequency with small motion Low voltage with high current excitation Low voltage with high current excitation Low frequency with large motion Very high voltage excitation Good resistance to mechanical shock and vibration Low frequency with large force

Magnetostrictive Shape Memory Alloy Electrorheological fluids

Micro- and Nanoactuators Micromotors Microvalves

Suitable for micromechanical system Can use available silicon processing technology, such as electrostatic motor Can use any smart material

Micropumps

From Anjanappa, M., Datta, K., and Song, T., Introduction to sensors and actuators, in The Mechatronics Handbook, Bishop, R.H., Ed., CRC Press, Boca Raton, FL, 2002, pp. 16-9 to 16-10.

Performances of Two Deep-Sea Armored Coaxes Cable Parameter

1972 Navy/SIO

1983 UNOLS

Diameter (mm) Strength (kg) Ends fixed One end free Weight (kg/km) In air In water Free length (m) Ends fixed One end free Payload (kg)a Ends fixed One end free

17.3

17.3

17,000 11,900

17,800 17,300

1070 820

1020 795

20,800 14,500

22,300 21,800

1880 None

2350 2150

aFor operations to 6000 m, with the lower cable end free to rotate. The system’s static strength/weight safety factor is 2.5. From Wilkins, G., Fiber optics telemetry in ocean cable systems, in The Ocean Engineering Handbook, El-Hawary, F., Ed., CRC Press, Boca Raton, FL, 2001, p. 5-60.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

50 Data

Relative Load

40

30

20 Voice

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

10

Past and projected future growth of data and voice traffic. (From Gencata, A., Singhel, N., and Makherjee, B., Overview of optical communication networks, in The Handbook of Optical Communication Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 3.)

Bit-Rate

Metro

Access

100 Gb/s

Parallel Array

10 Gb/s

1550 nm DFB-ExM 1310 nm DFB-DM

1 Gb/s

100 Mb/s

Long Haul

850 nm Devices e.g. VCSELs

1310 nm FP-DM Long Wavelength

10 Mb/s 0.01 km

0.1 km

1 km

10 km

100 km 1000 km

10000 km

Distance Nominal geographical spans of access, metro-core/regional, and long-haul networks as well as corresponding transmission rates with short- and long-wavelength transmitter devices. (From Raja, M.Y.A., Evolution of optical networks architecture, in The Handbook of Optical Communication Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 36.)

© 2004 by CRC Press LLC

1587_Book.fm Page 173 Sunday, August 31, 2003 9:44 PM

Electrical and Computer Engineering

1-173

ITU-T-approved hand assignment in the low attenuation window of the silica fibers; the wavelength range involves 1260–1360 nm = O-band; 1360–1460 nm = E-band; 1460–1530 nm = S-band; 1530–1565 nm = C-band; 1565–1625 nm = L-band; and 1625–1675 nm = U-band (used in monitoring). (Courtesy EXFO Electro-Optical Engineering Inc. Printed with permission.) (From Raja, M.Y.A. and Ilyas, M., Optical transport networks: A physical layer perspective, in The Handbook of Optical Communication Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 391.)

© 2004 by CRC Press LLC

Wavelength (nm) Sensor Hydrogen sulphide pH pH Hydrogen Carbon monoxide

Technique Porous fiber and sol-gel coating Porous fiber and sol-gel coating Porous fiber and sol-gel coating Palladium coated fiber Porous fiber

Fiber dipped in HPTS solution

Oxygen dissolved oxygen

Porous fiber and sol-gel coating

pH

Porous cellulose tricaetate fiber

Thionine Bromocresol green Bromocresol purple Palladium thin films Organometallic complex in chloroform solution Aqueous solution of 8-hydroxy-1,3,6pyrenetrisulfonic acid-trisodium salt Ruthenium complex

Congo-red

Principle

Excitation

Emission

Absorption

Florescence quenching Transmission/ absorption Transmission/ absorption Transmission/ absorption Transmission/ absorption

580

630

—

—

615

—

Detection limits

Sensitivity

Response Time

Ref.

~5 ppb

~5 S

57

—

>50 ppb in H2S in water 3–6

~0.01 pH

~2 S

37

—

580

6–9

~0.01 pH

~2 S

37

—

—

650

0.2–0.6%

—

20–30 S

41

—

—

450

9–28 vol.% in N2 gas

~0.5 vol%

~ 100 S

27

Fluorescence

450

530

—

0–600 ppm

—

5 min

58

Fluorescence quenching

450

610

—

—

—

46

Transmission

610

—

—

0–10% Oxygen 0.25–9 ppm dissolved oxygen —

—

1–2 min

59

From Iqbal, T., Fiber optics sensors, in The Handbook of Optical Communication Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 428.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Carbon dioxide dissolved in sea water

Indicator

1587_Book.fm Page 174 Sunday, August 31, 2003 9:44 PM

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Fiber Optics Chemical Sensors

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Electrical and Computer Engineering

Typical Components of Various Glass Systems Glass Type Silica glass Fluoride glass (ZrF4-based) Fluoride glass (AlF3-based) Chalcogenide Chalcohalide Sulphide glass

Glass-Forming Systems Na2O - Ba2O3 -SiO2 ZrF42-BaF2-LaF3-AlF32-NaF AlF3-BaF2-CaF2-YF3-SrF2-NaF-ZrF4 Ge-As-Se As-S-Cl As2S3-La2S3

From Iqbal, T., Fiber optics sensors, in The Handbook of Optical Communication Networks, Ilyas, M., Ed., CRC Press, Boca Raton, FL, 2003, p. 411.

(a) Thyristor symbol and (b) volt-ampere characteristics. (From Rajashekara, K., Overview, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-2. Originally from Bose, B.K., Modern Power Electronics: Evaluation, Technology, and Applications, p. 5 © 1992 IEEE. With permission.)

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

(a) Triac symbol and (b) volt-ampere characteristics. (From Rajashekara, K., Overview, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-3. Originally from Bose, B.K., Modern Power Electronics: Evaluation, Technology, and Applications, p. 5 © 1992 IEEE. With permission.)

(a) GTO symbol and (b) turn-off characteristics. (From Rajashekara, K., Overview, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-4. Originally from Bose, B.K., Modern Power Electronics: Evaluation, Technology, and Applications, p. 5 © 1992 IEEE. With permission.)

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Power MOSFET circuit symbol. (From Rajashekara, K., Overview, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-6. Originally from Bose, B.K., Modern Power Electronics: Evaluation, Technology, and Applications, p. 7 © 1992 IEEE. With permission.)

Total Elongation at Failure of Selected Polymers Polymer

Elongation

ABS Acrylic Epoxy HDPE Nylon, type 6 Nylon 6/6 Phenolic Polyacetal Polycarbonate Polyester Polypropylene PTFE

5–20 2–7 4.4 700–1000 30–100 15–300 0.4–0.8 25 110 300 100–600 250–350

From Whitaker, J.C., Fundamental electrical properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 10.

© 2004 by CRC Press LLC

1587_Book.fm Page 178 Friday, September 26, 2003 12:10 PM

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CRC Handbook of Engineering Tables

Tensile Strength of Selected Wrought Aluminum Alloys Alloy

Temper

TS (MPa)

1050 1050 2024 2024 3003 3003 5050 5050 6061 6061 7075 7075

0 H16 0 T361 0 H16 0 H34 0 T6, T651 0 T6, T651

76 130 185 495 110 180 145 195 125 310 230 570

From Whitaker, J.C., Fundamental electrical properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 10.

Density of Selected Materials, mg/m3 Metal Ag Al Au Co Cr Cu Fe Ni Pb Pt Ti W

10.50 2.7 19.28 8.8 7.19 8.93 7.87 8.91 11.34 21.44 4.51 19.25

Ceramic Al2O3 BN(cub) BeO MgO SiC(hex) Si3N4(a) Si3N4 (b) TiO2 (rutile) UO2 ZrO2 (CaO) Al2O3 MgO 3Al2O3 2SiO2

3.97–3.986 3.49 3.01–3.03 3.581 3.217 3.184 3.187 4.25 10.949–10.97 5.5 3.580 2.6–3.26

Glass SiO2 SiO2 10 wt% Na2O SiO2 19.55 wt% Na2O SiO2 29.20 wt% Na2O SiO2 39.66 wt% Na2O SiO2 39.0 wt% CaO

Polymer 2.20 2.291 2.383 2.459 2.521 2.746

ABS Acrylic Epoxy HDPE Nylon, type 6 Nylon 6/6 Phenolic Polyacetal Polycarbonate Polyester Polystyrene PTFE

1.05–1.07 1.17–1.19 1.80–2.00 0.96 1.12–1.14 1.13–1.15 1.32–1.46 1.425 1.2 1.31 1.04 2.1–2.3

From Whitaker, J.C., Fundamental electrical properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p.11.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Applications in the Microwave Bands Aeronavigation: Global positioning system (GPS) down link: Military communications (COM)/radar: Miscellaneous COM/radar: L-band telemetry: GPS downlink: Military COM (troposcatter/telemetry): Commercial COM and private line of sight (LOS): Microwave ovens: Commercial COM/radar: Instructional television: Military radar (airport surveillance): Maritime navigation radar: Miscellaneous radars: Commercial C-band satellite (SAT) COM downlink: Radar altimeter: Military COM (troposcatter): Commercial microwave landing system: Miscellaneous radars: C-band weather radar: Commercial C-band SAT COM uplink: Commercial COM: Mobile television links: Military LOS COM: Military SAT COM downlink: Military LOS COM: Military SAT COM uplink: Miscellaneous radars: Precision approach radar: X-band weather radar (and maritime navigation radar): Police radar: Commercial mobile COM [LOS and electronic news gathering (ENG)]: Common carrier LOS COM: Commercial COM: Commercial Ku-band SAT COM downlink: Direct broadcast satellite (DBS) downlink and private LOS COM: ENG and LOS COM: Miscellaneous radars and SAT COM: Commercial Ku-band SAT COM uplink: Military COM (LOS, mobile, and Tactical): Aeronavigation: Miscellaneous radars: DBS uplink:

0.96–1.215 GHz 1.2276 GHz 1.35–1.40 GHz 1.40–1.71 GHz 1.435–1.535 GHz 1.57 GHz 1.71–1.85 GHz 1.85–2.20 GHz 2.45 GHz 2.45–2.69 GHz 2.50–2.69 GHz 2.70–2.90 GHz 2.90–3.10 GHz 2.90–3.70 GHz 3.70–4.20 GHz 4.20–4.40 GHz 4.40–4.99 GHz 5.00–5.25 GHz 5.25–5.925 GHz 5.35–5.47 GHz 5.925–6.425 GHz 6.425–7.125 GHz 6.875–7.125 GHz 7.125–7.25 GHz 7.25–7.75 GHz 7.75–7.9 GHz 7.90–8.40 GHz 8.50–10.55 GHz 9.00–9.20 GHz 9.30–9.50 GHz 10.525 GHz 10.55–10.68 GHz 10.70–11.70 GHz 10.70–13.25 GHz 11.70–12.20 GHz 12.20–12.70 GHz 12.75–13.25 GHz 13.25–14.00 GHz 14.00–14.50 GHz 14.50–15.35 GHz 15.40–15.70 GHz 15.70–17.70 GHz 17.30–17.80 GHz

From Whitaker, J.C., Electromagnetic spectrum, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 31.

© 2004 by CRC Press LLC

1587_Book.fm Page 180 Sunday, August 31, 2003 9:44 PM

1-180

CRC Handbook of Engineering Tables

The Electromagnetic Spectrum

10 10 10 10 10 10 10 10 10 10 10 10 10 (1 GHz) 10 10 10 (1 MHz) 10 10 10 (1 kHz) 10 10 10

E22 E21 E20 E19 E18 E17 E16 E15 E14 E13 E12 E11 E10 E9 E8 E7 E6 E5 E4 E3 E2 E1 0

Cosmic Rays Gamma Rays Visible Light X-Rays

400 450 500 550 600 650 700 750 800

Ultraviolet Light

Infrared Light

Radar Television and FM Radio Shortwave Radio AM Radio

nm nm nm nm nm nm nm nm nm

Ultraviolet Violet Blue Green Yellow Orange Red Infrared

Radio Frequencies

Sonic Subsonic

Wavelength =

Speed of Light Frequency

From Whitaker, J.C., Light, vision, and photometry, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 154.

Typical Luminance Values Illumination Sun at zenith Perfectly reflecting, diffusing surface in sunlight Moon, clear sky Overcast sky Clear sky Motion-picture screen

Illuminance, ft-L 4.82 ¥ 108 9.29 ¥ 103 2.23 ¥ 103 9–20 ¥ 102 6–17.5 ¥ 102 10

From Whitaker, J.C., Light, vision, and photometry, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 166. After Fink, D.G., Television Engineering, 2nd ed., McGraw-Hill, New York, 1952.

© 2004 by CRC Press LLC

1587_Book.fm Page 181 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Resistivity of Selected Ceramics Resistivity, W · cm

Ceramic Borides Chromium diboride (CrB2) Hafnium diboride (HfB2) Tantalum diboride (TaB2) Titanium diboride (TiB2) (polycrystalline) 85% dense 85% dense 100% dense, extrapolated values

21 ¥ 10–6 10 – 12 ¥ 10–6 at room temp. 68 ¥ 10–6 26.5–28.4 ¥ 10–6 at room temp. 9.0 ¥ 10–6 at room temp. 8.7–14.1 ¥ 10–6 at room temp. 3.7 ¥ 10–6 at liquid air temp.

Titanium diboride (TiB2) (monocrystalline) Crystal length 5 cm, 39 deg. and 59 deg. orientation with respect to growth axis Crystal length 1.5 cm, 16.5 deg. and 90 deg. orientation with respect to growth axis Zirconium diboride (ZrB2)

6.6 + 0.2 ¥ 10–6 at room temp. 6.7 ± 0.2 ¥ 10–6 at room temp. 9.2 ¥ 10–6 at 20˚C 1.8 ¥ 10–6 at liquid air temp. 0.3–0.8

Carbides: boron carbide (B4C)

From Whitaker, J.C., Resistors and resistive materials, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 187.

Properties of Magnetic Materials and Magnetic Alloys

Material (Composition)

Initial Relative Permeability, mi/m0

Maximum Relative Permeability, mmax/m0

Coercive Force He, A/m (Oe)

Residual Field Br, Wb/m2 (G)

Saturation Field Bs, Wb/m2 (G)

Electrical Resistivity r ¥ 10–8 W · m

Uses

Soft Commercial iron (0.2 imp.) Purified iron (0.05 imp.) Silicon-iron (4 Si) Silicon-iron (3 Si) Silicon-iron (3 Si) Mu metal (5 Cu, 2 Cr, 77 Ni) 78 Peralloy (78.5 Ni) Supermalloy (79 Ni, 5 Mo) Permendur (50 Cs) Mn-Zn ferrite

250

9000

ª80 (1)

10,000

200,000

4 (0.05)

1500

7000

7500

55,000

—

0.77 (7700) —

2.15 (21,500)

10

2.15 (21,500)

10

Relays

20 (0.25)

0.5 (5000)

1.95 (19,500)

60

Transformers

8 (0.1)

0.95 (9500)

2 (20,000)

50

Transformers

116,000

4.8 (0.06)

1.22 (12,200) 2 (20,100)

50

Transformers

20,000

100,000

4 (0.05)

0.23 (2300)

0.65 (6500)

62

Transformers

8000

100,000

4 (0.05)

0.6 (6000)

1.08 (10,800)

16

Sensitive relays

100,000

1,000,000

0.16 (0.002) 0.5 (5000)

0.79 (7900)

60

Transformers

800

5000

160 (2)

1.4 (14,000)

2.45 (24,500)

1500

2500

16 (0.2)

—

0.34 (3400)

20 ¥ 106

2500

5000

8 (0.1)

—

0.32 (3200)

1011

Ni-Zn ferrite

7

Electromagnets Core material for coils

From Whitaker, J.C., Inductors and magnetic properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 216. After Plonus, M.A., Applied Electromagnetic, McGraw-Hill, New York, 1978.

© 2004 by CRC Press LLC

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1-182

CRC Handbook of Engineering Tables

Thermal Conductivity of Common Materials Material

Btu/(hu·ft·˚F)

W/(m·˚C)

242 228 172 140 30 0.67 0.11 0.015

419 395 298 242 52 1.67 0.19 0.026

Silver Copper Gold Beryllia Phosphor bronze Glass (borosilicate) Mylar Air

From Whitaker, J.C., Thermal properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 234.

Relative Thermal Conductivity of Various Materials As a Percentage of the Thermal Conductivity of Copper Material

Relative Conductivity

Silver Copper Berlox high-purity BeO Aluminum Beryllium Molybdenum Steel High-purity alumina Steatite Mica Phenolics, epoxies Fluorocarbons

105 100 62 55 39 39 9.1 7.7 0.9 0.18 0.13 0.05

From Whitaker, J.C., Thermal properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 235.

Variation of Electrical and Thermal Properties of Common Insulators As a Function of Temperature Parameters Thermal conductivity

Power dissipation2 Electrical resistivity3

Dielectric constant4 Loss tangent4 1

20˚C 1

99.5% BeO 99.5% Al2O3 95.0% Al2O3 Glass BeO BeO Al2O3 Glass BeO Al2O3 BeO

140 20 13.5 0.3 2.4 1016 1014 1012 6.57 9.4 0.00044

120˚C 120 17

2.1 1014 1014 1010 6.64 9.5 0.00040

260˚C

400˚C

538˚C

65 12

50 7.5

50 6

1.1 5 ¥ 1012 1012 108 6.75 9.6 0.00040

0.9 1012 1012 106 6.90 9.7 0.00049

0.7 1011 1011 7.05 9.8 0.00080

Heat transfer in Btu/ft2/hr/˚F Dissipation in W/cm/˚C 3 Resistivity in W-cm 4 At 8.5 GHz From Whitaker, J.C., Thermal properties, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, p. 239. 2

© 2004 by CRC Press LLC

1.

Schematic

Noninverting amplifier

R R

− +

−+

vi

2.

∞

+

−+

∞

R

−

i

+

i

4.

Adder

Ra −+

v

−+

vn

−+

Rin = • (ideally)

no =

∞ vo

−+

v

no =1 ni

Rb

R

i

R

i Rn in

+ − R Ï R no = - Ìn1 f + n2 f R R2 1 ÓÔ

R − +

∞

R2 (n - n1 ) R1 2

vo

+ −

+ L + nn

Rf ¸ ý Rn Ôþ

n1 - n2 i1 =

(R

a

R1

i2 =

n2 Ra + Rb

i1 =

n1 R1

i2 =

n2 R2

Rb + Rb )

R1 Ra = R2 Rb

M in =

nn Rn

1-183

© 2004 by CRC Press LLC

Special care of circuit 1

− R

v

Rin = • (ideally)

vo +

Difference amplifier −+

no R =1+ 2 ni R1

Special Requirements or Remarks

−

vi

v

Input Resistance or Input Currents or Voltages

vo +

Buffer −

3.

Circuit Gain or Variable of Interest

1587_Book.fm Page 183 Sunday, August 31, 2003 9:44 PM

No.

Type of Circuit

Electrical and Computer Engineering

Common Op-Amp Circuits

No. 5.

Type of Circuit Variable gain circuit

Circuit Gain or Variable of Interest

Schematic R/K

i + −

no = (2 Kx - K ) ni

R

R/(K−1)

−

vi

∞

+

xR!

vo

+

Input Resistance or Input Currents or Voltages i=

n1 Kni (1 - x ) + R3 R

Special Requirements or Remarks Potentiometer R3 adjusts the gain over the range –K to +K.

0 £ x £ 1, K > 1

−

R!

6.

Voltage-tocurrent converter −+

i

Current-tovoltage converter

R + −

+

v

−

+

∞

Ri

n1 R1

i=

ni R

The current through RL is independent of RL

vo + −

R ∞

is =

ni R

vo +

Ê RL ˆ Á1 - ˜ Ë R¯

n0 = ni (2RL /R). The current i is independent of RL. Circuit has wide band-with for RL R.

−

R

R

ii ii

© 2004 by CRC Press LLC

−

R L is vi

+

i=

n0 = Rii

R − +

∞

RL

vo + −

n=0

The voltage n0 is independent of RL and Ri

CRC Handbook of Engineering Tables

8.

Voltage-tocurrent converter with grounded load

−

R

vi

7.

RL

i

1587_Book.fm Page 184 Sunday, August 31, 2003 9:44 PM

1-184

Common Op-Amp Circuits (continued)

9.

Schematic

Current-tovoltage converter

v

−

R

R

Inverting amplifier with single supply

+ −

Noninverting amplifier with single supply

10 uF vi

+ −

vo

n=0

+ −

R"

no = 7.5 - ni

R2 +15

∞

R2 R1

R = 3.9 kW

vo +

−

0.1 uF

10 uF − + R1

− +

R!

+

R

11.

∞

Special Requirements or Remarks

R

−

R

+

R"

R4 R3

Input Resistance or Input Currents or Voltages

∞

+

10 uF +15 vi

R!

−

− + R1

−

∞

+

+

no = -2iR1

R

− i

10.

Circuit Gain or Variable of Interest

−

+15

+

Ê R ˆ no = 7.5 + ni Á1 + 2 ˜ Ë R1 ¯

R2 +5

∞

100 K +15

R = 3.9 kW

vo +

−

R

+ 1 uF −

R

1-185

© 2004 by CRC Press LLC

1587_Book.fm Page 185 Sunday, August 31, 2003 9:44 PM

No.

Type of Circuit

Electrical and Computer Engineering

Common Op-Amp Circuits (continued)

No.

Type of Circuit

12.

Integrator

Schematic

+ −

vi

+

DeBoo integrator

R

−

R

i + −

vi

+

−

∞

vo + −

no = 2V (0) +

R

∞

2 RC

vo + −

+

C

Ú

1 t n (t )dt RC 0 i V(0) is the initial voltage across the capacitor. RC is very large. no = -V (0) -

RC C R + v −

i

13.

Circuit Gain or Variable of Interest

Ú

t

0

ni (t )dt

Input Resistance or Input Currents or Voltages

Special Requirements or Remarks

i=

ni R

Negative feedback is required at DC. A large value of RC can be used or a feedback path can be established through an external circuit.

i=

ni no R 2R

One end of capacitor is physically grounded.

dni dt

Differentiators are usually avoided in the design of circuits because they accentuate noise.

R

v

−

14.

Differentiator

C

i

15.

Generalized impedance converter (GIC)

+

∞

− Z in =

Z

in

Z

2

i =C

vo +

∞ + −

Z

dni dt

Z − + ∞

3

Z

4

Z

5

Z 1Z 3 Z 5 Z 2Z 4

From Whitaker, J.C., Analog circuits, in The Resource Handbook of Electronics, CRC Press, Boca Raton, FL, 2001, pp. 267–269.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

vi

−

+ −

no = -RC

R

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Common Op-Amp Circuits (continued)

1587_Book.fm Page 187 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Wavelength (m) Electromagnetic frequency spectrum and associated wavelengths. (From Fay, P., Introduction, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 1-2.)

Modulation Schemes, Glossary of Terms Abbreviation

Description

ACSSB AM APK BLQAM BPSK CPFSK CPM DEPSK DPM DPSK DSB-AM DSB-SC-AM FFSK FM FSK FSOQ GMSK GTFM HMQAM IJF LPAM LRC LREC LSRC MMSK MPSK MQAM MQPR MQPRS MSK m-h OQPSK PM PSK QAM

Amplitude Companded Single SideBand Amplitude Modulation Amplitude Phase Keying modulation Blackman Quadrature Amplitude Modulation Binary Phase Shift Keying Continuous Phase Frequency Shift Keying Continuous Phase Modulation Differentially Encoded PSK (with carrier recovery) Digital Phase Modulation Differential Phase Shift Keying (no carrier recovery) Double SideBand Amplitude Modulation Double SideBand Suppressed Carrier AM Fast Frequency Shift Keying ∫ MSK Frequency Modulation Frequency Shift Keying Frequency Shift Offset Quadrature modulation Gaussian Minimum Shift Keying Generalized Tamed Frequency Modulation Hamming Quadrature Amplitude Modulation Intersymbol Jitter Free ∫ SQORC L-ary Pulse Amplitude Modulation LT symbols long Raised Cosine pulse shape LT symbols long Rectangularly EnCoded pulse shape LT symbols long Spectrally Raised Cosine scheme Modified Minimum Shift Keying ∫ FFSK M-ary Phase Shift Keying M-ary Quadrature Amplitude Modulation M-ary Quadrature Partial Response M-ary Quadrature Partial Response System ∫ MQPR Minimum Shift Keying multi-h CPM Offset (staggered) Quadrature Phase Shift Keying Phase Modulation Phase Shift Keying Quadrature Amplitude Modulation

© 2004 by CRC Press LLC

Remarks/Use Satellite transmission Broadcasting

Spread spectrum systems

Includes digital schemes NMT data and control Broadcasting, AMPS, voice AMPS data and control GSM voice, data, and control

A subclass of DSB-SC-AM Radio-relay transmission

Low capacity radio 4PSK ∫ QPSK

1587_Book.fm Page 188 Friday, September 26, 2003 12:10 PM

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CRC Handbook of Engineering Tables

Modulation Schemes, Glossary of Terms (continued) Abbreviation

Description

Remarks/Use

QAPSK QPSK QORC SQAM SQPSK SQORC SSB S3MQAM TFM TSI QPSK VSB WQAM XPSK p/4 DQPSK 3MQAM 4MQAM 12PM3

Quadrature Amplitude Phase Shift Keying Quadrature Phase Shift Keying ∫ 4 QAM Quadrature Overlapped Raised Cosine Staggered Quadrature Amplitude Modulation Staggered Quadrature Phase Shift Keying Staggered Quadrature Overlapped Raised Cosine Single SideBand Staggered class 3 Quadrature Amplitude Modulation Tamed Frequency Modulation Two-Symbol-Interval QPSK Vestigial SideBand Weighted Quadrature Amplitude Modulation Crosscorrelated PSK p/4 shift DQPSK with a = 0.35 raised cosine filtering Class 3 Quadrature Amplitude Modulation Class 4 Quadrature Amplitude Modulation 12 state PM with 3 bit correlation

Low capacity radio

Low and High capacity radio

TV Includes most digital schemes IS-54 TDMA voice and data

Source: 4U Communications Research Inc., 2000.06.10~00:09, c:/tab/modulat.tab From Kucar, A.D., Nomadic communications, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 2-33.

Radar Bands Band

Frequency Range

Principal Applications

HF VHF UHF L S

3–30 MHz 30–300 MHz 300–1000 MHz 1000–2000 MHz 2000–4000 MHz

C

4000–8000 MHz

X

8–12 GHz

Ku

12–18 GHz

Ka

27– 40 GHz

V

40–75 GHz

W

75–110 GHz

Over-the-horizon radar Long-range search Long-range surveillance Long-range surveillance Surveillance Long-range weather characterization Terminal air traffic control Fire control Instrumentation tracking Fire control Air-to-air missile seeker Marine radar Airborne weather characterization Short-range fire control Remote sensing Remote sensing Weapon guidance Remote sensing Weapon guidance Remote sensing Weapon guidance

From Belcher Jr., M.L. and Nessmith, J.T., Pulse radar, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 2-183.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Thermal Conductivities of Typical Metals (W/m K) at Room Temperature Metal

Thermal Conductivity

Silver Copper Gold Aluminum Brass Lead Kovar

419 395 298 156 101 32 17

From Golio, M., Materials properties — Metals, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 9-68.

Thermal Coefficient of Linear Expansion of Some of the Materials Used in Microwave and RF Packaging Applications (at Room Temperature, in 10–6/K) Material

Thermal Coefficient of Expansion Dielectrics

Aluminum nitride Alumina 96% Beryllia Diamond Glass-ceramic Quartz (fuzed)

4 6 6.5 1 4–8 0.54 Metals

Aluminum Beryllium Copper Gold Kovar Molybdenum Nickel Platinum Silver

23 12 16.5 14.2 5.2 5.2 13.3 9 18.9 Semiconductors

GaAs Silicon Silicon Carbide

5.9 2.6 2.2

From Golio, M., Materials properties — Metals, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 9-69.

© 2004 by CRC Press LLC

1587_Book.fm Page 190 Friday, September 26, 2003 12:10 PM

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CRC Handbook of Engineering Tables

Properties of Some Typical Engineering Insulating Materials Material Vacuum Air Glass Vycor 7910 Glass Corning 0080 Al2O3 Teflon (PTFE) Arlon 25N circuit board Epoxy-glass circuit board Beryllium oxide Diamond PZT (lead zirconium oxide) Undoped silicon TaO5 Quartz (SiO2) Mica (Ruby) Water

k

Loss

Frequency

Resistivity

1.00 1.0006 3.8 6.75 8.5 2.0 3.28 4.5 7.35 5.58 ~1000 11.8 28 3.75–4.1 6.5–8.7 78.2

0 0 9.1*10–4 5.8*10–2 10–3 2*10–4 2.5*10–3

All

Zero

1 MHz 1 MHz 1 MHz

1017

1016

2*10–4 3.5*10–4 0.04

1 MHz

From Golio, M., Materials properties — Metals, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 9-72.

Selected Material Properties of Semiconductors for Microwave and RF Applications Property

Si

Atoms/cm3 Atomic weight Breakdown Field (V/cm)

5.0 ¥ 1022 28.09 3 ¥ 105 32

Crystal structure Density (g/cm3) Dielectric constant

Diamond 2.328323 11.823

Effective mass m*/m0 Electron Electron Affinity, eV Energy Gap (eV) at 300 K

1.1

Intrinsic carrier concentration (cm–3) Lattice constant (Angstroms) Linear Coeff. of thermal expansion (10–6 K–1) Melting point (K) Electron mobility (cm2/V-S) µm

4.0531 1.10723 1.45 ¥ 1010 23 5.43131 2.4923 168523 190023

Holes mobility µp (cm2/V-S)

50023

Optical phonon energy (eV) Refractive index

0.063 eV31 3.4223

Resistivity, intrinsic (W-cm)

100031

Specific heat (J/kg°K) Thermal conductivity at 300°K (Watt/cm°K)

70223 1.2423

SiC

InP

GaAs

3.95 ¥ 1022 40.1 20 ¥ 104 3C-SiC27 30 ¥ 105 4H-SiC27 Zincblende 4.78723 9.7517 9.6618 0.37 3C-SiC19 0.45 6H-SiC20 — 2.403 3C-SiC23 3.101 6H-SiC23 3 ¥ 106 3C-SiC21 1015–1016 6H-SiC22 4.359627 5.4822

4.43 ¥ 1022 72.90 5 ¥ 105 32

4.96 ¥ 1022 72.32 6 ¥ 105

Zincblende 5.31633 12.423

Zincblende 6.123 12.523

Wurtzite

0.06723

0.06823

0.2235,36

4.3831 1.2931

4.0731 1.3531

3.434 3.3437

1.6 ¥ 107 23

1.8 ¥ 106 23

3-6 ¥ 109 23

5.86031 4.623

5.65131 5.423

3.19038 5.627

133531 460023

151131 880023

— 100039

15023

40023

3039

0.4331 3.131

0.3531 3.6631

8.2 ¥ 107 31

3.8 ¥ 108 31

.91240 2.741 (at band edge) >1013 27

31031 0.7732

32532 0.5631

847.3942 1.343

307023 1000 3C-SiC24 600 6H-SiC24 40 3C-SiC24 40 6H-SiC24 — 2.65 3C-SiC25 2.72 6H-SiC26 150 3C-SiC27 >1012 4H-SiC27 64028 3.2 3C-SiC29 4.9 6H-SiC30

GaN 41.87 >10 ¥ 105

935

From Harris, M., Materials properties — semiconductors, in The RF and Microwave Handbook, Golio, M., Ed., CRC Press, Boca Raton, FL, 2001, p. 9-105.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Channel Designations for VHF and UHF Television Stations in the U.S. Channel Designation

Frequency Band (MHz)

Channel Designation

Frequency Band (MHz)

Channel Designation

Frequency Band (MHz)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

54–60 60–66 66–72 76–82 82–88 174–180 180–186 186–192 192–198 198–204 204–210 210–216 470–476 476–482 482–488 488–494 494–500 500–506 506–512 512–518 518–524 524–530 530–536 536–542 542–548 548–554 554–560 560–566

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

566–572 572–578 578–584 584–590 590–596 596–602 602–608 608–614 614–620 620–626 626–632 632–638 638–644 644–650 650–656 656–662 662–668 668–674 674–680 680–686 686–692 692–698 698–704 704–710 710–716 716–722 722–728

57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

728–734 734–740 740–746 746–752 752–758 758–764 764–770 770–776 776–782 782–788 788–794 794–800 800–806 806–812 812–818 818–824 824–830 830–836 836–842 842–848 848–854 854–860 860–866 866–872 872–878 878–884 884–890

From Whitaker, J.C., Applications of RF technology, in The RF Transmission Systems Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-16.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Radar Frequency Bands Name VHF UHF P-bandb

Frequency Range

Radiolocation Bands based on ITU Assignments in Region II

30–300 MHz 300–1,000 MHz 230–1,000 MHz

L-band S-band

1,000–2,000 MHz 2,000–4,000 MHz

C-band X-band Ku-band

4,000–8,000 MHz 8,000–12,500 MHz 12.5–18 GHz

K-band Ka-band Millimeter

18–26.5 GHz 26.5–40 GHz >40 GHz

137–144 MHz 216–225 MHz 420–450 MHz 890–940a MHz 1,215–1,400 MHz 2,300–2,550 MHz 2,700–3,700 MHz 5,255–5,925 MHz 8,500–10,700 MHz 13.4–14.4 GHz 15.7–17.7 GHz 23–24.25 MHz 33.4–36 MHz

a

Sometimes included in L-band. Seldom used nomenclature. From Whitaker, J.C., Applications of RF technology, in The RF Transmission Systems Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-31. Originally from Fink, D. and Christiansen, Eds., Electronics Engineers’ Handbook, 3rd ed., McGraw-Hill, New York, 1989, Table 302. IEEE standard 521–1976. b

Common-Carrier Microwave Frequencies Used in the U.S. Band (GHz) 2

Allotted Frequencies (MHz)

4

2110–2130 2160–2180 3700–4200

6 11 18 30

5925–6425 10,700–11,700 17,700–19,700 27,500–29,500

Bandwidth (MHz)

Application

20

Limited

20

Major long-haul microwave relay band Long and short haul Short haul Short haul, limited use Short haul, experimental

500 500 1000 2000

From Whitaker, J.C., Applications of RF technology, in The RF Transmission Systems Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-35.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

Comparison of Amplitude Modulation Techniques Modulation Scheme

Advantages

Disadvantages

DSB-SC

Good power efficiency. Good low-frequency response.

DSB+C (AM)

Easier to generate than DSB-SC, especially at high-power levels. Inexpensive receivers using envelope detection. Excellent spectrum efficiency.

SSB-SC

SSB+SC

Good spectrum efficiency. Low receiver complexity.

VSB-SC

Good spectrum efficiency. Excellent low-frequency response. Transmitter easier to build than for SSB. Good spectrum efficiency. Good low-frequency response. Inexpensive receivers using envelope detection. Good low-frequency response. Good spectrum efficiency.

VSB+C

QAM

Comments

More difficult to generate than DSB+C. Detection requires coherent local oscillator, pilot, or phase-locked loop (PLL). Poor spectrum efficiency. Poor power efficiency. Poor spectrum efficiency. Poor lowfrequency response. Exhibits threshold effect in noise. Complex transmitter design. Complex receiver design (same as DSB-SC). Poor lowfrequency response.

Used in commercial AM.

Used in military communication systems, and to multiplex multiple phone calls onto longhaul microwave links.

Poor power efficiency. Complex transmitters. Poor lowfrequency response. Poor noise performance. Complex receivers (same as DSB-SC).

Poor power efficiency. Poor performance in noise.

Used in commercial TV.

Complex receivers. Sensitive to frequency and phase errors.

Two SSB signals may be preferable.

From Kubichek, R., Amplitude modulation, in The RF Transmission Systems Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 3-14.

Representative Specifications for Various Types of Flexible Air-Dielectric Coaxial Cable Average Power

Attenuationa

Cable Size (in.)

Maximum Frequency (MHz)

Velocity (%)

Peak Power 1 MHz (kW)

100 MHz (kW)

1 MHz (kW)

100 MHz (dB)

1 MHz (dB)

1 5/8 3 4 5

2.7 1.64 1.22 0.96

92.1 93.3 92 93.1

145 320 490 765

145 320 490 765

14.4 37 56 73

0.020 0.013 0.010 0.007

0.207 0.14 0.113 0.079

a

Attenuation specified in dB/100 ft. From Whitaker, J.C., Coaxial transmission lines, in The RF Transmission Systems Handbook, Whitaker, J.C., Ed., CRC Press, Boca Raton, FL, 2002, p. 12-7.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Four drivers of change in telecommunications. (From Wery, B., Growth strategies for telecommunications operators, in The Telecommunications Handbook, Terplan, K. and Morreale, P., CRC Press, Boca Raton, FL, 2000, p. 1-35.)

Summary and Comparison of Second-Generation TDMA-Based System Parameters

Access method Carrier spacing Users per carrier Modulation Voice codec Voice frame Channel code Coded bit rate TDMA frame duration Interleaving ACCH Handoff

Europe (GSM)

North America (IS-54/136)

Japan (PDC)

TDMA 200 kHz 8 (16) GMSK RPE 13 kbps 20 ms Convolutional 22.8 kbps 4.6 ms 40 ms Extra slot MAHO

TDMA 30 kHz 3 (6) p/4-DQPSK VSELP 7.95 kbps 20 ms Convolutional 13 kbps 20 ms 27 ms In slot MAHO

TDMA 25 kHz 3 (tbd) p/4-DQPSK VSELP 6.7 kbps 20 ms Convolutional 11.2 kbps 20 ms 27 ms In slot MAHO

From Zori, M., Mobile and wireless telecommunications networks, in The Telecommunications Handbook, Terplan, K. and Morreale, P., Eds., CRC Press, Boca Raton, FL, 2000, p. 2-48.

© 2004 by CRC Press LLC

1587_Book.fm Page 195 Sunday, August 31, 2003 9:44 PM

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Electrical and Computer Engineering

Some Milestones for Multimedia 1982 1984 1986 1987 1988 1990 1992 1994 1995

1998

Introduction of compact disk — consumer audio Introduction of CD-ROMs; Macintosh GUIs Initial CD-I (Compact Disk Interactive) specification; Microsoft Windows DVI (digital video interactive) technology announced Erasable optical disks; initial ATM standards MPC (multimedia PC) standard; IMA (Interactive Multimedia Association) Compatibility Project; commercial multimedia applications ATM-based LAN development (155 Mbps to the desktop); FDDI 100 Mbps connections possible for less than $1000 Wide-area ATM networks; networked multimedia systems and applications New low-speed voice compression standards (e.g., G.729, G.723.1, G.729A) and other interoperability standards for desktop multimedia are developed; also, DVD launched, H.323 developed Increased penetration of multimedia in corporate America for “mission-critical” applications; by then, IP had become ubiquitous in intranets and in the Internet; multimedia over LANs sees penetration

From Minoli, D., Minoli, E., and Sookchand, L., Video communications, in The Telecommunications Handbook, Terplan, K. and Morreale, P., Eds., CRC Press, Boca Raton, FL, 2000, p. 4-8.

Comparison of Interconnect Characteristics for Al and Cu Material

Specific Resistance (mW-cm)

Melting Point (°C)

Al Cu

2.66 1.68

660 1073

From Shenai, K. and McShane, E., VLSI technology: A system perspective, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-8.

Comparison of High-Permittivity Constant Materials for DRAM Cell Capacitors Material

Dielectric Constant

Minimum Equivalent Oxide Thickness (nm)

NO Ta2O5 BST

7 20–25 200–400

3.5 to 4 2 to 3 ?

From Shenai, K. and McShane, E., VLSI technology: A system perspective, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-11.

© 2004 by CRC Press LLC

1587_Section_1d.fm Page 196 Wednesday, October 8, 2003 4:27 PM

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CRC Handbook of Engineering Tables

Summary of Some Architectures and Applications Possible from a Molecular Computing System Mechanisms and Architectures Light-energy transducing proteins Light-energy transducing proteins (with controlled switching) Optoelectronic transducing Evolutionary structures

Applications Biosensors Organic memory storage Pattern recognition and processing Adaptive control

From Shenai, K. and McShane, E., VLSI technology: A system perspective, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 1-19.

Comparison of Selected Important Semiconductors of Major SiC Polytypes with Silicon and GaAs Property Bandgap (eV) Relative dielectric constant Breakdown field ND = 1017 cm–3 (MV/cm) Thermal conductivity (W/cm-K) Intrinsic carrier concentration (cm–3) Electron mobility @ ND =1016 cm–3 (cm2/V-s) Hole mobility @ NA =1016 cm–3 (cm2/V-s) Saturated electron velocity (107 cm/s) Donor dopants and shallowest ionization energy (meV) Acceptor dopants and shallowest ionization energy (meV) 1998 Commercial wafer diameter (cm)

Silicon

GaAs

4H-SiC

6H-SiC

3C-SiC

1.1 11.9 0.6

1.42 13.1 0.6

3.2 9.7 //c-axis: 3.0

2.3 9.7 >1.5

1.5 1010 1200

0.5 1.8 ¥ 106 6500

420

320

3–5 ~10–7 //c-axis: 800 ^c-axis: 800 115

3.0 9.7 // c-axis: 3.2 ^c-axis: >1 3–5 ~10–5 //c-axis: 60 ^c-axis: 400 90

1.0 P: 45 As: 54 B: 45

1.2 Si: 5.8

2 N: 45 P: 80 Al: 200 B: 300 5

2 N: 85 P: 80 Al: 200 B: 300 5

2.5 N: 50

30

Be, Mg, C: 28 15

3–5 ~10 750 40

Al: 270 None

From Neudeck, P.G., SiC technology, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 6-3.

© 2004 by CRC Press LLC

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Electrical and Computer Engineering

MEMS Processing Technologies

Process

Physical Dimension Range/ Aspect Ratio

Bulk micromachining

mm-cm/1:400

Single-crystal silicon, GaAs glass etching

Reactive ion etch Laser ablation Electrodischarge machining Precision mechanical cutting Focussed ion beam machining Chemical etching

mm-mm/1:100 1-100 mm/1:50 2 mm-mm/*

Ultrasonic machining

25 mm-mm/*

Materials

Etch Stop Techniques Through-put

Cost

Subtractive processes High

Low

Wide range of materials Various Si, metals

Dopant-selective electrochemical Buried layer Buried layer Timed Timed

Low Low Low

High High Med

nm-cm/*

PMMA

Tool position

Low

High

nm-mm

various

Timed

Low

High

mm/1:10

Metals, semiconductors, insulators Glass, ceramic, semiconductor, metals

Timed

High

Low

Tool position

Moderate

Moderate

Moderate

High

High

Moderate

Low Low Low High High High High

High Very high High Low Moderate Low Low

Additive processes Physical vapor depositon Chemical vapor deposition

Wide range of materials Surface micromachining

Electron beam or thermal evaporation/sputtering LPCVD of polysilicon/PSG or sputtered aluminum/ photoresist

Laser-assisted CVD Molecular beam epitaxy LIGA Electroplating into a mold:

nm-mm nm mm-cm mm-mm mm-mm/1:10 mm-mm mm-mm

Various Semiconductors PMMA Cu, Ag, Au, Fe, permalloy Polyimide SU-8 Thick photoresist

— Selectivity of sacrificial etch to sacrificial layer to structural layer — — — — — — —

* Function of total geometry. From Hesketh, P.J., Micromachining, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 10-3.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Materials Properties of LPCVD Deposited MEMS Materials Material

Growth Conditions Film Thickness

Property

Value

Comments

Polysilicon 3 mm

MUMPS process Thick polysilicon 1100°C, SiH4/B2H6 or 610°C, Sitty Thin polysilicon 565°C, SiH4, 620°C, SiH4, 100 mTorr CMOS

Young’s modulus Tensile strength Young’s modulus Fracture toughness As-deposited residual stress Young’s modulus Tensile strength Young’s modulus Intrinsic stress Intrinsicties

2.5-10 mm 1 mm 0.33 mm

169 ± 6.15 GPa — 1.20 ± 0.15 GPa 150 ± 3- GPa 2.3 ± 0.1 Undoped film MPa ÷m 280 MPa

168 ± 7 GPa 2.11 ± 0.10 GPa 162.8 ± 6 GPa –350 ± 12 GPa 162.8 ± 6 GPa

— — As deposited After 1000°C anneal

Silicon Nitride Standard process 800°C, SiCl2H2lNH3 Si-rich, variable 800, 850°C 200, stoichiometry 410 mTorr SiCl2H2/ NH3 Silicon-rich, 850°C 200 mTorr variable SiCl2H2/NH3 stoichiometry PECVD

— ~0.1 mm 0.25–0.45 mm

Intrinsic stress Intrinsic stress

~1.2 GPa (See Figure 10.10)

—

Young’s modulus

(190 GPa)

From Hesketh, P.J., Micromachining, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 10-18.

Wafer Bonding Techniques Bonding Technique Anodic bonding Siliconsilicon Borosilicate glass Eutectic Solder

Glass frit

Materials Silicon/7740 Pyrex glass Si-Si SiO2-Si and SiO2/SiO2 Si/Si02 and Si3N4 Si-Au-SiO2 SiO2Pb/Sn/AgSiO2 SiO2-glass Ag mixture-SiO2

Surface Treatment Clean Hydrophobic Hydrophilic

Clean and oxide-free Needs solder flux Clean

Process

Time

Bond Strength/Comments

350–450°C ~500–1000V 500–1100

~1–10 min

450

30 min

1–3 MPaa/uniform reliable hermetic bond formed Difficult to avoid voids unless processed at higher temperatures —

~350

—

250–400

min

~350

hrs

148 MPab/Nonuniform bonding area Large difference in thermal expansion coefficient can lead to mechanical fracture Difficult to form thin layers

From Hesketh, P.J., Micromachining, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 10-32.

© 2004 by CRC Press LLC

Fabrication Process

Drive

Contact On-Resistance

Maximum Current

Off- Resistance/ Breakdown voltage

Switching Time

Insertion Loss

—

—

<20 ms

—

—

<1 ms

—

—

0.1 db at 4 GHz

—

—

—

0.3 dB at 20 GHz

>100 V

—

—

Electrostatic <3 W

Automated test equipment

Bulk micromachining and anodic bonding

<100 V

Switching

CMOS compatible

1-10 V with DC bias of 30-54 V

RF to microwave

Surface micromachining

28 V at >50 nA

RF to microwave

Surface micromachining on GaAs

~30 V

Switching

Electroplated metal films

24 V

0.05 W (initial)

5 mA (single contact); 150 mA (multiple contacts)

Small-signal RF

Surface micromachining

20–100 V [10 mW]

10–80 W

1 mA

—

2.6– 20 ms

—

Switching

MUMPS

7-12 V

2.4 W

80 mA

—

—

—

RF impedance matching

Surface micromachining in polysilicon

12 mW

2.1–35.6 W

>1 mA

>1012 W 400 V

<0.5 ms

—

—

0.5–2.5 ms

—

— ~0.22 W

200 mA

—

Thermal

Magnetic Electrical control circuits

Polyimide mold and electroplated metals

180 mA (33 mW)

0.022 W

1.2 A

From Hesketh, P.J., Micromachining, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 10-46.

1-199

© 2004 by CRC Press LLC

1587_Section_1d.fm Page 199 Friday, September 26, 2003 5:15 PM

Application

Electrical and Computer Engineering

Microrelays

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CRC Handbook of Engineering Tables

Electronic Packaging Requirements Speed • Large bandwidth • Short inter-chip propagation delay

Size • Compact size

Thermal and Mechanical • High heat removal rate • A good match between the thermal coefficients of the dice and the chip carrier

Test and Reliability • Easy to test • Easy to modify • Highly reliable • Low cost

Pin Count and Wireability • Large I/O count per chip • Large I/O between the first and second level package

Noise • Low noise coupling among wires • Good-quality transmission line • Good power distribution

From Khandelwal, P. and Shenai, K., Microelectronics packaging, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 11-2.

Thermal and Electrical Properties of Materials Used in Packaging Metals Coefficient of Thermal Expansion (CTE) (10–6 K–1)

Thermal Conductivity (W/cm-K)

Specific Electrical Resistance 10–6W-cm

23 19 17 5 4.6

2.3 4.3 4.0 1.4 1.7

2.8 1.6 1.7 5.3 5.3

Insulating Substrates

Coefficient of Thermal Expansion (CTE) (10–6 K–1)

Thermal Conductivity (W/cm-K)

Dielectric Constant

Alumina (Al2O3) Beryllia (BeO) Silicon carbide (SiC) Silicon dioxide (SiO2)

6.0 6.0 3.7 0.5

0.3 2.0 2.2 0.01

9.5 6.7 42 3.9

Semiconductors

Coefficient of Thermal Expansion (CTE) (10–6 K–1)

Thermal Conductivity (W/cm-K)

Dielectric Constant

Silicon Germanium Gallium arsenide

2.5 5.7 5.8

1.5 0.7 0.5

11.8 16.0 10.9

Metals Aluminum Silver Copper Molybdenum Tungsten

Substrates

Semiconductors

From Khandelwal, P. and Shenai, K., Microelectronics packaging, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 11-6.

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Electrical and Computer Engineering

Some Properties of Ceramic Packaging Materials Property 3

Density (g/cm ) CTE (ppm/K) TC (W/cm-K) Dielectric const. Loss tangent

BeO

AlN

Al2O3 (96%)

Al2O3 (99.5%)

2.85 6.3 285 6.7 0.0001

3.28 4.3 180 10 0.0005

3.75 7.1 21 9.4 0.0001

3.8 7.1 25.1 10.2 0.0001

From Khandelwal, P. and Shenai, K., Microelectronics packaging, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 11-6.

Interconnect Technologies Interconnection Type

Line Width (mm)

Line Thickness (mm)

Line Resistance (ohm/cm)

Maximum Length (cm)

On-chip Thin-film Ceramic Printed circuit board Shielded cables

0.5–2 10–25 75–100 60–100 100–450

0.7–2 5–8 16–25 30–50 35–450

100–1000 1.25–4 0.4–0.7 0.06–0.08 0.0013–0.033

0.3–1.5 20–45 20–50 40–70 150–500

From Nakhla, M.S., Interconnect modeling and simulation, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 17-5.

Voltage Buffer Performance Power Supply DC gain (no load) Output impedance HD2 (Vin = 200 mVrms)

IM3 (Vin=200 mVrms) Slew rate Input referred noise

5V

Dissipation

5 mW

–3.3dB 75W 1 MHz 10 MHz 20 MHz 20 MHz, Df = 200 KHz (Load = 10 pF) 10 nV Hz

Bandwidth Min. load resistance –50 dB –49 dB –45 dB –53 dB + 130 V/ms

140 MHz 10 KW

–72 V/ms

Note: Load = 10 kW/10 pF, except for slew rate measurement. From Toumazou, C. and Payne, A., High-frequency amplifiers, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 21-7.

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Embedded Memory Technologies and Applications Embedded Memory Technology ROM

E/E2prom SRAM

DRAM

Compatibility to Logic Process

Applications

Diffusion, Vt, Contact programming High compatibility to logic process High-voltage device, tunneling insulator required 6-Tr/4-Tr single/double poly load cells Wide range of compatibility Gate capacitor/4-T/planar/ stacked/trench cells Wide range of compatibility

Microcode, program storage PAL, ROM-based logic

Program, parameter storage, sequencer, learning machine High-speed buffers, cache memory

High-density, high bit rate storage

From Wu, C.-Y., Embedded memory, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 50-4. Originally from Iizuda, T., Embedded memory: A key to highperformance system VLSIs, Proc. of 1990 Symp. on VLSI Circuts, pp. 1–4, June 1990.

Recent high-speed ADC applications. (From Song, B.-S., Nyquist-rate ADC and DAC, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 54-5.)

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Electrical and Computer Engineering

Microprocessor Statistics Part Name

# Transistors (millions)

Frequency (MHz)

Die Size (mm2)

Technology (µm)

Alpha 21264 PowerPC PA-8000 Ultrasparc-I Pentium II

15.2 6.35 3.8 5.2 7.5

600 250 250 167 450

314 66.5 338 315 118

0.35 0.3 0.5 0.5 0.25

Manufacturer Compaq IBM HP Sun Intel

From Karnik, T., Microprocessor layout method, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 62-1.

Comparing Electrical Parameters for BJT/HBT vs. FET Parameter Input impedance Z

Turn-on Voltage

Transconductance Current gain

Unity current gain cutoff frequency fT Maximum frequency of oscillation fmax Feedback capacitance 1/f Noise Thermal behavior Other

BJT/HBT

FET

Low Z due to forward-biased junction; large diffusion capacitance Cbe Forward voltage VBE highly repeatable; set by thermodynamics High gm [ = IC/(kT/q)] b (or hFE) = 50 to 150; b is important due to low input impedance fT = gm/2pCBE is usually lower than for FETs fmax = [fT/(8prb’Cbc]½

High Z due to reverse biased junction or insulator; small depletion layer capacitance Cgs Pinch-off voltage VP not very repeatable; set by device design Low gm [@ vsatCgs] Not meaningful at low frequencies and falls as 1/w at high frequencies fT = gm/2pCgs ( = vsat/2pLg) higher for FETs fmax = fT [rds/Rin]½

Cbc large because of large collector junction Low in BJT/HBT

Usually Cgd is much smaller than Cbc Very high 1/f noise corner frequency No thermal runaway

Thermal runaway and second breakdown

Backgating is problem in semiinsulating substrates

From Estreich, O.B., Compound semiconductor devices for digital circuits, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 70-13.

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Status of Conventional and Renewable Power Sources Conventional Coal, nuclear, oil, and natural gas Fully matured technologies Numerous tax and investment subsidies embedded in national economies Accepted in society under the ‘grandfather clause’ as necessary evil

Renewables Wind, solar, biomass geothermal, and ocean Rapidly developing technologies Some tax credits and grants available from some federal and/or state governments Being accepted on its own merit, even with limited valuation of their environmental and other social benefits

From Patel, M.R., Wind and Solar Power Systems, CRC Press, Boca Raton, FL, 1999, p. 3.

Benefits of Using Renewable Electricity Traditional Benefits Monetary value of kWh consumed U.S. average 12 cents/kWh U.K. average 7.5 pence/kWh

Nontraditional Benefits Per Million kWh consumed Reduction in emission 750–1000 tons of CO2 7.5–10 tons of SO2 3–5 tons of NOx 50,000 kWh reduction in energy loss in power lines and equipment Life extension of utility power distribution equipment Lower capital cost as lower capacity equipment can be used (such as transformer capacity reduction of 50 kW per MW installed)

From Patel, M.R., Wind and Solar Power Systems, CRC Press, Boca Raton, FL, 1999, p. 3.

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Electromagnetic Radiation and Stable Elementary Particles Charge

Mass

Examples or Sources

Alpha particle Electron Gamma ray Neutrino

+2 –1 0 0

4 1/1836 0 0

Neutron† Photon Positron Proton X-ray

0 0 +1 +1 0

1 0 1/1836 1 0

Alpha “rays” emitted by heavy radioisotopes; cosmic rays Ionosphere; atoms of matter; beta rays from radioactive elements Radioactive decay; nuclear transitions; nuclear reactors; cosmic rays Emitted by sun, stars, nuclear reactors. Accompanies radioactive emission (beta decay) Vicinity of planets and sun; atomic nuclei; nuclear reactors All light flux from sun, stars, etc.; radiation belts Fast anti-electrons emitted from radioactive materials Cosmic rays; radiation belts; atomic nuclei Radiation belts; solar radiation; high-voltage vacuum tubes

†

Secondary particle; not stable; life about 1,000 seconds. Electrons are negatively-charged “atoms of electricity”; in ordinary matter they form an ordered “cloud” surrounding the heavy, positively-charged atomic nuclei. Photons are electromagnetic waves; they carry energy in discrete quantity, proportional to the frequency of the associated wave. Beta decay involves the emission of an electron or positron. (The terms beta-ray and beta-particle are sometimes used.) Gamma rays consist of high-energy photons (electromagnetic waves); they are emitted in radioactive decay. X-rays consist of photons emitted in the acceleration (deceleration) of charged particles, as when highspeed electrons strike a heavy, metal target. Atomic nucleus is the heavy core of the atom, consisting of protons and neutrons. The number of protons is called the atomic number. The number of neutrons plus protons is called the mass number. The energy required to separate all of the neutrons and protons of the nucleus is called the binding energy. Radioactive nucleus is one that spontaneously changes by radioactive decay, electron capture, or fission. It becomes ultimately transformed into a different kind of nucleus. Isotopes of an element contain the same number of protons but slightly different numbers of neutrons. They are chemically indistinguishable, except by very much refined procedures and in some biological reactions. Ions are electrically-charged atoms. If the negative electron charges just balance the total positive charge of the nucleus, the atom is neutral; with more electrons the atom becomes a negative ion, and with fewer electrons it becomes a positive ion. Fission is the breakup of nuclei into fragments that are themselves nuclei. Mass is usually lost; hence energy is released. Fusion is the coalescing of two nuclei to form a heavier one. From Bolz, R.E. and Tuve, G.L., Electromagnetic radiation, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 205.

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Electromagnetic Frequency Spectra Ranges and Applications Typical Frequency, cps†

Application or Common Name

Typical Wavelength‡

Approximate Frequency Range, cps†

Electric a-c power Eddy-current heating (metals) Servo and instrument power Audio frequency standard Induction furnace power

60 60 400 440 2000

5 ¥ 106 m 5 ¥ 106 m 7.5 ¥ 105 m 6.8 ¥ 105 m 1.5 ¥ 105 m

25–60 50–1000 100–1000 440 and 600 500–3000

R-F heating of metals Power-line communication Maritime and radio beacon Radio broadcasting Shortwave radio

10 kc 30 kc 400 kc 1000 kc 20 mc

3 ¥ 104 m 104 m 750 m 300 m 15 m

1 kc–1 mc wide 20–550 kc 550–1600 kc 3–300 mc

27 mc 40 mc 100 mc 180 mc 500 mc

11 m 7.5 m 3m 1.67 m 60.0 cm

— 10–200 mc 91–108 mc 54–216 mc 200–1200 mc

Television (channels 14–83) Tracking stations Intercity relay Radar Super high frequency

800 mc 960 mc 2000 mc 10,000 mc 20,000 mc

37.5 cm 31.3 cm 15.0 cm 3.0 cm 1.5 cm

470–890 mc 440–5600 mc 1200–20,000 mc 1200–20,000 mc 3000–30,000 mc

Far infrared (germanium detector) Infrared (PbS detector) Infrared heaters Night infrared searchlight Near infrared photography

3 ¥ 1013 1.25 ¥ 1014 1.5 ¥ 1014 3 ¥ 1014 3.75 ¥ 1014

10 mm 2.4 mm 2 mm 1 mm 0.8 mm

Cadmium red line Yellow (max visual) Solar max intensity Germicidal lamps—ultraviolet Soft X-rays

4.65 ¥ 1014 5.3 ¥ 1014 7.1 ¥ 1014 1015 1018

.64385 mm .56 mm .42 mm .3 mm 3Å

Microwave diathermy Dielectric heating and drying F-M radio Television (channels 2–13) Radar

1020 1021 3 ¥ 1023

Hard X-rays Gamma rays Cosmic rays

.03 Å .003 Å 10–5 Å

†

The name hertz is widely used by electrical engineers for cycles per second. Units: 1 meter = 100 cm = 39.37 in. = 106 micrometers (mm) = 1010 angstrom units (Å). Velocity = 186,290 mi/s = 2.99793 ¥ 108 m/s = frequency ¥ wavelength. ‡

Visible Spectrum — Representative Colors Color

Frequency

Wavelength

Violet Blue Green Yellow Orange Red

7.3 ¥ 1014 6.38 ¥ 1014 5.75 ¥ 1014 5.17 ¥ 1014 5.0 ¥ 1014 4.6 ¥ 1014

0.41 0.47 0.52 0.58 0.60 0.65

From Bolz, R.E. and Tuve, G.L., Electromagnetic radiation, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 206.

© 2004 by CRC Press LLC

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Dynamic Response of RCL System to a Step-Change Input With little or no damping a step-change input will cause an oscillatory RCL system to respond at its natural frequency fn. The oscillations decrease with time, and this decay may be defined in terms of the logarithmic decrement or exponential decay ratio. At critical damping the response is similar to that of a linear system subjected to the same step input. With large amounts of damping, the response is non-oscillatory 1.8 0.1

1.6 0.2

1.4 0.1 0.4 1.2

Amplitude

0.2 0.7

0.4

1.0 1.0

0.4

1.5

0.8

0.2 2.0 0.6 0.1

0.4

0.2

0 0

0.5/fn

1.0/fn

1.5/fn

2.0/fn

Time Response of a simple oscillatory system to a unit step input. Damping ratios, z = c/cc, from 0.1 to 2.0. From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 598. Originally from Tuve, G.L. and Domholdt, L.C., Engineering Experimentation, McGraw-Hill, New York, 1966.

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CRC Handbook of Engineering Tables

Amplitude Response — Second-Order System If the input frequency is low, the response of an oscillatory system will almost duplicate the input. At the higher frequencies the response will depend on the ratio of actual damping c to critical damping cc. For the electrical system critical damping is 2 L § C ; for the mechanical mass-spring-damper system the critical damping is 2 km, where k is the spring constant and m is the mass. These figures show the response of a simple oscillatory (RCL) system to a sine-wave input, with damping ratios c/cc from 0.1 to 20.0. 0.1 db 20 10

0.2

0.3

0.4

0.6

0.8 1

3

4

6

0

8 6 5

0.1

4 10

2

0.14

3

0.2

2

0.3 0.4

0

0.5 0.6 0.7

1 0.8

0.8 0.9 1

0.6 0.5 0.4 3

0.3

2

1st order

4 5

0.2 9

Amplitude rato (gain)

10 0.1 20

0.08 0.06 0.05 0.04 0.03 0.02 0.015 0.01 0.008 0.006 0.005 0.004 0.003 0.002 0.0015

0.001 0.1

0.15 0.2

0.3 0.4 0.50.6

0.8

2 3 Frequency ratio f/fn

4

6

8 10

20

30 40

From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 599.

© 2004 by CRC Press LLC

This figure shows phase lag vs. frequency ratio for a second-order system (RCL) in response to a sine-wave input (semilog coordinates). Damping ratios of 0.1 to 20.0 are given. 0° −10° −20°

0.5 0.7 1 0.9

−30° −40°

2

−50°

Phase lag

0.1 0.2 0.3

−60°

9

−70°

10

7

5

3 1st order

20

−80° −90° 20

−100°

10

−110°

7 9

−120°

5

−130° −140° −150° 0.1

−170° 0.015 0.02

0.03

0.06

0.07

0.1

0.015 0.2

0.3

0.5

0.7

1

2

0.7 0.5

0.3

−160° −180° 0.01

3

0.9 1

0.2

0.015

2

3

5

7

10

0.015 20

30

50

70

100

Frequency ratio f/fn

From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 600.

© 2004 by CRC Press LLC

1-209

Reference For large-scale curves giving values for damping ratios to 20, frequency ratios to 40, and gains as low as 0.001, see Handbook of the Engineering Sciences, J.H. Potter, Ed., Vol. 2, D. Van Nostrand Co., 1967. pp. 786–787.

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Phase Response—Second-Order System

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Frequency-Response Approximations and Corrections When the magnitude of the output–input ratio and the phase-angle response are each plotted against frequency on logarithmic coordinates, the work of obtaining the transfer function becomes largely a matter of graphical addition and subtraction. (Semilog plots may also be used.) A simplification is attained by treating separately each of the four basic types of factors in the transfer function and by starting with straight-line approximations of the actual curves.* Corrections from the straight-line approximations, to obtain the actual curves, are given in the following table and also in the following figure. Values of Log Magnitude and Angles of (1 + jT)–1 The corner frequency wcf is used as the index, i.e., 1/(1 + jwT) = 1/(1 + jw/wcf ). Range is one decade above and below wcf. wcf

Exact Magnitude, db

Value of the Asymptote, db

Error, db

Angle, Degrees

0.10 0.50 0.76 1.00 1.31

–0.04 –0.97 –2.00 –3.01 –4.35

0 0 0 0 –2.35

–0.04 –0.97 –2.00 –3.01 –2.00

–5.7 –26.6 –45.0

2.00 4.00 10.00

–6.99 –12.30 –20.04

-6.02 –12.04 –20.00

–0.97 –0.26 –0.04

–63.4 –84.3

* For a full discussion of the method, with examples, see: Feedback Control System Analysis and Synthesis, 2nd ed., J.J. D’Azzo and C.H. Houpis, McGraw-Hill Book Company, New York, 1966, pp. 278–303. From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 601.

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Electrical and Computer Engineering

Corrections to the Log Magnitude and Phase Diagram For [1 + j2zw/wn + (jw/wn)2]–1 14

Phase departure

0.10

0

ζ = 0.10 0.15 12 0.20

0.25

10 0.30 10

0.15

0.50

20 0.71 0.20 1.00

30 0.25 40 0.30

4 50

Phase departure, degrees

Correction, db

6

2 60 ζ = 0.50

0

0.71

Attenuation departure

70 1.00

−2 80 −4 90 −6

0.1

0.2

0.4

0.6

0.8

1 ω ωn

2

4

6

8

10

From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 602. Originally from H.M. James, N.B. Nichols, and R.S. Phillips, Theory of Servomechanisms, McGraw-Hill Book Company, New York, 1947.

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CRC Handbook of Engineering Tables

Block and Signal-Flow Diagrams SYMBOLS: a = input b = output G = transfer function Operation Block Diagram a

Basic element

Signal-Flow Diagram G

b

G

b = Ga

a Elements in cascade

a

G1

G3

b

G1

Elements in parallel

+

+ +

G2 b

b

b

G1

a

G2

G3

G1 G2 G3

a a

G1

a

b

b = G1 G2 G3a

b c C = (G1 + G2 ) a + G3b -

G2

+ G3

G3

a + Feedback

G2

Equation

b

b −

c

a

1 b

G

G H

c C=

G a 1 + GH

−H

From Bolz, R.E. and Tove, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 1061.

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Electrical and Computer Engineering

Block-Diagram Manipulations Manipulation 1. Interchange of elements 2. Interchange of summing points

Original Network

±

±±

± ′

±

7. Moving a takeoff point ahead of an element

8. Moving a takeoff point beyond an element

±

10. Moving a takeoff point beyond a summing point 11. Combining cascade elements

© 2004 by CRC Press LLC

± ±

± ±

±

9. Moving a takeoff point ahead of a summing point

6. Moving a summing point beyond an element

±±

±

±±

±

±± ±

5. Moving a summing point ahead of an element

3. Rearrangement of summing points

4. Interchange of takeoff points

Equivalent Network

±

±

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CRC Handbook of Engineering Tables

Block-Diagram Manipulations (continued) Manipulation

14. Eliminating a forward loop

±

±

±

±

±

±

±

±

16. Inserting an element in a feedback loop

17. Elminating a feedback loop

±

±

±

13. Inserting an element in a forward loop

15. Removing an element from a feedback loop

Equivalent Network

±

12. Removing an element from a forward loop

Original Network

±

±

21. Different form of 20

±

19. Special form of 17

20. Inserting a feedback loop to replace an element

±

18. Special form of 17

−

−

=

−

−

From Bolz, R.E. and Tove, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1062–1063. Originally from E.M. Grabbe, S. Ramo, and D.E. Wooldridge, Eds., Handbook of Automation, Computation, and Control, Vol. 1, John Wiley & Sons, New York, 1958, pp. 20-62 and 20-63.

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Electrical and Computer Engineering

Signal-Flow Diagrams Cascade =

1.

>

N1

N2

=>

≡

N3

N1

N3

N3 = >N2 = >=N1 Parallel =

2.

N1

>

=+>

≡

N2

N1

N2

N2 = = + >N1 C

1

1

≡

N3

N2

N1

3.

1 1−g N1

1 N2

N3

N2 = N + CN2 N2 = N1 (1/1-C) =

1

4.

N0

N1

N1 = N + >N2 N2 = =N1 = =N0 + =>N2 N3/N0 = =/1-=>

© 2004 by CRC Press LLC

>

1 N2

N3

≡

1

=

N0

N2 =>

≡

= 1 − => N1

N3

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CRC Handbook of Engineering Tables

Signal-Flow Diagrams (continued)

5.

−

−

−

6.

7.

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Electrical and Computer Engineering

Signal-Flow Diagrams (continued)

8.

9.

≡

≡

+

From Bolz, R.E. and Tove, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1064–1066. Originally from D.P. Campbell, Process Dynamics, John Wiley & Sons, New York, 1958.

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CRC Handbook of Engineering Tables

Root Loci Continuous Systems Overall Transfer Function

Sketch of Root Locus jω

1.

k s + s2

− s2

σ 0

jω

2.

σ

k s( s + s2 )

− s2

0

jω

3.

k

s + s1 s + s2

jω

σ − s1

− s2

σ − s2

0

− s1

0

jω 4.

σ

k

(s + s )(s + s ) 2

− s4

4

− s2

0

jω

jω

5.

k( s + s1 )

(s + s )(s + s ) 2

4

σ − s1

− s1

− s2

0

σ − s4

− s2

− s1 0

jω

6.

k( s + s1 )

(s + s )(s + s ) 2

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4

σ − s1

− s2

− s4

0

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Electrical and Computer Engineering

Root Loci (continued) Overall Transfer Function

Sketch of Root Locus − α + jβ

7.

jω

jω − α + jβ

k( s + s1 )

(s + a + jb)(s + a - jb)

− s1

σ

σ

− s1

0

0

− α − jβ − α − jβ jω

8.

k( s + s ) (s + s )(s + s )

σ

1

2

− s2

− s1

4

− s4

0

jω

9.

k

(s + s )(s + s )(s + s ) 2

4

− s2

5

− s4

jω

− s6 0

σ

jω

− α + jβ

− α + jβ 10.

k (s + s2 )(s + a + jb)(s + a - jb)

σ

− s2 − α − jβ

k s + s s jb)( s + a - jb) + a + ( ( 2)

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jω

− s2 − α − jβ

0

− α − jβ

− α + jβ

11.

σ

− s2

0

σ 0

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CRC Handbook of Engineering Tables

Root Loci (continued) Overall Transfer Function

Sketch of Root Locus j

12.

k( s + s ) (s + s )(s + s )(s + s )

− s

1

2

4

−s

6

− s"

k( s + s1 )

(s + s )(s + s )(s + s ) 2

4

6

k( s + s ) (s + s )(s + s )(s + s )

− s$

−s

4

6

−s

− s − s"

− s"

(s + s )(s + a + jb)(s + a - jb)

− s$

s( s + s2 )( s + s 4 )

© 2004 by CRC Press LLC

− s

σ

j

σ −s

−s

− s

ω

σ

− s" − s$

ω

− s

σ

− α − jβ

j

k( s + s1 )( s + s2 )

ω

− α + jβ

k( s + s1 )

2

16.

σ

ω

j

15.

ω

− s$ − s"

− s$

σ

1

2

−s

j

j

14.

− s

ω

− s" − s − s

j

σ

− s$

j

13.

ω

−s − s

− s" − s!

ω

σ

j

− s − s

− s! − s"

ω

σ

1587_Section_1d.fm Page 221 Tuesday, September 2, 2003 2:16 PM

1-221

Electrical and Computer Engineering

Root Loci (continued) Overall Transfer Function

Sketch of Root Locus jω

17.

k( s + s1 )( s + s3 )

s( s + s2 )( s + s 4 )

− s2

− s4

− s1

− s3

jω

− s3

σ 0

− s1 − s2 − s4

jω

18.

k( s + s1 )( s + s3 )

s( s + s2 )( s + s 4 )

σ

− s2 − s4 − s1 − s3

0

jω

19.

k( s + s1 )( s + s3 )

3

(s + s )

− s1

2

− s3

σ

− s2

0

jω

20.

− s6 − s2

k (s + s2 )(s + s 4 )(s + s6 )(s + s8 )

− s2

− s4

− α + jβ

21.

k s( s + s2 )( s + a + jb)( s + a - jb)

jω

σ − s2

0 − α − jβ

© 2004 by CRC Press LLC

σ 0

σ 0

1587_Section_1d.fm Page 222 Tuesday, September 2, 2003 2:16 PM

1-222

CRC Handbook of Engineering Tables

Root Loci (continued) Overall Transfer Function

Sketch of Root Locus − α + jβ

22.

k s( s + s2 )( s + a + jb)( s + a - jb)

jω

σ

− s2

0

− α − jβ

jω

− α + jβ

23.

k ÏÔ( s + s2 )( s + s 4 )( s + a + jb)¸Ô ý Ì ¥( s + a - jb)þÔ ÓÔ

− s2

σ

− s4

0 − α − jβ

jω

− α1 + jβ1 24.

− α2 + jβ2

k ÏÔ ( s + a1 + jb)( s + a - jb1 )¸Ô Ì ý ÔÓ¥( s + a 2 + jb2 )( s + a 2 - jb2 )Ôþ

σ 0

− α2 − jβ2 − α1 − jβ1

− α + jβ 25.

jω

k( s + s1 )

ÏÔs( s + s2 )( s + a + jb)¸Ô ý Ì ¥( s + a - jb)þÔ ÓÔ

σ − s1

− s2

0

− α − jβ

26.

k( s + s1 )

ÏÔs( s + s2 )( s + a + jb)¸Ô Ì ý ¥( s + a + jb)þÔ ÓÔ

− α + jβ

jω

σ − s1

− s2

0 − α − jβ

© 2004 by CRC Press LLC

1587_Section_1d.fm Page 223 Tuesday, September 2, 2003 2:16 PM

1-223

Electrical and Computer Engineering

Root Loci (continued) Overall Transfer Function

Sketch of Root Locus jω +j3π/L

27.

+jπ/L

ke - sL

σ 0 −jπ/L −j3π/L

jω

28.

ke - sL s + s2

σ − s2

0

Handbook of Automation, Computation and Control, E.M. Grabbe, S. Ramo, and D.E. Wooldridge, Eds., Vol. 1, John Wiley & Sons, New York, 1958. From Bolz, R.E. and Tuve, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1073–1078. Originally from Mathematics of Automatic Control, Takahashi, T. (translation edited by George M. Kranc), English translation, Holt, Rinehart and Winston, Inc., New York, 1966.

© 2004 by CRC Press LLC

1587_Section_1d.fm Page 224 Tuesday, September 2, 2003 2:16 PM

1-224

CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Function G(s)

Polar Plot

Bode Diagram 0°

−45° −ω 1.

K st1 + 1

−1

90°

M Kdb0 db/oct

φ

ω=∞

ω=0

−180°

Phase margin 1 τ1

0 db

log ω

−6 db/oct

+ω

0°

−ω φ 2.

K s t + 1 ( 1 )(st2 + 1)

−1

ω=0

ω=∞

M

−180°

φ 0

Phase margin

−6 1 τ1

0 db

1 τ2

log ω

−12 db/oct

+ω

φ

0°

−ω

3.

(st

1

K + 1)( st 2 + 1)( st3 + 1)

−1

ω=∞ ω=0

M

φ

−180°

0

0 db

−270°

−6 1 τ1

1 τ2

Gain margin

−12 db/oct 1 log ω τ3

Phase margin

+ω

−18 db/oct

ω=0 φ

−ω 4.

K S

−1

ω=∞ +ω

ω→0

© 2004 by CRC Press LLC

−90°

M

−180°

Phase margin 0 db

log ω

−6 db/oct

1587_Section_1d.fm Page 225 Tuesday, September 2, 2003 2:16 PM

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Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments ω

ω M

Phase margin

0 db −180°

−90°

φ

0°

1 Root locus − τ1

σ

Stable; gain margin = •

ω=∞

ω ω

Phase margin

M

0 db −180°

R1

−90°

φ

0°

−

1 τ2

−

σ

1 τ1

R2

ω→∞

ω

M

ω

Phase margin Gain margin 0 db −180°

Elementary regulator; stable; gain margin = •

−90°

0°

φ

R1

R3 −

1 τ3

−

1 τ2

−

1 τ1

σ

Regulator with additional energystorage component; unstable, but can be made stable by reducing gain

R2

ω→∞

ω ω

M Phase margin 0 db −180°

−90°

ω→∞

© 2004 by CRC Press LLC

φ

σ

Ideal integrator; stable

1587_Section_1d.fm Page 226 Tuesday, September 2, 2003 2:16 PM

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CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Function (continued) G(s)

Polar Plot

Bode Diagram

ω→0 −ω

5.

K s( st1 + 1)

−1

φ ω=∞

−6 db/oct

M

−180°

−90° Phase margin

1 τ1

0 db

log ω

−12 db/oct

+ω ω→0

ω→0 −90°

−ω 6.

K s( st1 + 1)( st 2 + 1)

−1

φ ω=∞

+ω

M

−180°

Phase margin Gain margin

−6 0 db

−

−270°

1 τ1 −12

ω→0 −90°

−ω

7.

K ( st a + 1)

s( st1 + 1)( st 2 + 1)

log ω

−18 db/oct

ω→0

−1

1/τ2

ω=∞

φ

M

−180°

Phase margin

−6 db/oct −12 0 db

+ω

1 τ1

φ

1/τ2

1 τa −6

log ω

−12 db/oct

ω→0

φ 8.

K s3

© 2004 by CRC Press LLC

ω→ − ω −1 +ω

ω=∞

M

−180°

−12 db/oct

Gain margin = 0 Phase margin = 0

φ 0 db

log ω

1587_Section_1d.fm Page 227 Tuesday, September 2, 2003 2:16 PM

1-227

Electrical and Computer Engineering

Nichols Diagram

Root Locus

Comments ω

ω

M

R

− °

− °

Elementary instrument servo; inherently stable; gain margin = •

σ

−

φ

τ

R

ω→∞

ω

M

R

ω

R

− °

− °

φ

−

−

τ

σ

τ

R

Instrument servo with fieldcontrol motor or power servo with elementary Ward-Leonard drive; stable as shown, but may become unstable with increased gain

ω→∞

ω ω

M

R

− °

R

− °

φ

−

τ

−

τ

τ

Elementary instrument servo with phase-lead (derivative) compensator; stable

σ

−

R

ω→∞

ω

ω

M

−° − °

− °

R σ

φ

R ω→∞

© 2004 by CRC Press LLC

Inherently unstable; must be compensated

1587_Section_1d.fm Page 228 Tuesday, September 2, 2003 2:16 PM

1-228

CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Function (continued) G(s)

Polar Plot

Bode Diagram

−12 db/oct

φ M 9.

K s 2 ( st1 + 1)

+ω

−1

ω=∞

Phase margin −180°

−ω −270°

10.

11.

K ( st a + 1) s 2 ( st1 + 1)

−ω −1

ω=∞

+ω ω=∞

+ω K ( st a + 1)

−1

s3

−ω

© 2004 by CRC Press LLC

log ω φ

−18 db/oct

−12 db/oct

Phase margin φ

0 db

1/τ1 1 τa −6 db/oct

log ω

−12 db/oct

−ω

12.

−180°

1 τ1

+ω

−1

K s3

φ M

0 db

−180° 0 db Phase margin −270°

φ M ω=∞

−18 db/oct

φ M

−180°

−270°

log ω φ

−18 db/oct Phase margin 0 db

log ω

1 τa −12 db/oct

φ

1587_Section_1d.fm Page 229 Tuesday, September 2, 2003 2:16 PM

1-229

Electrical and Computer Engineering

Nichols Diagram

Root Locus ω

M φ

−° −°

Comments

R

R

σ

− °

Inherently unstable; must be compensated

R

ω→∞

ω

M

R

−°

R φ

− °

− τ

σ

− τ

Stable for all gains

R

ω→∞

ω

M

−°

−°

R

R

φ

σ

− °

Inherently unstable

R ω→∞

M

−°

ω→∞

© 2004 by CRC Press LLC

− °

R

R

φ

−°

ω

−

τ

σ

R

Inherently unstable

1587_Section_1d.fm Page 230 Tuesday, September 2, 2003 2:16 PM

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CRC Handbook of Engineering Tables

Transfer Function Plots for Typical Transfer Function (continued) G(s)

Polar Plot

Bode Diagram

−90°

+ω

13.

K ( st a + 1)( st b + 1)

φ −1

ω=∞

s3

−ω

−18 db/oct

M

φ

−12 db/oct

−180°

1 0 db 1 τa τb Gain −270° margin

Phase margin log ω

−6 db/oct

−6 −90°

−ω

14.

K ( st a + 1)( st b + 1)

−1

s( st1 + 1)( st 2 + 1)( st3 + 1)( st 4 + 1)

φ ω=∞

+ω

M

−180°

−270°

−12

Gain margin −18 1 τ4 −12 1 1 log ω τ3 τb 1/ τ 0 db 1 1 a −6 τ1 τ2 −12 Phase −18 margin

−12 φ 15.

K ( st a + 1)

s 2 ( st1 + 1)( st 2 + 1)

© 2004 by CRC Press LLC

−ω +ω

−1

ω=∞

M −6

−180°

0 db

1 τa

Phase margin 1 1 τ1 τ2

−12 Gain margin

log ω

−18

1587_Book.fm Page 231 Friday, September 26, 2003 12:10 PM

1-231

Electrical and Computer Engineering

Nichols Diagram

Gain margin

Phase margin

ω→∞

M 0 db

−270° Gain margin

−90°

−

1 τb

−

σ

1 τa

−180°

Conditionally stable; becomes unstable if gain is too low

R2

ω→∞

R1

M

0 db −270° −180°

Triple pole

R3

φ

0 db

Comments ω

R1

N

−270° −180°

Gain margin

Root Locus

R5 −90° φ

−1 τ4

R4

R3

−1 −1 −1 τ3 τb τa

−1 −1 τ2 τ1

Phase margin

σ

Conditionally stable; stable at low gain, becomes unstable as gain is raised, again becomes stable as gain is further increased, and becomes unstable for very high gains

R2 ω

Phase margin

φ −90° φ

R4 −

R3 1 τ2

−

R1

1 1 − τ1 τa

Double pole

σ

Conditionally stable; becomes unstable at high gain

R2

ω→∞ From Bolz, R.E. and Tuve, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1080–1087. Originally from G.J. Thaler and R.G. Brown, Analysis and Design of Feedback Control Systems, 2nd ed., McGraw-Hill Book Company, New York, 1960.

© 2004 by CRC Press LLC

1587_Book.fm Page 1 Friday, September 26, 2003 12:10 PM

2 Civil and Environmental Engineering Properties of Dressed Lumber ...................................................................................................................2-3 Beam Formulas ..........................................................................................................................................2-4 Phases in the Value Engineering Job Plan ................................................................................................2-5 Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) ......................2-6 National Ambient Air Quality Standards................................................................................................2-10 Standard Normal Probability ..................................................................................................................2-11 Typical Values of Elastic Modulus and Poisson's Ratio for Granular Soils ...........................................2-12 Representative Applications and Controlling Functions of Geotextiles ................................................2-13 Physical Properties of Water in SI Units .................................................................................................2-14 Physical Properties of Air at Standard Atmospheric Pressure in English Units ...................................2-14 Physical Properties of Common Liquids at Standard Atmospheric Pressure in SI Units ....................2-15 Physical Properties of Common Gases at Standard Sea-Level Atmosphere and 68°F in English Units .....................................................................................................................................................2-15 Typical Physical Properties of and Allowable Stresses for Some Common Materials (in U.S. Customary System Units)....................................................................................................................2-16 Typical Physical Properties of and Allowable Stresses for Some Common Materials (in SI System Units) .......................................................................................................................................2-17 Some Distribution Types .........................................................................................................................2-18 Typical Compound Composition of Ordinary Portland Cement .........................................................2-19 Properties of Some Lightweight Concretes.............................................................................................2-19 Mechanical Properties of Hardened Concrete ........................................................................................2-20 ACI 318 Maximum Chloride-Ion Content for Corrosion Protection ...................................................2-21 Properties of Typical Air-Entraining Admixtures...................................................................................2-21 Total Target Air Content for Concrete ....................................................................................................2-21 Beam formulas for one-, two-, and three-span conditions....................................................................2-22 Theoretical Maximum Load Ratios on Floor and Prop for Various Shore/Reshore Combinations .....2-23 Selected Earthquakes Since 1900 (Fatalities Greater than 1,000) ..........................................................2-23 Selected U.S. Earthquakes ........................................................................................................................2-26 Earthquake Loss Process ..........................................................................................................................2-28 Earthquake Risk Management Decision Process ....................................................................................2-29 Principle Elemental Components of Structural Steel ............................................................................2-30 Three Levels of Analysis in the EIA Process ...........................................................................................2-30

2-1 © 2004 by CRC Press LLC

1587_Book.fm Page 2 Sunday, August 31, 2003 9:44 PM

2-2

CRC Handbook of Engineering Tables

Public Participation in Environmental Impact Assessment ...................................................................2-31 Priority Chemicals Targeted in the 33/50 Project for the Industrial Sector Pollution Preventation Strategy.................................................................................................................................................2-32 Main Membrane Separation Processes: Operating Principles and Application....................................2-32 Summary of NAAQSs ..............................................................................................................................2-33 National Emission Standards for Hazardous Air Pollutants ..................................................................2-33 Molecular and Aerosol Particle Diameters .............................................................................................2-37 Radon Risk Evaluation Chart ..................................................................................................................2-38 Mechanical Characteristics of Sound Waves...........................................................................................2-39 Representative Sound Pressures and Sound Levels ................................................................................2-39 Typical Wastewater Flow Rates from Residential Sources ......................................................................2-40 Estimated Distribution of World's Water ...............................................................................................2-40 Currently Developed Types of Fuel Cells and Their Characteristics and Applications........................2-41 Hydrogen Storage Properties for a Range of Metal Hydrides ...............................................................2-41 Typical Gas Composition of Biogas from Organic Household Waste ..................................................2-42 Performance of Different Battery Types .................................................................................................2-42 Thermodynamic Data for Selected Chemical Compounds ...................................................................2-43 Shear Force and Bending Moment Diagrams for Beams with Simple Boundary Conditions Subjected to Selected Loading Cases ..................................................................................................2-44 Shear Force and Bending Moment Diagrams for Built-Up Beams Subjected to Typical Loading Cases .....................................................................................................................................................2-47 Typical Loading on Plates and Loading Functions ................................................................................2-49 Typical Loading and Boundary Conditions for Rectangular Plates ......................................................2-51 Typical Loading and Boundary Conditions for Circular Plates ............................................................2-52 Frequencies and Mode Shapes of Beams in Flexural Vibration ............................................................2-53 Fundamental Frequencies of Portal Frames in Asymmetrical Mode of Vibration ...............................2-54 Basic Weld Symbols .................................................................................................................................2-55 Strength of Welds .....................................................................................................................................2-56 Reinforcing Bar Dimensions and Weights ..............................................................................................2-57 Eurocode 4 Maximum Width-to-Thickness Ratios for Steel Webs .......................................................2-57 Mechanical Properties of Steels Referred to in the AISI 1996 Specification .........................................2-58 Some Nominal Properties of Aluminum Alloys .....................................................................................2-60 Minimum Mechanical Properties............................................................................................................2-60 Steel Plate Materials .................................................................................................................................2-61 Mechanical Properties of Common Design Materials ...........................................................................2-62 Properties of Sections ..............................................................................................................................2-62 Components of the Atmosphere .............................................................................................................2-64 Sound Transmission Through Partition Walls .......................................................................................2-65 Sound-Absorption Coefficients ...............................................................................................................2-66

© 2004 by CRC Press LLC

1587_Book.fm Page 3 Sunday, August 31, 2003 9:44 PM

2-3

Civil and Environmental Engineering

Properties of Dressed Lumber Standard Size Width ¥ Depth

S4S Dressed Size Width ¥ Depth

Cross-Sectional Area A (in.2)

Moment of Inertia I (in.4)

Section Modulus S (in.3)

Weight in Pounds per Lineal Foota

1¥4 1¥6 1¥8 1 ¥ 12 2¥4 2¥6 2¥8 2 ¥ 10 2 ¥ 12 4¥2 4¥4 4¥6 4¥8 6¥2 6¥4 6¥6 6¥8 8¥2 8¥4 8¥6 8¥8

¾ ¥ 3½ ¾ ¥ 5¼ ¾ ¥ 7¼ ¾ ¥ 11¼ 1 ½ ¥ 3½ 1 ½ ¥ 5½ 1 ½ ¥ 7¼ 1 ½ ¥ 9¼ 1½ ¥ 11¼ 3 ½ ¥ 1½ 3 ½ ¥ 3½ 3 ½ ¥ 5½ 3 ½ ¥ 7¼ 5 ½ ¥ 1½ 5 ½ ¥ 3½ 5 ½ ¥ 5½ 5 ½ ¥ 7¼ 7¼ ¥ 1½ 7¼ ¥ 3½ 7¼ ¥ 5½ 7¼ ¥ 7¼

2.63 4.13 5.44 8.44 5.25 8.25 10.88 13.88 16.88 5.25 12.25 19.25 25.38 8.25 19.25 30.25 41.25 10.88 25.38 41.25 56.25

2.68 10.40 23.82 88.99 5.36 20.80 47.64 98.93 177.98 .98 12.51 48.53 111.15 1.55 19.65 76.26 193.36 2.04 25.90 103.98 263.67

1.53 3.78 6.57 15.82 3.06 7.56 13.14 21.39 31.64 1.31 7.15 17.65 30.66 2.06 11.23 27.73 51.53 2.72 14.80 37.81 70.31

0.64 1.00 1.32 2.01 1.28 2.01 2.64 3.37 4.10 1.28 2.98 4.68 6.17 2.01 4.68 7.35 10.03 2.64 6.17 10.03 13.67

a

Weights are for wood with a density of 35 pounds per cubic foot. From Alexander, A., Design and construction of concrete formwork, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 4-4.

© 2004 by CRC Press LLC

1587_Book.fm Page 4 Sunday, August 31, 2003 9:44 PM

2-4

CRC Handbook of Engineering Tables

Beam Formulas Simply Supported Beam with Concentrated Load at Center

Simply Supported Beam with Uniformly Distributed Load W

P ∆

∆

∆

∆

L

L 2

M max = wL 8 4 ∆max = 5wL 384 EI Vmax = wL 2

M max = PL 4 3 ∆ = PL 48EI Vmax = P 2 Two Span Continuous Beam with Uniformly Distributed Load W ∆

L

∆

L

Three Span Continuous Beam with Uniformly Distributed Load W ∆

∆

∆

∆

L

∆

L

2

L

2

M max = wL 8 4 ∆max = wL 185EI Vmax = 5wL 8

M max = wL 10 4 ∆max = wL 145EI Vmax = .6wL

Cantilever Beam with Uniformly Distributed Load

Three Span Continuous Beam with Concentrated Loads at Span Third Points

P

W ∆

L

P

P

L/3 L/3 L/3

L

P

∆

P

P

∆

L

∆

L

2

M max = wL 2 4 ∆max = wL 8EI Vmax = wL

Mmax = .267PL Vmax = 1.27P

From Alexander, A., Design and construction of concrete formwork, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 4-23.

© 2004 by CRC Press LLC

1587_Book.fm Page 5 Sunday, August 31, 2003 9:44 PM

2-5

Civil and Environmental Engineering

Information Phase

Getting the facts

Objectives: • Provide Speculation information base Phase • Select areas of study Objective: • Generate alternatives for solving problem

Brainstorming Alternatives

Evaluating the alternatives

Analysis Phase

Objectives: • Evaluate alternatives • Rank alternatives

Development Phase

Objectives: • Develop details • Finalize selection

Developing the program

Recommendation Phase

Selling the recommendations

Objectives: • Develop implementation plan • Present recommendation

Phases in the value engineering job plan. From Chua, D.K.H., Value improvement methods, in The Civil Engineering Handbook, 2nd ed., Chen, W.F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 7-2.

© 2004 by CRC Press LLC

1587_Book.fm Page 6 Sunday, August 31, 2003 9:44 PM

2-6

CRC Handbook of Engineering Tables

Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) Authority U.S. PHSa

Parameter

U.S. EPAb,c

WHOd

<5% positive samples in a set of = 40 per month, or <1 sample positive in a set of <40 per month

0

Pathogens and Parasites Total coliform bacteria (no./100mL)

1

Inorganic Poisons (mg/L) Antimony Arsenic

— 0.05

Asbestos (Million fibers > 10 µM per liter) Barium Beryllium Cadmium Chromium (Total) Copper

—

Cyanide Fluoride Lead

1 — 0.01 0.05 —

0.2 See nuisances 0.05

Mercury (inorganic) Nickel Nitrate (as N) Nitrite (as N) Nitrate plus nitrite (as N) Selenium Sulfate

— — 10 — — 0.01 —

Thallium

—

0.006 0.05 (Interim) 7

— 0.05

2 0.004 0.005 0.1 1.3 90th percentile action level, requires corrosion control 0.2 4 0.015 90th percentile action level, requires corrosion control 0.002 0.1 10 1 10 0.05 Deferred (400 to 500?) 0.002

— — 0.005 0.05 —

—

0.1 — 0.05

0.001 — 10 — — 0.01 — —

Organic Poisons (µg/L, Except as Noted) Acrylamide Alachor Aldicarb Aldicarb sulfoxide Aldicarb Sulfone Aldrin and Dieldrin Atrazine Benzene Benzo[a]pyrene Bromobenzene Bromochloromethane Bromodichloromethane Bromoform Bromomethane n-Butylbenzene sec-Butylbenzene tert-Butylbenzene Carbofuran Carbon chloroform extract

© 2004 by CRC Press LLC

— — — — — — — — — — — — — — — — — — 200

Use in treatment, storage, and distribution; restricted 2 3 4 3 — 3 5 0.2 Monitor Monitor if ordered Monitor Monitor Monitor Monitor if ordered Monitor if ordered Monitor if ordered 40 —

— — — — — 0.03 — 10 0.01 — — — — — — — — — —

1587_Book.fm Page 7 Sunday, August 31, 2003 9:44 PM

2-7

Civil and Environmental Engineering

Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) (continued) Authority Parameter Carbon tetrachloride Chlordane Chlorobenzene Chlorodibromomethane Chloroethane Chloroform Chloromethane m-Chlorotoluene p-Chlorotoluene 2,4-D Dalapon DDT 1,2-Dibromo-3-chloropropane (DBCP) Dibromomethane m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene Dichlorodifluoromethane 1,1-Dichloroethane 1,2-Dichloroethane 1,1-Dichloroethylene cis-1,2-Dichloroethylene trans-1,2-Dichloroethylene Dichloromethane 1,2-Dichloropropane 1,3-Dichloropropane 2,2-Dichloropropane 1,1-Dichloropropene 1,3-Dichloropropene Di(2-ethylhexyl)adipate Di(2-ethylhexyl)phthalate Dinoseb Dioxin (2,3,7,8-TCDD) Diquat Endothall Endrin Epichlorhydrin Ethylbenzene Ethylene dibromide (EDB) Fluorotrichloromethane Glyphosate (aka Rodeo™ and Roundup™) Heptachlor Heptachlor epoxide Hexachlorobenzene Hexachlorobutadiene Hexachlorocyclopentadiene (HEX) Isopropylbenzene p-Isopropyltolulene Lindane Methoxychlor Naphthalene Oxamyl (Vydate) Pentachlorophenol

© 2004 by CRC Press LLC

U.S. PHSa

U.S. EPAb,c

WHOd

— — — — — — — — — — — — —

5 2 100 Monitor Monitor Monitor Monitor Monitor Monitor 70 200 — 0.2

— 0.3 — — — 30 — — — 100 — 1 —

— — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — 10 0.3 — — — — — — — — — — — — — — — —

— — — —

Monitor Monitor 600 75 Monitor if ordered Monitor 5 7 70 100 5 5 Monitor Monitor Monitor Monitor 400 6 7 30 ¥ 10–9 20 100 2 Use in treatment, storage, and distribution; restricted 700 0.05 Monitor if ordered 700

— — — — — — — — — — — —

0.4 0.2 1 Monitor if 50 Monitor if Monitor if 0.2 40 Monitor if 200 1

0.1 — 0.01 — — — — 3 30 — — 10

ordered ordered ordered

ordered

— — — —

1587_Book.fm Page 8 Sunday, August 31, 2003 9:44 PM

2-8

CRC Handbook of Engineering Tables

Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) (continued) Authority Parameter PCB (polychlorinate biphenyl) Picloram n-Propylbenzene Silvex (2,4,5-TP) Simazine Styrene 2,3,7,8-TCDD (Dioxin) 1,1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane Tetrachloroethylene Toluene Toxaphene 1,2,3-Trichlorobenzene 1,2,4-Trichlorobenzene 1,1,1-Trichloroethane 1,1,2-Trichloroethane Trichloroethylene 1,2,3-Trichloropropane 2,4,6-Trichlorophenol Trihalomethanes (Total) 2,4-Trimethylbenzene 1,3,5-Trimethylbenzene Vinyl chloride Xylene (Total) m-Xylene o-Xylene p-Xylene

U.S. PHSa — — — — — — — — — — — — — — — — — — — — — — — — — — —

U.S. EPAb,c 0.5 500 Monitor if 50 4 100 30 ¥ 10–6 Monitor Monitor 5 1000 3 Monitor if 70 200 5 5 Monitor — 100 Monitor if Monitor if 2 10,000 Monitor Monitor Monitor

ordered

ordered

ordered ordered

WHOd — — — — — — — — — — — — — — — — — — 10 — — — — — — — —

Radioactivity (pCi/L, except as noted) Gross alpha (excl. Ra, u) Gross beta Gross beta/photon (mrem/yr) Radium-226 Radium-226 and 228 Radon-222 Strontium-90 Uranium (mg/L)

— 1000 — 10 — — 3 —

15 — 4 5 300 — .03

2.7 27 — — — — — —

Nuisances (mg/L, except as noted) Alkyl benzene sulfonate Aluminum Chloride Color (Pt-Co Units) Copper Corrosivity (Langelier Index) Fluoride

Hardness (as CaCO3) Hydrogen sulfide Iron Manganese Methylene blue active substances

© 2004 by CRC Press LLC

0.5 — 250 15 1 — 0.8–1.7 Depending on air temperature — — 0.3 0.05 —

— —250 15 See above —e See above

— 0.2 250 15 1 — —

— — 0.3 0.05 0.5

500 —f 0.3 0.1 —

1587_Book.fm Page 9 Sunday, August 31, 2003 9:44 PM

2-9

Civil and Environmental Engineering

Maximum Contaminant Concentrations Allowable in Drinking Water (Action Levels) (continued) Authority U.S. PHSa

Parameter Odor (threshold odor no.) pH Phenol (µg/L) Silver Sodium Sulfate Taste Total dissolved solids Turbidity (nephelometric units) Zinc

3 — 1 0.05 — 250 — 500 5 5

U.S. EPAb,c 3 6.5/8.5 — 0.05 —e 500 — 500 All samples = £5; 95% of samples £ 0.5 5

WHOd —g 6.5/8.5 — — 200 400 —g 1000 5 5

Disinfectants and Disinfection Byproducts (mg/L) Chlorine Chloramines Chlorine dioxide Total trihalomethanes Haloacetic acids Chlorite Bromate Total organic carbon a

— — — — — — —

4. 4. 0.8 0.080 0.060 1.0 0.010 Treatment

— — — — — — — —

Hopkins, O. C. 1962. Public Health Service Drinking Water Standards 1962. U.S. Department of Health Education, and Welfare, Public Health Service, Washington, DC. b Pontius, F. W. 1990. “Complying with the New Drinking Water Quality Regulations,” Journal of the American Water Works Association, 82(2): 32. c Auerbach, J. 1994. “Cost and Benefits of Current SDWA Regulations,” Journal of the American Water Works Association, 86(2): 69. d Anonymous. 1984. Guidelines For Drinking Water Quality: Volume 1. Recommendations. World Health Organization, Geneva, Switzerland. e To be monitored and reported to appropriate agency and/or public. f Not detectable by consumer. g Not offensive for most consumers. From Sykes, R.M., Water and wastewater planning, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, pp. 8-3 to 8-6.

© 2004 by CRC Press LLC

1587_Book.fm Page 10 Sunday, August 31, 2003 9:44 PM

2-10

CRC Handbook of Engineering Tables

National Ambient Air Quality Standards Criteria Pollutant

Averaging Period

Primary NAAQS (mg/m3)

Secondary NAAQS (mg/m3)

PM10

Annual 24 hours Annuala 24 hoursa Annual 24 hours 3 hours Annual 1 hour 8 hoursa 8 hours 1 hour Quarterly

50 150 15 65 80 365

150 150 15 65

PM2.5 Sulfur dioxide (SO2)

Nitrogen dioxide (NO2) Ozone Carbon monoxide (CO) Lead a

100 235 157 10,000 40,000 1.5

1300 100 235 157 10,000 40,000 1.5

The 1997 Revised PM2.5 and 8-hour ozone were challenged in court and were the subject of a significant question regarding the constitutionality of EPA’s power to make policy without legislative review and EPA’s responsibility to consider economic implications of policymaking. A February 27, 2001, ruling by the Supreme Court found the EPA could move forward with the PM2.5 standard but must review the proposed ozone standard. The revised standards were cleared of remaining legal hurdles in March 2002. From Jacko, R.B. and LaBreche, T.M.C., Air pollution, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 12-4.

© 2004 by CRC Press LLC

1587_Book.fm Page 11 Sunday, August 31, 2003 9:44 PM

2-11

Civil and Environmental Engineering

Standard Normal Probability –1/2 2 exp – z for z > 2.2, y(z) 1 – 1 (2p) 2 2 2

[ ]

p( z) z=

x -x s [x ]

Area = y (z)

z

z

z

0

0

1

2

3

4

5

6

7

8

9

.1 .2 .3 .4

0 .039828 .079260 .117911 .155422

.003969 .043795 .083166 .121720 .159097

.007978 .047758 .087064 .125516 .162757

.011966 .051717 .090954 .129300 .166402

.015953 .055670 .094835 .133072 .170031

.019939 .059618 .098706 .136831 .173645

.023922 .063559 .102568 .140576 .177242

.027903 .067495 .106420 .144309 .180822

.031881 .071424 .110251 .148027 .184386

.035856 .075345 .114092 .151732 .187933

.5 .6 .7 .8 .9

.191462 .225747 .258036 .288145 .315940

.194974 .229069 .261148 .291030 .318589

.198466 .232371 .264238 .293892 .321214

.201944 .235653 .267305 .296731 .323814

.205401 .238914 .270350 .299546 .326391

.208840 .242154 .273373 .302337 .328944

.212260 .245373 .276373 .305105 .331472

.215661 .248571 .279350 .307850 .333977

.219043 .251748 .282305 .310570 .336457

.222405 .254903 .285236 .313267 .338913

1.0 1.1 1.2 1.3 1.4

.341345 .364334 .384930 .403200 .419243

.343752 .366500 .386861 .404902 .420730

.346136 .368643 .388768 .406582 .422196

.348495 .370762 .390651 .408241 .423641

.350830 .372857 .392512 .409877 .425066

.353141 .374928 .394350 .411492 .426471

.355428 .376976 .396165 .413085 .427855

.357690 .379000 .397958 .414657 .429219

.359929 .381000 .399727 .416207 .430563

.362143 .382977 .401475 .417736 .431888

1.5 1.6 1.7 1.8 1.9

.433193 .445201 .455435 .464070 .471283

.434476 .446301 .456367 .464852 .471933

.435745 .447384 .457284 .465620 .472571

.436992 .448449 .458185 .466375 .473197

.438220 .449497 .459070 .467116 .473610

.439429 .450529 .459941 .467843 .474412

.440620 .451543 .460796 .468557 .475002

.441792 .452540 .461636 .469258 .475581

.442947 .453521 .462462 .469946 .476148

.444083 .454486 .463273 .470621 .476705

2.0 2.1 2.2 2.3 2.4

.477250 .482136 .486097 .489276 .491802

.477784 .482571 .486447 .489556 .492024

.478308 .482997 .486791 .489830 .492240

.478822 .483414 .487126 .490097 .492451

.479325 .483823 .487455 .490358 .492656

.479818 .484222 .487776 .490613 .492857

.480301 .484614 .488089 .490863 .493053

.480774 .484997 .488396 .491106 .493244

.481237 .485371 .488696 .491344 .493431

.481691 .485738 .488989 .491576 .493613

2.5 2.6 2.7 2.8 2.9

.493790 .495339 .496533 .497445 .498134

.493963 .495473 .496636 .497523 .498193

.494132 .495604 .496736 .497599 .498250

.494297 .495731 .496833 .497673 .498305

.494457 .495855 .496928 .497744 .498359

.494614 .495975 .497020 .497814 .498411

.494766 .496093 .497110 .497882 .498462

.494915 .496207 .497197 .497948 .498511

.495060 .496319 .497282 .498012 .498559

.495201 .496427 .497365 .498074 .498605

3.0 3.1 3.2 3.3 3.4

.498650 .499032 .499313 .499517 .499663

.498694 .499065 .499336 .499534 .499675

.498736 .499096 .499359 .499550 .499687

.498777 .499126 .499381 .499566 .499698

.498817 .499155 .499402 .499581 .499709

.498856 .499184 .499423 .499596 .499720

.498893 .499211 .499443 .499610 .499730

.498930 .499238 .499462 .499624 .499740

.498965 .499264 .499481 .499638 .499749

.498999 .499289 .499499 .499651 .499758

3.5 3.6 3.7 3.8 3.9

.499767 .499841 .499892 .499928 .499952

.499776 .499847 .499896 .499931 .499954

.499784 .499853 .499900 .499933 .499956

.499792 .499858 .499904 .499936 .499958

.499800 .499864 .499908 .499938 .499959

.499807 .499869 .499912 .499941 .499961

.499815 .499874 .499915 .499943 .499963

.499822 .499879 .499918 .499946 .499964

.499828 .499883 .499922 .499948 .499966

.499835 .499888 .499925 .499950 .499967

0

From Harr, M.E., Accounting for variability, in The Civil Engineering Handbook, 2nd ed., Chen. W.F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 16-11.

© 2004 by CRC Press LLC

1587_Book.fm Page 12 Sunday, August 31, 2003 9:44 PM

2-12

CRC Handbook of Engineering Tables

Typical Values of Elastic Modulus and Poisson’s Ratio for Granular Soils Elastic Modulus, Es Type of Soil Loose sand Medium dense sand Dense sand Silty sand Sand and gravel

MPa

lb/in.2

Poisson’s ratio, m

10–24 17–28

1,500–3,500 2,500–4,000

0.20–0.40 0.25–0.40

35–55 10–17 69–170

5,000–8,000 1,500–2,500 10,000–25,000

0.30–0.45 0.20–0.40 0.15–0.35

From Humphrey, D.N., Strength and deformation, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 17-8. Originally from Das, B. M. 1990. Principles of Foundation Engineering, 2nd ed., p. 161. PWSKent Publishing Co., Boston. With permission.

© 2004 by CRC Press LLC

1587_Book.fm Page 13 Sunday, August 31, 2003 9:44 PM

2-13

Civil and Environmental Engineering

Representative Applications and Controlling Functions of Geotextiles Primary Function Separation

Drainage-transmission

Reinforcement

Filter

Application Unpaved roads (temporary and permanent) Paved roads (secondary and primary) Construction access roads Working platforms Railroads (new construction) Railroads (rehabilitation) Landfill covers Preloading (stabilization) Marine causeways General fill areas Paved and unpaved parking facilities Cattle corrals Coastal and river protection Sports fields Retaining walls Vertical drains Horizontal drains Below membranes (drainage of gas and water) Earth dams Below concrete (decking and slabs) Pavement overlays Concrete overlays Subbase reinforcement in roadways and railways Retaining structures Membrane support Embankment reinforcement Fill reinforcement Foundation support Soil encapsulation Net against rockfalls Fabric retention systems Sandbags Reinforcement of membranes Load redistribution Bridging nonuniformity soft soil areas Encapsulated hydraulic fills Bridge piles for fill placement Trench drains Pipe wrapping Base course drains Frost protection Structural drains Toe drains in dams High embankments Filter below fabric-form Silt fences Silt screens Culvert outlets Reverse filters for erosion control: Seeding and mulching Beneath gabions Ditch amoring Embankment protection, coastal Embankment protection, rivers and streams Embankment protection, lakes Vertical drains (wicks)

Secondary Functions Filter, drains, reinforcement Filter, drains Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Drains, reinforcement Drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains, reinforcement Filter, drains Separation, filter Separation, filter Reinforcement Reinforcement Filter — — — Filter Drains Separation, drains, filter Drains Drains Drains Drains, filter separation Drains Drains — — Separation Separation Separation — Separation, drains Separation, drains Separation, drains Separation, drainage, reinforcement Separation, drains Separation, drains Drains Separation, drains Separation, drains Separation Separation

Separation

From Holtz, R.D., Geosynthetics, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 24-3. Originally from Christopher, B. R., and Holtz, R. D. 1989. Geotextile Design and Construction Guidelines., U.S. Federal Highway Administration, National Highway Institute, Report No. FHWA-HI-90-001.

© 2004 by CRC Press LLC

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2-14

CRC Handbook of Engineering Tables

Physical Properties of Water in SI Units* Surface Tension s ¥ 102 lb/ft

Vapor Pressure pu, psia

Vapor Pressure Head pu /g, ft

Bulk Modulus of Elasticity Eu ¥ 10–3, psi

Temperature, °F

Specific Weight y, lb/ft3

Density r, slugs/ft3

Viscosity m ¥ 105, lb·s/ft2

Kinematic Viscosity n ¥ 105, ft2/s

0 5 10 15 20

9.805 9.807 9.804 9.798 9.789

999.8 1000.0 999.7 999.1 998.2

1.781 1.518 1.307 1.139 1.002

1.785 1.519 1.306 1.139 1.003

0.0756 0.0749 0.0742 0.0735 0.0728

0.61 0.87 1.23 1.70 2.34

0.06 0.09 0.12 0.17 0.25

2.02 2.06 2.10 2.14 2.18

25 30 40 50 60

9.777 9.764 9.730 9.689 9.642

997.0 995.7 992.2 988.0 983.2

0.890 0.798 0.653 0.547 0.466

0.893 0.800 0.658 0.553 0.474

0.0720 0.0712 0.0696 0.0679 0.0662

3.17 4.24 7.38 12.33 19.92

0.33 0.44 0.76 1.26 2.03

2.22 2.25 2.28 2.29 2.28

70 80 90 100

9.589 9.530 9.466 9.399

977.8 971.8 965.3 958.4

0.404 0.354 0.315 0.282

0.413 0.364 0.326 0.294

0.0644 0.0626 0.0608 0.0589

31.16 47.34 70.10 101.33

3.20 4.96 7.18 10.33

2.25 2.20 2.14 2.07

* In this table and in the others to follow, if m ¥ 105 = 3.746 then m = 3.746 ¥ 10–5 lb·s/ft2, etc. For example, at 80°F, s ¥ 102 = 0.492 or s = 0.00492 lb/ft and Eu ¥ 10–3 = 322 or Eu = 322,000 psi. From Lyn, D.A., Fundamentals of hydraulics, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 29-27. Originally from Daugherty, R.L., Franzini, J.B., and Finnemore, E.J. (1985) Fluid Mechanics with Engineering Applications, 8th ed., McGraw-Hill, New York. With permission.

Physical Properties of Air at Standard Atmospheric Pressure in English Units Temperature T, °F

T, °C

Density r ¥ 103, slugs/ft3

Specifc Weight g ¥ 102, lb/ft3

Viscosity m ¥ 107, lb·s/ft2

Kinematic Viscosity n ¥ 104, ft2/s

–40 –20 0 10 20

–40.0 –28.9 –17.8 –12.2 –6.7

2.94 2.80 2.68 2.63 2.57

9.46 9.03 8.62 8.46 8.27

3.12 3.25 3.38 3.45 3.50

1.06 1.16 1.26 1.31 1.36

30 40 50 60 70

–1.1 4.4 10.0 15.6 21.1

2.52 2.47 2.42 2.37 2.33

8.11 7.94 7.79 7.63 7.50

3.58 3.62 3.68 3.74 3.82

1.42 1.46 1.52 1.58 1.64

80 90 100 120 140

26.7 32.2 37.8 48.9 60.0

2.28 2.24 2.20 2.15 2.06

7.35 7.23 7.09 6.84 6.63

3.85 3.90 3.96 4.07 4.14

1.69 1.74 1.80 1.89 2.01

160 180 200 250

71.1 82.2 93.3 121.1

1.99 1.93 1.87 1.74

6.41 6.21 6.02 5.60

4.22 4.34 4.49 4.87

2.12 2.25 2.40 2.80

From Lyn, D.A., Fundamentals of hydraulics, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 29-28. Originally from Daugherty, R.L., Franzini, J.B., and Finnemore, E.J. (1985) Fluid Mechanics with Engineering Applications, 8th ed., McGraw-Hill, New York. With permission.

© 2004 by CRC Press LLC

1587_Book.fm Page 15 Sunday, August 31, 2003 9:44 PM

2-15

Civil and Environmental Engineering

Physical Properties of Common Liquids at Standard Atmospheric Pressure in SI Units

Liquid

Temperature T, °F

Density r, kg/m3

Specific Gravity, s

Viscosity m ¥ 104, N·s/m2

Surface Tension s, N/m

20 20 20 20 20 –257 20 20 –195 20 20 20

895 1588 856 678 1258 72 808 13,550 1206 918 918 998

0.90 1.59 0.86 0.68 1.26 0.072 0.81 13.56 1.21 0.92 0.92 1.00

6.5 9.7 72 2.9 14,900 0.21 19.2 15.6 2.8 820 4400 10.1

0.029 0.026 0.03 …… 0.063 0.003 0.025 0.51 0.015 0.037 0.036 0.073

Benzene Carbon tetrachloride Crude oil Gasoline Glycerin Hydrogen Kerosene Mercury Oxygen SAE 10 oil SAE 30 oil Water

Vapor Pressure pu, kN/m2, abs

Modulus of Elasticity Eu ¥ 10–6, N/m2

10.0 12.1

1030 1100

55 0.000014 21.4 3.20 0.00017 21.4

4350

26,200

2.34

2070

From Lyn, D.A., Fundamentals of hydraulics, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 29-29. Originally from Daugherty, R.L., Franzini, J.B., and Finnemore, E.J. (1985) Fluid Mechanics with Engineering Applications, 8th ed., McGraw-Hill, New York. With permission.

Physical Properties of Common Gases at Standard Sea-Level Atmosphere and 68°F in English Units

Liquid Air Carbon dioxide Carbon monoxide Helium Hydrogen Methane Nitrogen Oxygen Water vapor

Chemical Formula

Molecular Weight

Specific Weight, g, lb/ft3

CO2 CO He H2 CH4 N2 O2 H 2O

29.0 44.0 28.0 4.00 2.02 16.0 28.0 32.0 18.0

0.0753 0.114 0.0726 0.0104 0.00522 0.0416 0.0728 0.0830 0.0467

Viscosity m ¥ 107, lb·s/ft2

Gas Constant R, ft·lb/(slug·°R) [= ft2/(s2 ·°R)]

3.76 3.10 3.80 4.11 1.89 2.80 3.68 4.18 2.12

1715 1123 1778 12,420 24,680 3100 1773 1554 2760

Specific Heat, ft·lb/(slug·°R) [= ft2/(s2 ·°R)] cp

cu

Specific Heat Ratio k = cp /cu

6000 5132 6218 31,230 86,390 13,400 6210 5437 11,110

4285 4009 4440 18,810 61,710 10,300 4437 3883 8350

1.40 1.28 1.40 1.66 1.40 1.30 1.40 1.40 1.33

From Lyn, D.A., Fundamentals of hydraulics, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 29-30. Originally from Daugherty, R.L., Franzini, J.B., and Finnemore, E.J. (1985) Fluid Mechanics with Engineering Applications, 8th ed., McGraw-Hill, New York. With permission.

© 2004 by CRC Press LLC

Material

Ultimate Strength (ksi)

Yield Strength (ksi)

Tension or Compression

Shear

25 20

10.6 10.0

4.00 3.75

12.9 13.0

— 36

— 24

13 25

— — 21

— — 22

— — —

–1350 –2250 —

66 86 —

48 80 100 150

36 60 75 150

24 36 45 90

±24,000

14,500

— —

— —

±1900 ±2250

Compression

Shear

Tension

Shear

0.100

60 38

— —

32 24

44 35

0.276

30 54

120 —

— 48

0.087

— — 40

3 5 —

65 100 120 200

— — — —

— —

7.4 8.4

0.283

0.018 0.021

Elastic Moduli (¥10–6 psi)

Coefficient of Thermal Expansion (¥106/°F)

Tension

0.065

Allow Stresses (psi)

1.1 1.5

Tension or Compression

Shear

3 5 6.5

30

120 135

1.76 1.76

6 12 — — 2.4

12

— —

5.8 6.7 6.0 — 14.0

6.5

— —

From Pan, A.D.E. and Popov, E.P., Mechanics of materials, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 46-7.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Aluminum alloy (extruded) 2024-T4 6061-T6 Cast iron gray malleable Concrete 8 gal/sack 6 gal/sack Magnesium alloy, AM100A Steel 0.2% carbon (hot rolled) 0.6% carbon (hot rolled) 0.6% carbon (quenched) 3½% Ni, 0.4% C Wood Douglas fir (coast) Southern pine (longleaf)

Unit Weight (lb/in.3)

1587_Book.fm Page 16 Sunday, August 31, 2003 9:44 PM

2-16

Typical Physical Properties of and Allowable Stresses for Some Common Materials (in U.S. Customary System Units)

Material Aluminum alloy (extruded) 2014-T6 6061-T6 Cast iron gray malleable Concrete 0.70 water-cement ratio 0.53 water-cement ratio Magnesium alloy, AM100A Steel 0.2% carbon (hot rolled) 0.6% carbon (hot rolled) 0.6% carbon (quenched) 3½% Ni, 0.4% C Wood Douglas fir (coast) Southern pine (longleaf)

Unit Mass (¥103 kg/m3)

Yield Strength (MPa)

Tension or Compression

Shear

170 138

73 70

27.6 25.9

23.2 23.4

— 250

— 165

90 170

41 83

10.4 12.1

— — 145

— — 150

— — —

20 35 45

— — 17

10.8

— — — —

330 550 690 1035

250 415 515 1035

165 250 310 620

+165.0

200

83

11.7

51 58

7 10

— —

— —

+13.1 +15.5

Compression

Shear

Tension

Shear

2.77

414 262

— —

220 165

300 241

7.64

210 370

825 —

— 330

2.41

— — 275

20 35 —

450 690 825 1380 — —

7.83

0.50 0.58

Elastic Moduli (GPa)

Coefficient of Thermal Expansion (¥10–6/°C)

Tension

1.80

Allow Stresses (MPa) Tension or Compression

–9.31 –15.5 —

Shear

0.455 0.592 —

25.2

100

0.825 0.930

12.1 12.1

— —

— —

From Pan, A.D.E. and Popov, E.P., Mechanics of materials, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 46-8.

2-17

© 2004 by CRC Press LLC

1587_Book.fm Page 17 Sunday, August 31, 2003 9:44 PM

Ultimate Strength (MPa)

Civil and Environmental Engineering

Typical Physical Properties of and Allowable Stresses for Some Common Materials (in SI System Units)

1587_Book.fm Page 18 Sunday, August 31, 2003 9:44 PM

2-18

CRC Handbook of Engineering Tables

Some Distribution Types Distribution Binomial

PMF (pX(x)) or PDF (fX(x))

Mean, E[X]

Ê nˆ n- x pX ( x ) = Á ˜ p x (1 - p) Ë x¯

Variance, Var[X]

np

np(1 – p)

nt

nt

m

s2

x = 0, 1, 2, º, n Poisson

pX ( x ) =

Normal

f X (x ) =

(vt )

x

e - vt

x!

È 1 Ê x - m ˆ2ù expÍ- Á ˜ ú s 2p ÍÎ 2 Ë s ¯ úû 1

-• < x < • Lognormal

f X (x ) =

È 1 Ê ln x - l ˆ 2 ù expÍ- Á ˜ ú Í 2Ë z ¯ ú xz 2p Î û

Ê 1 2ˆ Á l+ z ˜ 2 ¯

1

eË

[

(2l +z ) e z 2

e

2

]

-1

0<x<• È 1 Ê x ˆ2ù x expÍ- Á ˜ ú 2 a ÍÎ 2 Ë a ¯ úû

Rayleigh

f X (x ) =

Exponential

f X ( x ) = l exp - l( x - t)

0£x <•

[

]

t£x<• Gumbel type I maximum

[

- a x -u f X ( x ) = a exp -a( x - u) - e ( )

-• < x < •

Fretchet type II maximum

f X (x ) =

Weibull type III minimum

f X (x ) =

k Ê v -tˆ Á ˜ v - t Ë x - t¯

k +1

]

È Ê v - tˆkù expÍ-Á ˜ ú ÍÎ Ë x - t ¯ úû

a

p 2

pˆ 2 Ê Á2 - ˜ a Ë 2¯

t+

1 l

1 l2

u+

0.5772 a

p2 6a 2

(v - t)GÊÁË1 - 1k ˆ˜¯ + t

(v - t) ÍGÊÁË1 - 2k ˆ˜¯ ú - G 2 ÊÁË1 - 1k ˆ˜¯

(w - e)GÊÁË1 - 1k ˆ˜¯ + e

(w - e) ÍGÊÁË1 - 2k ˆ˜¯ + G 2 ÊÁË1 - 1k ˆ˜¯ ú

2

È

ù

Î

û

e<x<• k Ê x-eˆ Á ˜ w - e Ë w - e¯

k -1

È Ê x-eˆ expÍ-Á ˜ ÍÎ Ë w - e ¯

k

ù ú úû

2

È

ù

Î

û

e<x<•

From Quek, S.-T., Structural reliability, in The Civil Engineering Handbook, 2nd ed., Chen, W.-F. and Liew, J.Y.R., Eds., CRC Press, Boca Raton, FL, 2003, p. 52-4.

© 2004 by CRC Press LLC

1587_Book.fm Page 19 Sunday, August 31, 2003 9:44 PM

2-19

Civil and Environmental Engineering

Typical Compound Composition of Ordinary Portland Cement Chemical Formula 3CaO · SiO2 2CaO · SiO2 3CaO · Al2O3 4CaO · Al2O3 · Fe2O3 CaSO4 · 2H2O

Shorthand Notation

Chemical Name

Weight Percent

C 3S C 2S C 3A C4AF CSH2

Tricalcium silicate Dicalcium silicate Tricalcium aluminate Tetracalcium aluminoferrite Calcium sulfate dihydrate (gypsum)

50 25 12 8 3.5

From Mindness, S., Concrete constituent matenaus, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 1–4.

Properties of Some Lightweight Concretes Type of Lightweight Concrete Aerated Partially compacted

Structural lightweight aggregate concrete

Type of Aggregate

Aggregate Density, kg/m3

Concrete Density, kg/m3

— Expanded vermiculite and perlite Foamed slag Sintered pulverized-fuel ash Expanded clay or shale Foamed slag

— 5–240 480–960 640–960 560–1040 480–960

400–600 400–1150 960–1500 1100–1300 950–1200 1650–2050

Sintered pulverized-fuel ash Expanded clay or shale

640–960 560–1040

1350–1750 1350–1850

From Mindness, S., Concrete constituent matenaus, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 1–16.

© 2004 by CRC Press LLC

Mix

MK Content, %

Silica Fume Content, %

W/C or W/C + MK or W/C + SF

Unit Weight, kg/m3

Strength, MPa

1 Day

3 Days

7 Days

28 Days

90 Days

CO MK10 SF10

0 10 —

0 — 10

0.40 0.40 0.40

2350 2330 2320

20.9 25.0 23.2

25.5 32.9 28.6

28.9 37.9 34.7

36.4 39.9 44.4

42.5 43.0 48.0

Splitting-tensile†

Flexura‡

180 Days

28 Days

28 Days

E Modulus,§ GPa 28 Days

44.2 46.2 50.2

2.7 3.1 2.8

6.3 7.4 7.0

29.6 32.0 31.1

Compressive*

Note: MK, Metakaolin: W/C, water/cementitous material ratio; SF, silica fume. Average of three 102 ¥ 203-mm cylinders. † Average of two 152 ¥ 305-mm cylinders. ‡ Average of two 102 ¥ 76 ¥ 406-mm prims. § Average of two 152 ¥ 305-mm cylinders. From Malhotra, V.M., Mineral admixtures, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 2-38. Originally from Zhang, M.H. and Malhotra, V.M. 1995. Characteristics of a thermally activated alumina-silicate pozzolanic material and its use in concrete. Cement Concrete Res. 25(8):1713–1725. *

CRC Handbook of Engineering Tables

© 2004 by CRC Press LLC

1587_Book.fm Page 20 Tuesday, September 2, 2003 3:25 PM

2-20

Mechanical Properties of Hardened Concrete

1587_Book.fm Page 21 Tuesday, September 2, 2003 3:25 PM

2-21

Civil and Environmental Engineering

ACI 318 Maximum Chloride-Ion Content for Corrosion Protection Maximum Water-Soluble Chloride Ion (Cl–) in Concrete, Percent by Weight of Cement

Type of Application Prestressed concrete Reinforced concrete exposed to chloride in service Reinforced concrete that will be dry or protected from moisture in serviced Other reinforced concrete construction

0.06 0.15 1.00 0.30

From Whitney, D.P., Chemical admixtures, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 3-9. Originally from ACI 318-95/318R-95 Building Code and Commentary.

Properties of Typical Air-Entraining Admixtures Name Brand

Manufacturer

Active Ingredient

Dosage

Sp. Gr.

Protex regular Darex AEA Airex “D” Plastair Plastade

Protex Industries WR Grace & Co. Mulco, Inc. SikaChemical Corp. Sternson

Neutral vinusol resin Organic acid salts Sulfonated HC salt Vinusol resin Coconut acid amide

0.3–1.0 0.65–1.95 1.5–1.85 1.4 0.6–1.9

1.044 1.00–1.05 1.01–1.03 — 1.0

From Whitney, D.P., Chemical admixtures, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 3-11. Originally from Dolch, W.I. 1984. Air-entraining admixtures. In Concrete Admixtures Handbook Properties, Science, and Technology, V.S. Ramachandran, ed., pp. 269–302. Noyes Publications, Park Ridge, NJ.

Total Target Air Content for Concrete Nominal Maximum Aggregate Size, in. ⅜ ½ ¾ 1 1½ 2‡ 3‡

Air Content, %* Severe

Exposure† 7½ 7 6 6 5½ 5 4½

Moderate Exposure†

Mild Exposure†

6 5½ 5 4½ 4½ 4 3½

4½ 4 3½ 3 2½ 2 1½

* Project specifications often allow the air content of the delivered concrete to be within –1 to +2 percentage points of the table target values. † Severe exposure is an environment in which concrete is exposed to wet freeze-thaw conditions, deicers, or other aggressive agents. Moderate exposure is an environment in which concrete is exposed to freezing but will not be continually moist, will not be exposed to water for long periods before freezing, and will not be in contact with deicers or aggressive chemicals. Mild exposure is an environment in which concrete is not exposed to freezing conditions, deicers or aggressive agents. ‡ These air contents apply to total mix, as for the preceding aggregate sizes. When testing these concretes, however, aggregate larger than 1½ in. is removed by handpicking or sieving and air content is determined on the minus 1½ in. fraction of mix. (Tolerance on air content as delivered applies to this value.) Air content of the total mix is computed from the value determined on the minus 1½ in. fraction. From Whitney, D.P., Chemical admixtures, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 3-13. Originally from Kosmatka, S.H. and Panarese, W.C. 1988. Design and Control of Concrete Mixtures, 13th ed., Portland Cement Association, Skokie, Ill.

© 2004 by CRC Press LLC

1587_Book.fm Page 22 Tuesday, September 2, 2003 3:25 PM

2-22

CRC Handbook of Engineering Tables

l

> 5d

UNIFORMLY LOADED BEAM FORMULAS FOR WOOD DESIGN

d End Support

lc

lb

Interior Support

lb

w

ONE SPAN

Dmax = l M

Mmax = wl 2/8

+ 0.5 wl

VEM = [0.5 wl - w (d + lb 2 (end, modified)

V

TWO SPANS

0.5 wl

l

l M

D max = 1 185

0.375 wl

l

4

lb )] 2 lb VIM = [0.625 wl - w (d + )] 2 (interior, modified)

VEM =

0.625 wl

0.375 wl

0.625 wl

wl E'I

)]

M max = wl 2 /8

+

+

V

THREE (or more) SPANS

wl 4 E' I

5 384

l

[0.375 wl - w (d +

Dmax = 1 145

l

wl E'I

4

Mmax = wl 2 /10

M 0.4 wl

0.5 wl

0.6 wl

V 0.6 wl

0.5 wl

lb 2 lb = [0.6 wl - w (d + 2

VEM = [0.4 wl - w (d +

)]

VIM

)]

0.4 wl

DESIGN NOTES: 1. If l b is unknown, use l b = 0 for shear calculations. 2. If d is unknown when calculating shear force, either: a) Assume d = 0 in calc. and re-evaluate with d determined if shear controls. b) Assume a likely value of d and check with an additional iteration when d is determined.

Beam formulas for one-, two-, and three-span conditions. (From Johnston, D.W., Design and construction of concrete formwork, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 7-33.)

© 2004 by CRC Press LLC

1587_Book.fm Page 23 Sunday, August 31, 2003 9:44 PM

2-23

Civil and Environmental Engineering

Theoretical Maximum Load Ratios on Floor and Prop for Various Shore/Reshore Combinations Absolute Maximum Load Ratio

Converged Maximum Load Ratio

Shore + Reshore

On Floor Slab

On Prop

On Floor Slab

On Prop

1+1 1+2 1+3 1+4 1+5

1.50 1.34 1.25 1.20 1.17

1.0 1.0 1.0 1.0 1.0

1.50 1.34 1.25 1.20 1.17

1.0 1.0 1.0 1.0 1.0

2+0 2+1 2+2 2+3 2+4 2+5

2.25 1.83 1.75 1.61 1.60 1.55

2.0 2.0 2.0 2.0 2.0 2.0

2.00 1.78 1.67 1.60 1.56 1.53

1.0 1.11 1.17 1.21 1.25 1.24

3+0 3+1 3+2 3+3 3+4 3+5

2.36 2.10 1.97 1.84 1.77 1.77

3.0 3.0 3.0 3.0 3.0 3.0

2.00 1.87 1.80 1.76 1.72 1.70

1.34 1.37 1.40 1.42 1.43 1.43

From Ghosh, S.K., Construction loading in high-rise buildings, in Concrete Construction Engineering Handbook, Nawy, E.G., Ed., CRC Press, Boca Raton, FL, 1998, p. 8-7. Originally from Lasisi, M.Y. and Ng, S.F. 1979. Construction loads imposed on high-rise floor slabs. Concrete Int. 1(2):24–29.

Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a Year 1902 1903 1905 1906

1907 1908 1909 1912 1915 1917 1918 1920 1923

Day-Month 19-Apr 16-Dec 19-Apr 28-Apr 04-Apr 08-Sep 31-Jan 16-Mar 18-Apr 17-Aug 14-Jan 21-Oct 28-Dec 23-Jan 09-Aug 13-Jan 21-Jan 30-Jul 13-Feb 16-Dec 24-Mar 25-May 01-Sep

© 2004 by CRC Press LLC

Location Guatemala Turkestan Turkey Turkey India, Kangra Italy, Calabria Colombia Taiwan, Kagi San Francisco, CA Chile, Santiago Jamaica, Kingston Central Asia Italy, Messina Iran Turkey, Marmara Sea Italy, Avezzano Indonesia, Bali China China, Canton China, Gansu China Iran Japan, Kanto

Latitude 14N 40.8N 39.1N 39.1N 33.0N 39.4N 1N 23.6N 38N 33S 18.2N 38N 38N 33.4N 40.5N 42N 8.0S 28.0N 23.5N 35.8N 31.3N 35.3N 35.0N

Longitude

Deaths

M

91W 72.6E 42.4E 42.5E 76.0E 16.4E 81.5W 120.5E 123W 72W 76.7W 69E 15.5E 49.1E 27E 13.5E 115.4E 104.0E 117.0E 105.7E 100.8E 59.2E 139.5E

2,000 4,500 1,700 2,200 19,000 2,500 1,000 1,300 2,000+ 20,000 1,600 12,000 70,000 5,500 1,950 29,980 15,000 1,800 10,000 200,000 5,000 2,200 143,000

7.5 6.4 6.3 8.6 7.9 8.9 7.1 8.3 8.6 6.5 8.1 7.5 7.3 7.8 7.5 6.5 7.3 8.6 7.3 5.7 8.3

Comments/Damage ($ millions)

Conflagration Conflagration Conflagration Deaths possibly 100,000

Major fractures, landslides

$2800, conflagration

1587_Book.fm Page 24 Sunday, August 31, 2003 9:44 PM

2-24

CRC Handbook of Engineering Tables

Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a (continued) Year 1925 1927 1929 1930 1931 1932 1933 1934 1935

1939 1940 1942

1943 1944

1945 1946

1948 1949 1950 1954 1957

1960 1962 1963 1966 1968 1969 1970

1972 1974

Day-Month

Location

Latitude

Longitude

Deaths

M

16-Mar 07-Mar 22-May 01-May 06-May 23-Jul 31-Mar 25-Dec 02-Mar 25-Aug 15-Jan 20-Apr 30-May 16-Jul 25-Jan 26-Dec 10-Nov 26-Nov 20-Dec

China, Yunnan Japan, Tango China, nr Xining Iran Iran Italy Nicaragua China, Gansu Japan, Sanriku China India, Bihar-Nepal Formosa Pakistan, Quetta Taiwan Chile, Chillan Turkey, Erzincan Romania Turkey Turkey, Erbaa

25.5N 35.8N 36.8N 38N 38.0N 41.1N 13.2N 39.7N 39.0N 32.0N 26.6N 24.0N 29.6N 24.4N 36.2S 39.6N 45.8N 40.5N 40.9N

100.3E 134.8E 102.8E 58E 44.5E 15.4E 85.7W 97.0E 143.0E 103.7E 86.8E 121.0E 66.5E 120.7E 72.2W 38E 26.8E 34.0E 36.5E

5,000 3,020 200,000 3,300 2,500 1,430 2,400 70,000 2,990 10,000 10,700 3,280 30,000 2,700 28,000 30,000 1,000 4,000 3,000

7.1 7.9 8.3 7.4 7.2 6.5 5.6 7.6 8.9 7.4 8.4 7.1 7.5 6.5 8.3 8 7.3 7.6 7.3

10-Sep 26-Nov 15-Jan 01-Feb 07-Dec 12-Jan 27-Nov 31-May 10-Nov

Japan, Tottori Turkey Argentina, San Juan Turkey Japan, Tonankai Japan, Mikawa Iran Turkey Peru, Ancash

35.6N 41.0N 31.6S 41.4N 33.7N 34.8N 25.0N 39.5N 8.3S

134.2E 33.7E 68.5W 32.7E 136.2E 137.0E 60.5E 41.5E 77.8W

1,190 4,000 5,000 2,800 1,000 1,900 4,000 1,300 1,400

7.4 7.6 7.8 7.4 8.3 7.1 8.2 6 7.3

20-Dec 28-Jun 05-Oct 05-Aug 15-Aug

Japan, Tonankai Japan, Fukui Turkmenistan Ecuador, Ambato India, Assam; Tibet

32.5N 36.1N 38.0N 1.2S 28.7N

134.5E 136.2E 58.3E 78.5E 96.6E

1,330 5,390 110,000 6,000 1,530

8.4 7.3 7.3 6.8 8.7

09-Sep 27-Jun 02-Jul 13-Dec 29-Feb 22-May 01-Sep 26-Jul

Algeria, Orleansvl. USSR (Russia) Iran Iran Morocco, Agadir Chile Iran, Qazvin Yugoslavia, Skopje

36N 56.3N 36.2N 34.4N 30N 39.5S 35.6N 42.1N

1.6E 116.5E 52.7E 47.6E 9W 74.5W 49.9E 21.4E

1,250 1,200 1,200 1,130 10,000 4,000 12,230 1,100

6.8

19-Aug 31-Aug 25-Jul 04-Jan 28-Mar 31-May 10-Apr 23-Dec 10-May 28-Dec

Turkey, Varto Iran Eastern China Yunnan, China Turkey, Gediz Peru Iran, southern Nicaragua China Pakistan

39.2N 34.0N 21.6N 24.1N 39.2N 9.2S 28.4N 12.4N 28.2N 35.0N

41.7E 59.0E 111.9E 102.5E 29.5E 78.8W 52.8E 86.1W 104.0E 72.8E

2,520 12,000 3,000 10,000 1,100 66,000 5,054 5,000 20,000 5,300

7.1 7.3 5.9 7.5 7.3 7.8 7.1 6.2 6.8 6.2

© 2004 by CRC Press LLC

7.4 7.3 5.9 9.5 7.3 6

Comments/Damage ($ millions)

Large fractures

Deaths possibly 60,000 $100

Some reports of 1,000 killed

Deaths possibly 8,000 Deaths possibly 5,000

Landslides, great destruction Conflagration Large landslides Great topographical changes

Deaths possibly 15,000 Deaths possibly 5,000 Shallow depth just under city Deaths possibly 20,000

Great rockslide; $500 Managua

1587_Book.fm Page 25 Sunday, August 31, 2003 9:44 PM

2-25

Civil and Environmental Engineering

Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a (continued) Year 1975 1976

1977 1978 1980 1981 1982 1983 1985 1986 1987 1988 1990 1991 1992 1993 1995 1997 1998

1999

2001

Day-Month

Location

Latitude

Longitude

Deaths

M

04-Feb 06-Sep 04-Feb 06-May 25-Jun 27-Jul

China Turkey Guatemala Italy, northeastern New Guinea China, Tangshan

40.6N 38.5N 15.3N 46.4N 4.6S 39.6N

122.5E 40.7E 89.1W 13.3E 140.1E 118.0E

10,000 2,300 23,000 1,000 422 255,000

7.4 6.7 7.5 6.5 7.1 8

16-Aug 24-Nov 04-Mar 16-Sep 10-Oct 23-Nov 11-Jun 28-Jul 13-Dec 30-Oct 19-Sep 10-Oct 06-Mar 20-Aug 07-Dec 20-Jun 16-Jul 19-Oct 12-Dec 29-Sep 16-Jan 27-May 10-May

Philippines Iran-USSR border Romania Iran, Tabas Algeria, El Asnam Italy, southern Iran, southern Iran, southern W. Arabian Peninsula Turkey Mexico, Michoacan El Salvador Colombia-Ecuador Nepal-India border Armenia, Spitak Iran, western Philippines, Luzon India, northern Indonesia, Flores India, southern Japan, Kobe Sakhalin Island Iran, northern

6.3N 39.1N 45.8N 33.2N 36.1N 40.9N 29.9N 30.0N 14.7N 40.3N 18.2N 13.8N 0.2N 26.8N 41.0N 37.0N 15.7N 30.8N 8.5S 18.1N 34.6N 52.6N 33.9N

124.0E 44.0E 26.8E 57.4E 1.4E 15.3E 57.7E 57.8E 44.4E 42.2E 102.5W 89.2W 77.8W 86.6E 44.2E 49.4E 121.2E 78.8E 121.9E 76.5E 135E 142.8E 59.7E

8,000 5,000 1,500 15,000 3,500 3,000 3,000 1,500 2,800 1,342 9,500 1,000 1,000 1,450 25,000 40,000 1,621 2,000 2,500 9,748 6,000 1,989 1,560

7.9 7.3 7.2 7.8 7.7 7.2 6.9 7.3 6 6.9 8.1 5.5 7 6.6 7 7.7 7.8 7 7.5 6.3 6.9 7.5 7.5

04-Feb 30-May 17-Jul 25-Jan 17-Aug 20-Sep

Afghanistan Afghanistan Papua New Guinea Colombia Turkey Taiwan

37.1N 37.1N 2.96S 4.46N 40.7N 23.7N

70.1E 70.1E 141.9E 75.82W 30.0E 121.0E

2,323 4,000 2,183 1,185 17,118 2,297

6.1 6.9 7.1 6.3 7.4 7.6

26-Jan

India, Bhuj

23.3 N

70.3 E

19,988

7.7

Total Events = 108 a

Comments/Damage ($ millions)

$6,000 West Irian Deaths possibly 655,000; $2,000 Mindanao

$11

Deaths possibly 30,000

$16,200 Deaths possibly 50,000 Landslides, subsidence Tsunami wave height 25 m $100,000, conflagration 4,460 injured; 60,000 homeless Also Tajikistan Also Tajikistan Tsunami 50,000 injured; $7,000 8,700 injured; 600,000 homeless 166,812 injured; 600,000 homeless

Total Deaths = 1,762,802

Magnitude scale varies. From Scawthorn, C., Earthquakes: A historical perspective, in Earthquake Engineering Handbook, Chen, W.-F. and Scawthorn, C., Eds., CRC Press, Boca Raton, FL, 2003, pp. 1-2 to 1-4. Originally from National Earthquake Information Center, Golden, CO, http://neic.usgs.gov/neis/eqlists/eqsmajr.html.

© 2004 by CRC Press LLC

1587_Book.fm Page 26 Sunday, August 31, 2003 9:44 PM

2-26

CRC Handbook of Engineering Tables

Selected U.S. Earthquakesa

Year

Month

Day

1755 1774 1791

11 2 5

18 21 16

1811 1812

12 1 2 10

16 23 7 5

36N 36.6N 36.6N

6 6 1 10 4 10 3 9 2 4 5 5 9 4 10 6 11 3 12 10 5 9 4 8 7 12 3 7 8 8 3 4 2 3 8 11 1 5 7 11 5 10 11 4 7 10 11 6 10 2

10 0 9 8 3 21 26 1 24 19 16 31 4 18 3 29 4 11 31 19 19 5 13 21 21 16 9 10 18 30 28 29 9 28 1 29 24 25 27 8 2 28 16 24 8 1 24 26 18 28

38N 37.5N 35N 37N 19N 37.5N 36.5N 32.9N 31.5N 38.5N 14N

122W 123W 119W 122W 156W 122W 118W 80W 117W 123W 143W

60N 38N 40.5N 34.3N 34.5N 33.6N 31.8N 46.6N 32.7N 44.7N 47.1N 19.7N 35N 39.3N 51.3N 58.6N 44.8N 41.8N 61N 47.4N 34.4N 42.1N 39.4N 19.3N 37.8N 37.6N 38.2N 41.2N 36.2N 43.9N 19.5N 37.3N 34N 34.1N 33.2N 19.4N 37.1N 34.1N

142W 123W 118W 120W 121W 118W 116W 112W 116W 74.7W 123W 156W 119W 118W 176W 137W 111W 112W 148W 122W 118W 113W 122W 155W 122W 119W 83.9W 124W 120W 114W 155W 122W 117W 118W 116W 155W 122W 118W

1817 1836 1838 1857 1865 1868 1872 1886 1892

1897 1899 1906 1915 1925 1927 1933 1934 1935 1940 1944 1949 1951 1952 1954 1957 1958 1959 1962 1964 1965 1971 1975 1975 1980

1983

1984 1986 1987 1989 1990

© 2004 by CRC Press LLC

Latitude

Longitude

M

MMI

Fatalities

Damage US $ (millions)

8 7 8 90W 89.6W 89.6W

8.6 8.4 8.7

8.3

6.8 8.5 7.7

5.8 8.3 8.3 7.8 6.2 7.5 6.3 7.1 6.2 7.1 5.6 7 6.9 7.7 7 8.6 7.9 7.7 5.8 8.3 6.5 6.7 6.2 6.1 7.2 5.9 6.4 5.2 7 6.5 7.3 6.6 6.2 6.1 6 6.3 6.1 7.1 5.5

12 12 8 10 10 7 9 10 10 10 9 10 9

81 3 50 60

5

2,000

400

13

8

115

40

10

2 9

8

8

19 6 2 25

11 10

13

60

8 11

9 10

3 5

7 11 8

131 7 65

9 7 7

2 1

7 8

5 2

8 7 7 8 6 6 9 7

8 2 62

2 540 13 553 1 6 4 4 2 1 3 31 13 7 8 5 358

6,000 13

Locale Massachusetts, Nr Cape Ann Eastern Virginia (MMI from Sta) Connecticut, E. Haddam (MMI from Sta) Missouri, New Madrid Missouri, New Madrid Missouri, New Madrid Massachusetts, Woburn (MMI from Sta) California California California, Central California, San Jose, Santa Cruz Hawaii California, Hayward California, Owens Valley South Carolina, Charleston California, San Diego County California, Vacaville, Winters Guam, Agana Virignia, Giles County (Mb from Sta) Alaska, Cape Yakataga California, San Francisco (fire) Nevada, Pleasant Valley California, Santa Barbara California, Lompoc California, Long Beach California, Baja, Imperial Valley Montana, Helena California, southeast of El Centro New York, Massena Washington, Olympia Hawaii California, Kern County Nevada, Dixie Valley Alaska Alaska, Lituyabay (landslide) Montana, Hebgen Lake Utah Alaska Washington, Seattle California, San Fernando Idaho, Pocatello Valley California, Oroville Reservoir Hawaii California, Livermore California, Mammoth Lakes Kentucky, Maysville California, northern coast California, central, Coalinga Idaho, Borah Peak Hawaii, Kapapala California, Morgan Hill California, Palm Springs California, Whittier California, Superstition Hills Hawaii California, Loma Prieta California, southern, Claremont, Covina

1587_Book.fm Page 27 Sunday, August 31, 2003 9:44 PM

2-27

Civil and Environmental Engineering

Selected U.S. Earthquakesa (continued)

Year

Month

Day

Latitude

1992

4 4 6 6 6 3 9 1 1 2 10

23 25 28 28 29 25 21 16 17 3 6

34N 40.4N 34.2N 34.2N 36.7N 45N 42.3N 40.3N 34.2N 42.8N 65.2N

1993 1994

1995 a

Longitude 116W 124W 117W 116W 116W 123W 122W 76W 119W 111W 149W

M

MMI

6.3 7.1 6.7 7.6 5.6 5.6 5.9 4.6 6.8 6 6.4

7 8 8 9 7 7 5 9 7

Fatalities

Damage US $ (millions) 66

3

92

2 57

30,000

Locale California, Joshua Tree California, Humboldt, Ferndale California, Big Bear California, Landers, Yucca Valley California-Nevada border T.S. Washington-Oregon Oregon, Klamath Falls Pennsylvania (felt Canada) California, Northridge Wyoming, Afton Alaska (oil pipeline damaged)

Magnitude scale varies. From Scawthorn, C., Earthquakes: A historical perspective, in Earthquake Engineering Handbook, Chen, W.-F. and Scawthorn, C., Eds., CRC Press, Boca Raton, FL, 2003, pp. 1-4 to 1-5. Originally from National Earthquake Information Center (1996). Database of Significant Earthquakes Contained in Seismicity Catalogs, Golden, CO.

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RESULT

MITIGATION

Hazard mapping; ground remediation; tsunami walls…

Bracing and strengthening, reduction of mass, base isolation, structural control…

Improved storage/infrastructure, better emergency response…

PRIMARY HAZARDS: Faulting, Shaking, Liquefaction, Landsliding, Tsunami…

PRIMARY DAMAGE: Building / Structural Nonstructural / Equipment

SECONDARY HAZARD / DAMAGE: Fire, Hazmat, Flooding…

Demand (hazard) eliminated or reduced

Capacity (strength…) increased

PRIMARY LOSS: Life / Injury, Repair Costs, Function, Communications/Control… Improved emergency planning and response; insurance…

SECONDARY LOSS:

Loss avoided or shared

Business / Operations Interruption Market Share, Reputation…

Earthquake loss process. (From Scawthorn, C., Earthquake risk management: An overview, in Earthquake Engineering Handbook, Chen, W.-F. and Scawthorn, C., Eds., CRC Press, Boca Raton, FL, 2003, p. 2-7.)

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CRC Handbook of Engineering Tables

Secondary demands eliminated or reduced

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2-28

EARTHQUAKE OCCURS

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Civil and Environmental Engineering

Estimate the Risk

PROBLEM Define Define Problem Problem Estimate Estimate Baseline Baseline Risk Risk

Internal Internal Policy Policy External External Constraints Constraints

Determine Determine Further Further Action Action Needed Needed Y

N Stop Stop

Select Select Basis Basis for for Analysis Analysis Identify Identify Alternatives Alternatives

Examine Mitigation Alternatives

Alternatives Eliminated

Screen Screen Alternatives Alternatives

Further Further Analysis Analysis

Choose Choose Decision Decision Method Method Describe Describe Alternatives Alternatives Values Values Uncertainties Uncertainties

Collect Collect and and Organize Organize Data Data Apply Apply Decision Decision Method Method Communicate Communicate Results Results Make Make Decision Decision

Make Decision

ACTION Earthquake risk management decision process. (From Scawthorn, C., Earthquake risk management: An overview, in Earthquake Engineering Handbook, Chen, W.-F. and Scawthorn, C., Eds., CRC Press, Boca Raton, FL, 2003, p. 2-9.)

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CRC Handbook of Engineering Tables

Principle Elemental Components of Structural Steel Carbon

Manganese Phosphorus

Sulfur

Silicon Aluminum Vanadium and Columbium Titanium Nickel Chromium Copper Nitrogen Boron

Principal hardening element in steel, increases strength and hardness, decreases ductility, toughness, and weldability Moderate tendency to segregate Increases strength and toughness Controls negative effects of sulfur Increases strength and hardness, decreases ductility and toughness Considered as an impurity, but sometimes added for atmospheric corrosion resistance Strong tendency to segregate Considered undesirable except for machineability. Decreases ductility, toughness, and weldability Adversely affects surface quality Strong tendency to segregate Used to deoxidize or “kill” molten steel Increases strength Used to deoxidize or “kill” molten steel Refines grain size, thus increasing strength and toughness Small additions increase strength Refines grain size, thus increasing strength and toughness Small amounts refine the grain size, thus increasing toughness Increases strength and toughness Increases strength Increases atmospheric corrosion resistance Primary contributor to atmospheric corrosion resistance Increases strength Increases strength and hardness May decrease ductility and toughness Small amounts increase hardenability, used only in aluminum-killed steels Most cost effective at low carbon levels

From Hamburger, R.O. and Nazir, N.A., Seismic design of steel structures, in Earthquake Engineering Handbook, Chen, W.-F. and Scawthorn, C., CRC Press, Boca Raton, FL, 2003, p. 12-10.

FEDERAL ACTION (1508.18)

NONCATEGORICAL EXCLUSION

CATEGORICAL EXCLUSION (1508.4) LEVEL 1 ENVIRONMENTAL ASSESSMENT (1508.9)

NO SIGNIFICANT IMPACT (FONSI) (1508.13)

SIGNIFICANT IMPACT (1508.27)

LEVEL 2 EIS (1508.11) LEVEL 3

Three levels of analysis in the EIA process. Number in parentheses denotes paragraph in CEQ regulations which contains definition. (From Canter, L.W., Background conceptual and administrative information, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 43.)

© 2004 by CRC Press LLC

Analyze and evaluate plans and actions

Formulate plans

Recommend plan of action Transmit plan report

Develop plan of study

Inventory and data base Environmental assessment on environmental of plans of actions resources

EIS Reg’d?

Analyze environmental impact of plans

Prepare draft EIS

Submit final EIS Take action

Lead Agency

Public outputs

Seek public input on environmental problems and needs on the study

Input to inventories

Review Agencies

Publics

Disseminate findings on research and environmental inventories

Public reaction on important resources and environmental sensitivity areas

Input to inventories from public’s prespective review/critique

yes Present alternative plans and assessment of environmental no impacts

Analyze particular impacts of plans

Input public perceptions and concerns on impacts of alternatives

Notice of intent Negative declaration

Review and concur on decision

Review and concerns on decision

Draft EIS as a working document

Circulate finished draft

Public hearing

Review critique final draft

Hearing testimony

Review critique final draft

Hearing testimony

Take action

Input to draft EIS

Input to draft EIS: Impact assessment, public evaluation of relative significance of impacts, tradeoffs

Public participation in environmental impact assessment. (From Canter, L.W., Background conceptual and administrative information, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 45.)

2-31

© 2004 by CRC Press LLC

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Study tasks

Conduct studies: engineering, economics, environmental, social

Civil and Environmental Engineering

Planning Activity

Analysis of problems, needs, and study issues

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CRC Handbook of Engineering Tables

Priority Chemicals Targeted in the 33/50 Project for the Industrial Sector Pollution Prevention Strategy Target Chemicals

Million Pounds Released in 1988

Benzene Cadmium Carbon Tetrachloride Chloroform Chromium Cyanide Dichloromethane Lead Mercury Methyl Ethyl Ketone Methyl Isobutyl Ketone Nickel Tetrachloroethylene Toluene 1,1,1-Trichloroethane Trichloroethylene Xylene

33.1 2.0 5.0 26.9 56.9 13.8 153.4 58.7 0.3 159.1 43.7 19.4 37.5 344.6 190.5 55.4 201.6

From Liu, D.H.F., Regulations and definitions, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 85. Originally from U.S. Environmental Protection Agency, 1992, Pollution prevention 1991: Research program, EPA/600/R-92/189 (September). (Washington, D.C.: Office of Research and Development).

Main Membrane Separation Processes: Operating Principles and Application Separation Process

Membrane Type

Microfiltration

Symmetric microporous membrane, 0.1 to 10 mA pore radius Ultrafiltration Asymmetric microporous membrane, 1 to 10 mA pore radius Reverse osmosis Symmetric skin-type membrane Dialysis Symmetric microporous membrane, 0.1 to 10 mA pore size Electrodialysis Cation and anion exchange membranes Gas operation Homogeneous or porous polymer Supported liquid membranes Membrane distillation

Driving Force

Method of Separation

Range of Application

Hydrostatic pressure difference, 0.1 to 1 bar Hydrostatic pressure difference, 0.5 to 5 bar Hydrostatic pressure, 20 to 100 bar Concentration gradient

Sieving mechanism due to pore radius and adsorption Sieving mechanism

Sterile filtration clarification

Electrical potential gradient Hydrostatic pressure concentration gradient Chemical gradient

Symmetric microporous membrane with adsorbed organic liquid Microporous membrane Vapor-pressure

Separation of macromolecular solutions

Solution–diffusion Separation of salt and mechanism microsolutes from solutions Diffusion in convection- Separation of salts and free layer microsolutes from macromolecular solutions Electrical charge of Desalting of ionic solution particle and size Solubility, diffusion Separation from gas mixture

Solution diffusion via carrier

Separation

Vapor transport into Ultrapure water hydrophobic membrane concentration of solutions

From Liu, D.H.F., Separation and recycling systems, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 140. Originally from E. Orioli, R. Molinari, V. Calabrio, and A.B. Gasile, 1989, Membrane technology for production—integrated pollution control systems, Seminar on the Role of the Chemical Industry in Environmental Protection, CHEM/SEM. 18/R. 19, Geneva.

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Civil and Environmental Engineering

Summary of NAAQSs Standard (@ 25˚C and 760 mm Hg) Pollutant Particulate matter 10 micrometers (PM10) Sulfur dioxide (SO2)

Carbon monoxide (CO) Ozone (O3) Nitrogen dioxide (NO2) Lead (Pb)

Averaging Time

Primary

Secondary

Annual arithmetic mean 24-hour Annual arithmetic mean 24-hour 3-hour 8-hour 1-hour 1-hour per day Annual arithmetic mean Quarterly arithmetic mean

50 mg/m 150 mg/m3 0.03 ppm (80 mg/m3) 0.14 ppm (365 mg/m3) None 9 ppm (10 mg/m3) 35 ppm (40 mg/m3) 0.12 ppm (235 mg/m3) 0.053 ppm (100 mg/m3) 1.5 mg/m3

Same as primary Same as primary Same as primary Same as primary 0.5 ppm (1300 mg/m3) Same as primary Same as primary Same as primary Same as primary Same as primary

3

Notes: All standards with averaging times of 24 hours or less, and all gaseous fluoride standards, are not to have more than one actual or expected exceedance per year. mg/m3 or mg/m3 = microgram or milligram per cubic meter From Zegel, W.C., Setting standards, in Environmental Engineers’ Handbook, 2nd Ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 189. Originally from CFR Title 40, Part 50. Environmental Protection Agency, U.S. Government Printing Office, 1993.

National Emission Standards for Hazardous Air Pollutants Affected Facility

Emission Level

Monitoring

Asbestos Asbestos mills Roadway surfacing Manufacturing Demolition/renovation

Spraying friable asbestos Equipment and machinery Buildings, structures, etc. Fabricating products Friable insulation Waste disposal

Waste disposal sites

No visible emissions or meet equipment standards Contain no asbestos, except temporary use No visible emissions or meet equipment standards Wet friable asbestos or equipment standards and no visible emissions No visible emissions or meet equipment standards <1 percent asbestos dry weight No visible emissions or meet equipment standards No asbestos No visible emissions or met equipment and work practice requirements No visible emissions; design and work practice requirements

No requirement No requirement No requirement No requirement

No requirement No requirement No requirement No requirement No requirement

No requirement

Beryllium Extraction plants Ceramic plants Foundries Incinerators Propellant plants Machine shops (Alloy >5 percent by weight beryllium)

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1. 10 g/hour, or 2. 0.01 m/m3 (thirty-day)

1. Source test 2. Three years CEMa

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CRC Handbook of Engineering Tables

National Emission Standards for Hazardous Air Pollutants (continued) Affected Facility Rocket motor test sites Closed tank collection of combustion products

Emission Level 75 mg min/m3 of air within 10 to 60 minutes during two consecutive weeks 2 g/hour, maximum 10 g/day

Monitoring Ambient concentration during and after test Continuous sampling during release

Mercury Ore processing Chlor-alkali plants

2300 g/24 hour 2300 g/24 hour

Sludge dryers and incinerators

3200 g/24 hour

Source test Source test or use approved design, maintenance and housekeeping Source test or sludge test

Vinyl Chloride (VC) Ethylene dichloride (EDC) manufacturing

VC manufacturing Polyvinyl chloride (PVC) manufacturing Equipment Reactor opening loss Reactor manual vent valve Sources after stripper

EDC/VC/PVC manufacturing Relief valve discharge Loading/unloading Slip gauge Equipment seals Relief valve leaks Manual venting Equipment opening Sampling (>10 percent by weight VC) LDARd In-process wastewater

1. EDC purification: 10 ppmb

Source test/CEMa

2. Oxychlorination: 0.2 g/kg of EDC product 10 ppmb

Source test

10 ppmb 0.02 g/kg No emission except emergency Each calendar day: 1. Strippers—2000 ppm (PVC disposal resins excluding latex); 400 ppm other 2. Others—2 g/kg (PVC disposal resins excluding latex); 0.4 g/kg other

Source test/CEMa Source test

None, except emergency 0.0038 m3 after load/unload or 10 ppm when controlled Emission to control Dual seals required Rupture disc required Emissions to control Reduce to 2.0 percent VC or 25 gallon Return to process Approved program required 10 ppm VC before discharge

Source test/CEMa

Source test

Source test

Source test

Approved program Source test

Inorganic Arsenic Glass melting furnace

Copper converter

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Existing: <2.5 Mg/year c or 85 percent control New or modified: <0.4 Mg/year or 85 percent control Secondary hooding system Particle limit 11.6 mg/dscmd

Method 108 Continuous opacity and temperature monitor for control Methods 5 and 108A Continuous opacity for control

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Civil and Environmental Engineering

National Emission Standards for Hazardous Air Pollutants (continued) Affected Facility

Emission Level Approved operating plan

Arsenic trioxide and metallic arsenic plants using roasting/condensation process

Approved plan for control of emissions

Monitoring Airflow monitor for secondary hood Opacity monitor for control

Ambient air monitoring Benzene Equipment leaks (Serving liquid or gas 10 percent by weight benzene; facilities handling 1000 Mg/year and coke oven by-product exempt) Pumps Compressors Pressure relief valves Sampling connection systems Open-end valves/lines Valves

Pressure relief equipment Product accumulators Closed-vent systems and control devices Coke by-product plants Equipment and tanks

Light-oil sumps Napthalene equipment Equipment leaks (serving 10 percent by weight) Exhauster (1 percent by weight) Benzene storage vessels Vessels with capacity >10,000 gallon

Benzene transfer Producers and terminals (loading >1,300,000/year) Loading racks (marine rail, truck) Exemptions: Facilities loading <70 percent benzene Facilities loading less than required of >70 percent benzene Both of above subject to recordkeeping Waste Operations

© 2004 by CRC Press LLC

Leak is 10,000 ppm using Method 21; no detectable emissions (NDE) is 500 ppm using Method 21 Monthly LDAR,e dual seals, 95 percent control or NDEf Seal with barrier fluid, 95 percent control or NDEf NDEf or 95 percent control Closed purge or closed vent Cap, plug, or second valve Monthly LDARe (quarterly if not leaking for two consecutive months) or NDEf LDARe 95 percent control NDE or 95 percent control Enclose source, recover, or destroy. Carbon adsorber or incinerator alternate Cover, no venting to sump Zero emissions See 40 CFR 61, subpart J. Quarterly LDARe or 95 percent control or NDEf Equipped with: 1. Fixed roof with internal floating roof-seals, or 2. External floating roof with seals, or 3. Closed vent and 95 percent control Vapor collection and 95 percent control Load vapor-tight vessels only

Test of NDEf Test for NDEf Test for NDEf

Test for NDEf

Monitor annually Semiannual LDAR,e annual maintenance Semiannual LDARe

Test for NDEf

Periodic inspection Periodic inspection Maintenance plant and monitoring Annual recertification Yes

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CRC Handbook of Engineering Tables

National Emission Standards for Hazardous Air Pollutants (continued) Affected Facility

Emission Level

Monitoring

Chemical manufacturing plants

1. Facilities ≥10 Mg/year in aqueous wastes must control streams ≥10 ppm. Control to 99 percent or <10 ppm

Monitor control and treatment. Also, periodically monitor certain equipment for emissions >500 ppm and inspect equipment

Petroleum refineries

2. If >10 ppm in wastewater treatment system: Wastes in <10 ppm Total in <1 Mg/year 3. >1 Mg/year to <10 Mg/year 4. <1 Mg facilities

Coke by-product plants TSDFg treating wastes from the three preceding

Report annually One-time report

Radionuclides DOE facilities (radon not included)

10 mrem/yearb radionuclides (any member of the public)

NRC licensed facilities and facilities not covered by subpart H

10 mrem/yearh radionuclides (any member of the public) 3 mrem/year iodine (any member of the public)

Calciners and nodulizing kilns at elemental phosphorus plants Storage and disposal facilities for radium-containing material, owned/operated by DOE Phosphogypsum stacks (waste from phosphorus fertilizer production) Disposal of uranium mill trailings (operational)

2 curies per year (polonium-210)

Approved EPA computer model and Method 114 or direct monitoring (ANSIN13.1-1969) Approved EPA computer model or Appendix E Emissions determined by Method 114 or direct monitoring (ANSIN13.1-1969) Method 111

20 pCi/m2 per secondi (radon-222)

None specified

20 pCi/m2 per secondi (radon-222)

Method 115

20 pCi/m2 per secondi (radon-222)

Method 115

a

CEM = continuous emission monitor. Before opening equipment, VC must be reduced to 2.0 percent (volume) or 25 gallons, whichever is larger. c Mg/year = megagrams per year. d mg/dscm = milligrams per dry standard cubic meter. e LDAR = leak detection and repair. f NDE = no detectable emissions. g TSDF = treatment, storage, and disposal facilities. h mrem/year = millirems per year (the rem is the unit of effective dose equivalent for radiation exposure). i pCi/m2 per second = picocuries per square meter per second. From Zegel, W.C., Technology standards, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, pp. 193–196. Originally adapted from David R. Patrick, Ed., Toxic Air Pollution Handbook, Van Nostrand Reinhold, New York, 1994. b

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Civil and Environmental Engineering

10-6

10-5

10-4

10-3

Setting velocity, cm/s (unit density spheres) 10-2 10-1 100 101 102

103

104

Particle diameter, (mm) 0.001

2 3 4 5 6789

0.01

2 3 4 5 6789

0.1

2 3 4 5 6789

1

2 3 4 5 67 89

10

2 3 4 5 67 89

2 3 4 5 67 89

100

1,000

2 3 4 5 6789

10,000

Visible X-rays

Ultraviolet

Far Infrared

Near Infrared

Gas Molecules

Mist

Fog O2

H2O SO2

He CO

Microwaves

Solar radiation

n-C8H18

Raindrops

Atmospheric aerosol Accumulation Coarse Mode Mode Particle size selective TLV Respirable Thoracic Inhalable Rickettsia Bacteria

Nuclei Mode

C2H6 N2 CO2 Virus

Cloud condensation nuclei CN CCN Condensation nuclei Zinc Oxide fume Carbon black Oil smoke Colloidal Silica

Paint Pigments Spray dried milk Alkali fume Tobacco smoke Contact Sulfuric mist Insecticide dusts Ground talc Sulfuric Concentrator mist Milled flour Pulverized coal Red blood cell Plant spores Pollens Floatation ores Sneezes Human hair Beach sand Visible to eye

Produced primarily by condensation or chemical reactions from the gas phase

Produced primarily by attrition, resuspension or coagulation of previously formed material

Molecular and aerosol particle diameters, copyright © P.C. Reist. Molecular diameters calculated from viscosity data. From Altwicker, E.R. et al., Air pollution, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 334. Originally adapted from Lapple, 1961, Stanford Research Institute Journal, 3rd quarter; and J.S. Eckert and R.F. Strigle, Jr., 1974, JAPCA, 24:961–965.

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CRC Handbook of Engineering Tables

Comparable pCi/l WL Exposure Levels 200 1

1000 times average outdoor level

100 0.5

100 times average indoor level

More than 75 times nonsmoker risk of dying from lung cancer 4-pack-a-day smoker 10,000 chest X rays per year

30 times nonsmokers risk of dying from lung cancer

40 0.2

20 0.1

Comparable Risk (Based on lifetime exposure)

10 times average outdoor level

2-pack-a-day smoker

1-pack-a-day smoker

10 0.05

4 0.02

10 times average indoor level

3 times nonsmoker risk of dying from lung cancer

2 0.01

10 times average outdoor level

200 chest X rays per year

1 0.005 Average indoor level

Nonsmoker risk of dying from lung cancer

0.2 0.001 Average outdoor level

Radon risk evaluation chart. This chart shows how the lung cancer risks of radon exposure compare to other causes of the disease. For example, breathing 20 pCi/l poses about the same lung cancer risk as smoking two packs of cigarettes a day. From Altwicker, E.R. et al., Air pollution, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 437. Originally reprinted from U.S. Environmental Protection Agency.

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Civil and Environmental Engineering

Mechanical Characteristics of Sound Waves RMS Sound Pressure (dynes/cm2)

RMS Sound Particle Velocity (cm/sec)

RMS Sound Particle Motion at (1,000 Hz cm)

Sound Pressure Level (dB 0.0002 bar)

0.0002 0.002 0.02 0.2 2.0 20.0 200 2000 20 ¥ 103 200 ¥ 103 2000 ¥ 103

0.0000048 0.000048 0.00048 0.0048 0.048 0.48 4.80 48.0 480 4800 48000

0.76 ¥ 10–9 7.6 ¥ 10–9 76.0 ¥ 10–9 760 ¥ 10–9 7.6 ¥ 10–6 76.0 ¥ 10–6 760 ¥ 10–6 7.6 ¥ 10–3 76.0 ¥ 10–3 760 ¥ 10–3 7.6

0 20 40 60 80 100 120 140 160 180 200

Threshold of hearing Quiet room Normal speech at 3¢ Possible hearing impairment Threshold of pain Incipient mechanical damage Atmospheric pressure

From Liu, D.H.F. and Roberts, H.C., The physics of sound and hearing, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 452.

Representative Sound Pressures and Sound Levels Source and Distance Saturn rocket motor, close by Military rifle, peak level at ear Jet aircraft takeoff; artillery, 2500¢ Planing mill, interior Textile mill Diesel truck, 60¢ Cooling tower, 60¢ Private business office Source Saturn rocket motor Turbojet engine Pipe organ, forte Conventional voice Soft whisper

Sound Pressure (dynes/cm2)

Sound Level (decibels 0.0002 m bar

1,100,000 20,000 2000 630 63 6 2 .06

195 160 140 130 110 90 80 50 Acoustic Power of Source 30,000,000 watts 10,000 watts 10 watts 10 microwatts 1 millimicrowatt

From Liu, D.H.F. and Roberts, H.C., The physics of sound and hearing, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 454.

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CRC Handbook of Engineering Tables

Typical Wastewater Flow Rates from Residential Sources Flow, gal/unit·d Source Apartment: High-rise Low-rise Hotel Individual residence: Typical home Better home Luxury home Older home Summer cottage Motel: With kitchen Without kitchen Trailer park

Unit

Range

Typical

Person Person Guest

35–75 50–80 30–55

50 65 45

Person Person Person Person Person

45–90 60–100 75–150 30–60 25–50

70 80 95 45 40

Unit Unit Person

90–180 75–150 30–50

100 95 40

Note: 1 = gal ¥ 3.7854. From Adams Jr., C.E. et al., Nature of wastewater, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 517. Originally from Metcalf and Eddy, Inc., Wastewater Engineering, 3rd ed., McGraw-Hill, New York, 1991.

Estimated Distribution of World’s Water Volume 1000 km3 Atmospheric water Surface water Salt water in oceans Salt water in lakes and inland seas Fresh water in lakes Fresh water in stream channels (average) Fresh water in glaciers and icecaps Water in the biomass Subsurface water Vadose water Groundwater within depth of 0.8 km Groundwater between 0.8 and 4 km depth Total (rounded)

13 1,320,000 104 125 1.25 29,000 50 67 4200 4200 1,360,000

Percentage of Total Water 0.001 97.2 0.008 0.009 0.0001 2.15 0.004 0.005 0.31 0.31 100

From Chae, Y.C. and Hamidi, A., Groundwater and aquifers, in Environmental Engineers’ Handbook, 2nd ed., Liu, D.H.F. and Liptak, B.G., Eds., CRC Press, Boca Raton, FL, 1997, p. 1009. Originally from Bouwer, H., Groundwater Hydrology, McGraw-Hill, Inc., New York, 1978.

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Civil and Environmental Engineering

Currently Developed Types of Fuel Cells and Their Characteristics and Applications

Fuel Cell Type

Electrolyte

Charge Carrier

Operating Temperature

Fuel

Electric Efficiency (System)

Power Range/Application

Alkaline FC (AFC)

KOH

OH–

60–120°C

Pure H2

35–55%

Proton exchange membrane FC (PEMFC)a Phosphoric acid FC (PAFC)

Solid polymer (such as Nafion)

H+

50–100°C

Pure H2 (tolerates CO2)

35–45%

Phosphoric acid

H+

~220°C

40%

CHP (200 kW)

Molten carbonate FC (MCFC)

Lithium and potassium carbonate

CO32–

~650°C

>46%

200 kW–MW range, CHP and standalone

Solid oxide FC (SOFC)

Solid oxide electrolyte (yttria, zirconia)

O2–

~1000°C

Pure H2 (tolerates CO2, approx. 1% CO) H2, CO, CH4, other hydrocarbons (tolerates CO2) H2, CO, CH4, other hydrocarbons (tolerates CO2)

>46%

2 kW–MW range, CHP and standalone

<5 kW, niche markets (military, space) Automotive, CHP (5–250 kW), portable

a

Also known as a solid polymer fuel cell (SPFC). From Hoogers, G., Introduction, in Fuel Cell Technology Handbook, Hoogers, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 1-4.

Hydrogen Storage Properties for a Range of Metal Hydrides Metal Hydride System Hydrogen content as mass fraction (%) Hydrogen content by volume (kg/dm3) Energy content (MJ/kg) (based on HHV) Energy content (MJ/kg) (LHV)a Heat of reaction (kJ/Nm3) (H2) Heat of reaction (kJ/mol)a Heat of reaction (as fraction of HHV, %)a Heat of reaction (as fraction of LHV, %)a a

Mg/MgH2

Ti/TiH2

V/VH2

Mg2Ni/ Mg2NiH4

FeTi/ FeTiH1.95

LaNi5/ LaNi5H5.9

LH2b

7.7

4.0

2.1

3.2

1.8

1.4

0.101

0.15

0.09

0.08

0.096

0.09

9.9

5.7

3.0

4.5

2.5a

1.95

143.0

8.4

4.8

2.5

3.8

2.1

1.6

120.0

3360

5600

—

2800

1330

1340

100.0 0.077

—

76.3 26.7

127.2 44.5

— —

63.6 22.2

30.2 10.6

30.4 10.6

— —

31.6

52.6

—

26.3

12.5

12.6

—

Raw data taken from Ullmann’s Encyclopedia of Industrial Chemistry, Sixth ed., Wiley-VCH, 2001. Data recalculated by the author. b LH : liquid hydrogen. 2 From Hoogers, G., The fueling problem: Fuel cell systems, in Fuel Cell Technology Handbook, Hoogers, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 5-6.

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CRC Handbook of Engineering Tables

Typical Gas Composition of Biogas from Organic Household Waste Component Methane Carbon dioxide Water vapor Nitrogen Oxygen Carbon monoxide Siloxanes Hydrogen sulfide

Concentration (Wet Gas) 60–75% < 35% 0–10% < 5% < 1% 0.2% <10 mg per m3 CH4 150 ppm

From Hoogers, G., The fueling problem: Fuel cell systems, in Fuel Cell Technology Handbook, Hoggers, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 5-20.

Performance of Different Battery Types

Battery Type Lead–acid Nickel–cadmium Nickel–metal hydride Lithium ion

Specific Energy Storage (Wh/kg)

Specific Power (for 30 sec at 80% capacity) (W/kg)

Specific Cost, ($/kWh)

Cycle Life (Charges and Discharges to 80% of Capacity)

35 (55)a [171]b 40 (57) [217] 70 (120) 120 (200)

200 (450) 175 (220) 150 (220) 300 (350)

125 (75) 600 (110) 540 (115) 600 (200+)

450 (2000) 1250 (1650) 1500 (2200) 1200 (3500)

a

Values in parentheses represent projections for the next five years. Values in brackets represent the theoretical limit on specific energy. From Stone, R., Competing technologies for transportation, in Fuel Cell Technology Handbook, Hoogers, G., Ed., CRC Press, Boca Raton, FL, 2003, p. 11-17. Theoretical limits on specific energy from Rand, R.A.J. et al., Batteries for Electric Vehicles, Research Studies Press, Baldock, U.K., 1998; other data from Ashton, R., in Design of a Hybrid Electric Vehicle, University of Oxford, Oxford, 1998. b

Thermodynamic Data for Selected Chemical Compounds Compound (gaseous/liquid)

Common Name

Molar Mass (g/mol)

H2O (l) H2O (g) CH4 C3H6 (g) C4H10 (g) C8H18 (l) C8H18 (l) CH3OH (l) CH3OH (g) C2H5OH (l) C2H5OH (g) CO CO2 H2 O2

water water (steam) methane propane butane octane iso-octane methanol methanol ethanol ethanol carbon monoxide carbon dioxide hydrogen oxygen

18,02 18,02 16,04 42,08 58,13 114,23 114,23 32,04 32,04 46,07 46,07 28,01 44,01 2,02 32,00

DHf (kJ/mol) –285,83 –241,82 –74,81 20,42 –126,15 –249,90 –255,10 –238,66 –200,66 –277,69 –235,10 –110,53 –393,51 0 0

DGf (kJ/mol) –237,13 –228,57 –50,72 62,78 –17,03 6,40 — –166,27 –161,96 –174,78 –168,49 –137,17 –394,36 0 0

Note: Tabulated are the standard heat of formation, DHf , and the Gibbs free energy, DGf, at 105 Pa and 298 K. From Hoogers, G., Ed., Appendix 1: Thermodynamic data for selected chemical compounds, in Fuel Cell Technology Handbook, Hoggers, G., Ed., CRC Press, Boca Raton, FL, 2003, p. A1-1.

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2-43

Shear force and bending moment diagrams for beams with simple boundary conditions subjected to selected loading cases. (From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-8 to 2-10.)

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CRC Handbook of Engineering Tables

(Continued) Shear force and bending moment diagrams for beams with simple boundary conditions subjected to selected loading cases.

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2-45

(Continued) Shear force and bending moment diagrams for beams with simple boundary conditions subjected to selected loading cases.

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CRC Handbook of Engineering Tables

Shear force and bending moment diagrams for built-up beams subjected to typical loading cases. (From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-12 to 2-13.)

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2-47

(Continued) Shear force and bending moment diagrams for built-up beams subjected to typical loading cases.

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CRC Handbook of Engineering Tables

Typical loading on plates and loading functions. (From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-46 to 2-47.)

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(Continued) Typical loading on plates and loading functions.

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2-49

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CRC Handbook of Engineering Tables

Case No.

Sructural System and Static Loading

Deflection and Internal Forces

16q w= 6 0 pD

ÂÂ m

mpx npy sin a b 2 Ê m2 n2 ˆ mnÁ 2 + 2 ˜ b ¯ Ëa

sin

a

q0 X Z,w X

0

1

16q 0a 2 mx = p4

ÂÂ m

Ê 2 n2 ˆ mpx npy Á m + v e 2 ˜ sin a sin b Ë ¯ Ê n2 ˆ mnÁ m 2 + 2 ˜ e ¯ Ë

n

b

16q 0a 2 my = p4

a Y

e=

q0

+

A

Z

q0

X

Small

2

0

b/2 X

ξ

b/2

Y

Ê n2 ˆ mnÁ m 2 + 2 ˜ e ¯ Ë

n

•

Pm Ê 2 + a m tanh a m 1cos l my 4 Á 2 cosh a m Ë

Âm m=1

l my sinh l my ˆ sin l mx 2 cosh a m ˜¯

2q 0 mpx sin a a

m = 1, 2, 3, º q0

A-A

3

Z, w A 0

X c/2 c/2 c η d ξ

w=

16q 0 Dp 6

ÂÂ m

sin

n

X b

a

2

where Pm =

A a

A-A

m

Ê n2 mpx npy 2ˆ Á e 2 + nm ˜ sin a sin b Ë ¯

b , m = 1, 3, 5, º, •; n = 1, 3, 5, º, • a

a4 Dp 4

w=

ÂÂ

2

¥ sin

lm =

mp a

am =

mpb 2a

mpx nph mpc npd sin sin sin a b b 2b 2 Ê m2 n2 ˆ mnÁ 2 + 2 ˜ b ¯ Ëa

mpx npy sin a b

m = 1, 2, 3, º

Y

n = 1, 2, 3, º p X

4

0

Z,w p

ξ

X b

a Y

η

4P w= Dp 4ab

ÂÂ m

n

sin

mpx nph mpx npy sin sin sin a b a b 2 Ê m2 n2 ˆ Á a 2 + b2 ˜ Ë ¯

m = 1, 2, 3, º n = 1, 2, 3, º

Typical loading and boundary conditions for rectangular plates. (From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-49.)

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Typical loading and boundary conditions for circular plates. (From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-52.)

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CRC Handbook of Engineering Tables

Frequencies and Mode Shapes of Beams in Flexural Vibration L = Length (m) EI = Flexural Rigidity (Nm2) M = Mass per unit length (kg/m)

kn EI HZ 2p mL4 n = 1, 2, 3…

fn =

Boundary Conditions

x Mode Shape yn Ê ---ˆ Ë L¯

Kn; n = 1, 2, 3

An; n = 1, 2, 3…

Pinned - Pinned X

(np)2 L

npx sin ---------L

y Fixed - Fixed X L y Fixed - Pinned X L y

Cantilever X y

L

22.37 61.67 120.90 199.86 298.55 2 p (2n + 1) ----- ; 4 n>5 15.42 49.96 104.25 178.27 272.03 2 p (4n + 1)2 ----- ; 4 n>5 3.52 22.03 61.69 120.90 199.86 2 p (2n + 1)2 ----- ; 4 n>5

cosh

Kn x L

- cos

Kn x L

Ê Kn x Kn x ˆ - An Á sinh - sin ˜ Á L L ˜¯ Ë

cosh

Kn x L

- cos

Kn x L

0.98250 1.00078 0.99997 0.99999 1.0; n > 5

1.00078 1.00000 1.0; n > 3

Ê Kn x Kn x ˆ - An Á sinh - sin ˜ Á L L ˜¯ Ë

cosh

Kn x L

- cos

Kn x L

Ê Kn x Kn x ˆ - An Á sinh - sin ˜ Á L L ˜¯ Ë

0.73410 1.01847 0.99922 1.00003 1.0; n > 4

From Liew, J.Y.R., Shanmugan, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 2-173.

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Civil and Environmental Engineering

Fundamental Frequencies of Portal Frames in Asymmetrical Mode of Vibration First Asymmetric In-Plane Mode

f=

E2I2, m2

l2 Ê E1I1 ˆ 2pL21 ÁË m1 ˜¯

12

HZ

L1 E = Modulus of elasticity I = Area moment of inertia m = mass per unit length

E1I1, m1

L2 l value m1 ------m2

Pinned Bases

E1 I1 ---------E2 I2

Clamped Bases

L1/L2

L1/L2

0.25

0.75

1.5

3.0

6.0

0.25

0.75

1.5

3.0

6.0

0.25

0.25 0.75 1.5 3.0 6.0

0.6964 0.6108 0.5414 0.4695 0.4014

0.9520 0.8961 0.8355 0.7562 0.6663

1.1124 1.0764 1.0315 0.9635 0.8737

1.2583 1.2375 1.2093 1.1610 1.0870

1.3759 1.3649 1.3491 1.3201 1.2702

0.9953 0.9030 0.8448 0.7968 0.7547

1.3617 1.2948 1.2323 1.1648 1.1056

1.6003 1.5544 1.5023 1.4329 1.3573

1.8270 1.7999 1.7649 1.7096 1.6350

2.0193 2.0051 1.9853 1.9504 1.8946

0.75

0.25 0.75 1.5 3.0 6.0

0.8947 0.7867 0.6983 0.6061 0.5186

1.1740 1.1088 1.0368 0.9413 0.8314

1.3168 1.2776 1.2281 1.1516 1.0485

1.4210 1.3998 1.3707 1.3203 1.2414

1.4882 1.4773 1.4617 1.4327 1.3822

1.2873 1.1715 1.0979 1.0373 0.9851

1.7014 1.6242 1.5507 1.4698 1.3981

1.9262 1.8779 1.8218 1.7454 1.6601

2.0994 2.0733 2.0390 1.9838 1.9072

2.2156 2.2026 2.1843 2.1516 2.0983

1.5

0.25 0.75 1.5 3.0 6.0

1.0300 0.9085 0.8079 0.7021 0.6011

1.2964 1.2280 1.1514 1.0482 0.9279

1.4103 1.3707 1.3203 1.2414 1.1335

1.4826 1.4616 1.4326 1.3821 1.3024

1.5243 1.5136 1.4982 1.4694 1.4191

1.4941 1.3652 1.2823 1.2141 1.1570

1.9006 1.8214 1.7444 1.6583 1.5808

2.0860 2.0390 1.9837 1.9070 1.8198

2.2090 2.1842 2.1515 2.0983 2.0234

2.2819 2.2695 2.2521 2.2206 2.1693

3.0

0.25 0.75 1.5 3.0 6.0

1.1597 1.0275 0.9161 0.7977 0.6838

1.3898 1.3202 1.2412 1.1333 1.0058

1.4719 1.4326 1.3821 1.3024 1.1921

1.5189 1.4981 1.4694 1.4191 1.3391

1.5442 1.5336 1.5182 1.4896 1.4395

1.7022 1.5649 1.4752 1.4015 1.3425

2.0612 1.9834 1.9063 1.8185 1.7382

2.1963 2.1515 2.0982 2.0233 1.9366

2.2756 2.2520 2.2206 2.1693 2.0964

2.3190 2.3070 2.2899 2.2595 2.2094

6.0

0.25 0.75 1.5 3.0 6.0

1.2691 1.1304 1.0112 0.8827 0.7578

1.4516 1.3821 1.3023 1.1919 1.0601

1.5083 1.4694 1.4191 1.3391 1.2277

1.5388 1.5181 1.4896 1.4395 1.3595

1.5545 1.5440 1.5287 1.5002 1.4502

1.8889 1.7501 1.6576 1.5817 1.5244

2.1727 2.0980 2.0228 1.9358 1.8550

2.2635 2.2206 2.1693 2.0963 2.0110

2.3228 2.2899 2.2595 2.2095 2.1380

2.3385 2.3268 2.3101 2.2802 2.2309

From Liew, J.Y.R., Shanmugam, E., and Yu, C.H., Structural analysis, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 2-176.

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CRC Handbook of Engineering Tables

BASIC WELD SYMBOLS

BACK

FILLET

PLUG OR SLOT

Groove or Butt SQUARE

V

BEVEL

U

FLARE V

J

FLARE BEVEL

SUPPLEMENTARY WELD SYMBOLS BACKING

SPACER

WELD ALL AROUND

FIELD WELD

CONTOUR FLUSH

CONVEX

For other basic and supplementary weld symbols, see AWS A2, 4–79

STANDARD LOCATION OF ELEMENTS OF A WELDING SYMBOL Finish symbol

Groove angle or included angle of countersink for plug welds

Contour symbol Root opening, depth of filling for plug and slot welds

Length of weld in inches Pitch (c, to c, spacing) of welds in inches

Effective throat Depth of preparation or size in inches Reference line

weld-all-around symbol

(Both sides) (Arrow (other side) side)

S(E) T

Basic weld symbol or detail reference

Field weld symbol

R

Specification, process or other reference Tail (omitted when reference is not used)

F A

L@P A

B

Arrow connects reference line to arrow side of joint. Use break as at A or B to signify that arrow is pointing to the grooved member in bevel or J-grooved joints.

Note: Size, weld symbol, length of weld and spacing must read in that order from left to right along the reference line. Neither orientation of reference line nor location of the arrow alters this rule. The perpendicular leg of , , , weld symbols must be at left. Arrow and Other Side welds are of the same size unless otherwise shown. Dimensions of fillet welds must be shown on both the Arrow Side and the Other Side Symbol. The point of the field weld symbol must point toward the tail. Symbols apply between abrupt changes in direction of welding unless governed by the “all around” symbol or otherwise dimensioned. These symbols do not explicitly provide for the case that frequently occurs in structural work, where duplicate material (such as stiffeners) occurs on the far side of a web or gusset plate. The fabricating industry has adopted this convention: that when the billing of the detail material discloses the existence of a member on the far side as well as on the near side, the welding shown for the near side shall be duplicated on the far side.

Basic weld symbols. (From Lui, E.M., Structural steel design, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 3-74.)

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Civil and Environmental Engineering

Strength of Welds Types of Weld and Stress

Material

ASD Allowable Stress

LRFD fFBM or fFW

Required Weld Strength Levela,b

Full Penetration Groove Weld Tension normal to effective area Compression normal to effective area

Base

Same as base metal

0.90 Fy

“Matching” weld must be used

Base

Same as base metal

0.90 Fy

Weld metal with a strength level equal to or less than “matching” must be used

Tension of compression parallel to axis of weld Shear on effective area

Base

Same as base metal

0.90 Fy

Base weld electrode

0.30 ¥ nominal tensile strength of weld metal

0.90[0.60 fy] 0.80[0.60 FEXX]

Base

Same as base metal

0.90 Fy

Base weld electrode Base weld electrode

0.30 ¥ nominal tensile strength of weld metal 0.30 ¥ nominal tensile strength of weld metal £0.18 ¥ yield stress of base metal

0.75[0.60 FEXX]

Stress on effective area

Base weld electrode

0.30 ¥ nominal tensile strength of weld metal

0.75[0.60 FEXX] 0.90 Fy

Tension or compression parallel to axis of weldc

Base

Same as base metal

0.90 Fy

Partial Penetration Groove Welds Compression normal to effective area Tension or compression parallel to axis of weldc Shear parallel to axis of weld Tension normal to effective area

Weld metal with a strength level equal to or less than “matching” weld metal may be used

0.90 Fy 0.80[0.60 FEXX]

Fillet Welds Weld metal with a strength level equal to or less than “matching” weld metal may be used

Plug or Slot Welds Shear parallel to faying surfaces (on effective area) a

Base weld electrode

0.30 ¥ nominal tensile strength of weld metal

0.75[0.60 FEXX]

Weld metal with a strength level equal to or less than “matching” weld metal may be used

See AWS D1.1 for “matching” weld material. Weld metal one strength level stronger than “matching” weld metal will be permitted. c Fillet welds partial-penetration groove welds joining component elements of built-up members such as flange-to-web connections may be designed without regard to the tensile or compressive stress in these elements parallel to the axis of the welds. From Lui, E.M., Structural steel design, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 3–75. b

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CRC Handbook of Engineering Tables

Reinforcing Bar Dimensions and Weights Nominal Dimensions Diameter

Area

Weight

Bar Number

(in.)

(nm)

(in.2)

(cm2)

(lb/ft)

(kg/m)

3 4 5 6 7 8 9 10 11 14 18

0.375 0.500 0.625 0.750 0.875 1.000 1.128 1.270 1.410 1.693 2.257

9.5 12.7 15.9 19.1 22.2 25.4 28.7 32.3 35.8 43.0 57.3

0.11 0.20 0.31 0.44 0.60 0.79 1.00 1.27 1.56 2.25 4.00

0.71 1.29 2.00 2.84 3.87 5.10 6.45 8.19 10.06 14.52 25.81

0.376 0.668 1.043 1.502 2.044 2.670 3.400 4.303 5.313 7.65 13.60

0.559 0.994 1.552 2.235 3.041 3.973 5.059 6.403 7.906 11.38 20.24

From Grider, A., Ramirez, J.A., and Yun, Y.M., Structural concrete design, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 4–6.

Eurocode 4 Maximum Width-to-Thickness Ratios for Steel Webs Webs: elements perpendicular to axis of bending

h

d

d

f

Class

h

f

d

Web subject to compression

+ fy

+ fy d h

αd

h

fy − d/t ≤ 72 ε

Web subject to bending and compression + fy

d

fy −

1

Axis of bending

f

Web subject to bending

Stress distribution

(Compression positive)

h

f

d h

fy − d/t ≤ 33 ε

when α> 0.5 d/t ≤ 396 ε /(13α−1) when α < 0.5 d/t ≤ 36 ε/α

d/t ≤ 83 ε

2

d/t ≤ 38 ε

when α > 0.5 d/t ≤ 456 ε /(13α−1) when α < 0.5 d/t ≤ 41.5 ε/α

Stress distribution

+ fy d/2

+ fy h

+ fy d h

d h

d/2 (compression positive)

d/t ≤ 124 ε

3

ψfy −

fy +

fy −

d/t ≤ 42 ε

when ψ > –1 d/t ≤ 42 ε/(0.67+ 0.33 ψ) when ψ ≤ –1 d/t ≤ 62 ε/(1−ψ)/ψ

ε = 235/fy

fy ε

1 (N/mm ) 235 1.0

275 0.92

355 0.81

From Consenza, E. and Zandonini, R., Composite construction, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 6-29.

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Mechanical Properties of Steels Referred to in the AISI 1996 Specification

Steel Designation Structural steel High-strength low-allow structural steel Low and intermediate tensile strength carbon plates, shapes and bars Cold-formed welded and seamless carbon steel structural tubing in rounds and shapes

Structural steel with 42 ksi minimum yield point Hot-rolled carbon steel sheets and stripes of structural quality

High-strength low-alloy columbium-vanadium steels of structural quality High-strength low-alloy structural steel with 50 ksi minimum yield point Hot-rolled and cold-rolled highstrength low-alloy steel sheet and strip with improved corrosion resistance

Hot-rolled and cold-rolled highstrength low-alloy columbium and/or vanadium steel sheet and strip

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Elongation (%) In 2-in. In 8-in. Gage Gage Length Length

Yield Point, Fy (ksi)

Tensile Strength, Fu (ksi)

36 50 46 24 27 30 33

58–80 70 67 45–60 50–65 55–75 60–80

23 — 21 30 28 25 23

— 18 18 27 25 22 20

33 42 46 36

45 58 62 58

25 23 21 23

— — — —

39 46 50 36 42 50 30 33 36 40 45 50 42 50 60 65 50

45 58 62 58 60–85 70–100 49 52 53 55 60 65 60 65 75 80 70

25 23 21 23 — — 21–25 18–23 17–22 15–21 13–19 11–17 24 21 18 17 21

— — — — 19 18 — — — — — — 20 18 16 15 18

45

65

22

—

50

70

22

—

45

60 (55)

50

50

65 (60)

55

55

70 (65)

60

60

75 (70)

65

65

80 (75)

70

70

85 (80)

Hot-rolled 23–25 Cold-rolled 22 Hot-rolled 20–22 Cold-rolled 20 Hot-rolled 18–20 Cold-rolled 18 Hot-rolled 16–18 Cold-rolled 16 Hot-rolled 14–16 Cold-rolled 15 Hot-rolled 12–14 Cold-rolled 14

— — — — — — — — — —

ASTM Designation A36 A242 (3/4 in. and under) (3/4 in. to 1-1/2 in.) A283 Gr. A B C D A500 Round tubing A B C D Shaped tubing A B C D A529 Gr. 42 50 A570 Gr. 30 33 36 40 45 50 A572 Gr. 42 50 60 65 A588

A60 Hot-rolled as rolled coils; annealed or normalized; and cold-rolled Hot-rolled as rolled cut lengths A607 Gr. 45

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Mechanical Properties of Steels Referred to in the AISI 1996 Specification (continued)

Steel Designation Cold-rolled carbon structural steel sheet

Zinc-coated steel sheets of structural quality

Hot-rolled high-strength lowalloy steel sheets and strip with improved formability Aluminum-zinc alloy-coated by the hot-dip process general requirements

ASTM Designation A611 Gr. A B C D E A653 SQ Gr. 33 37 40 50 (class 1) 50 (class 3) 80 HSLA Gr. 50 60 70 80 A715 Gr. 50 60 70 80 A792 Gr. 33 37 40 50 80

Yield Point, Fy (ksi)

Tensile Strength, Fu (ksi)

25 30 33 40 80 33 37 40 50 50 80 50 60 70 80 50 60 70 80 33 37 40 50 80

42 45 48 52 82 45 52 55 65 70 82 60 70 80 90 60 70 80 90 45 52 55 65 82

Elongation (%) In 2-in. In 8-in. Gage Gage Length Length 26 24 22 20 — 20 18 16 12 12 — 20 16 12 (14) 10 (12) 22–24 20–22 18 14 20 18 16 12 —

— — — — — — — — — — — — — — — — — — — — — — — —

Notes: 1. The tabulated values are based on ASTM Standards. 2. 1 in. = 25.4 mm; 1 ksi = 6.9 MPa. 3. A653 Structural Quality Grade 80, Grade E of A611, and Structural Quality Grade 80 of A792 are allowed in the AISI Specification under special conditions. For these grades, Fy = 80 ksi, Fu = 82 ksi, elongations are unspecified. See AISI Specification for reduction of yield point and tensile strength. 4. For A653 steel, HSLA Grades 70 and 80, the elongation in 2-in. gage length given in the parenthesis is for Type II. The other value is for Type I. 5. For A607 steel, the tensile strength given in the parenthesis is for Class 2. The other value is for Class I. From Yu, W.-W., Cold-formed steel structures, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, pp. 7–8 to 7–9.

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Some Nominal Properties of Aluminum Alloys Property

Value

Weight Modulus of elasticity Tension and compression Shear Poisson’s ratio Coefficient of thermal expansion (68 to 212°F)

0.1 lb/in.3 10,000 ksi 3,750 ksi 1/3 0.000013 per ˚F

From Fridley, M.J., Aluminum structures, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 8–2. Originally from Gaylord and Gaylord, Structural Engineering Handbook, McGraw-Hill, New York, 1990.

Minimum Mechanical Properties Tension

Shear

Bearing

Alloy and Temper

Product

Thickness Range, in.

TS

YS

Compression YS

US

YS

US

YS

3003-H14 5456-H116 6061–T6 6061-T6 6063–T5 6063-T6

Sheet and plate Sheet and plate Sheet and plate Shapes Shapes Shapes

0.009–1.000 0.188–1.250 0.010–4.000 All to 0.500 All

20 46 42 38 22 30

17 33 35 35 16 25

14 27 35 35 16 25

12 27 27 24 13 19

10 19 20 20 9 14

40 87 88 80 46 63

25 56 58 56 26 40

Note: All properties are in ksi. TS is tensile strength, YS is yield strength, and US is ultimate strength. From Fridley, M.J., Aluminum structures, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 8–3. Originally from The Aluminum Association, Structural Design Manual, 1994.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Steel Plate Materials Group

Class

Specification

I

C

I

B

I II

A C

ASTM A36 (to 2 in. thick) ASTM A131 Grade A (to ½ in. thick) ASTM A285 Grade C (to ¾ in. thick) ASTM A131 Grades B, D ASTM A516 Grade 65 ASTM A573 Grade 65 ASTM A709 Grade 36T2 ASTM A131 Grades CS, E ASTM A572 Grade 42 (to 2 in. thick) ASTM A591 required over ½ in. thick ASTM A572 Grade 50 (to 2 in. thick) ASTM A591 required over ½ in. thick ASTM A709 Grades 50T2, 50T3 ASTM A131 Grade AH32 ASTM A131 Grade AH36 API Spec 2H Grade 42 API Spec 2H Grade 50 (to 2½ in. thick) API Spec 2H Grade 50 (over 2½ in. thick) API Spec 2W Grade 42 (to 1 in. thick) API Spec 2W Grade 42 (over 1 in. thick) API Spec 2W Grade 50 (to 1 in. thick) API Spec 2W Grade 50 (over 1 in. thick) API Spec 2W Grade 50T (to 1 in. thick) API Spec 2W Grade 50T (over 1 in. thick) API Spec 2Y Grade 42 (to 1 in. thick) API Spec 2Y Grade 42 (over 1 in. thick) API Spec 2Y Grade 50 (to 1 in. thick) API Spec 2Y Grade 50 (over 1 in. thick) API Spec 2Y Grade 50T (to 1 in. thick) API Spec 2Y Grade 50T (over 1 in. thick) ASTM A131 Grades DH32, EH32 ASTM A131 Grades DH36, EH36 ASTM A537 Class I (to 2½ in. thick) ASTM A633 Grade A ASTM A633 Grades C, D ASTM A678 Grade A ASTM A537 Class II (to 2½ in. thick) ASTM A678 Grade B API Spec 2W Grade 60 (to 1 in. thick) API Spec 2W Grade 60 (over 1 in. thick) ASTM A710 Grade A Class 3 (to 2 in. thick) ASTM A710 Grade A Class 3 (2 in. to 4 in. thick) ASTM A710 Grade A Class 3 (over 4 in. thick)

II

B

II

A

III

A

a

Specified Minimum Yield Stress (ksi)a

Specified Minimum Tensile Stress (ksi)a

36 34 30 34 35 35 36 34 42

58 58 55 58 65 65 58 58 60

50

65

50 45.5 51 42 50 47 42 42 50 50 50 50 42 42 50 50 50 50 45.5 51 50 42 50 50 60 60 60 60 75 65 60

65 68 71 65 70 70 62 62 65 65 70 70 62 62 65 65 70 70 68 71 70 63 70 70 80 80 75 75 85 75 70

1 ksi = 6.895 MPa From Miller, C.D., Shell structures in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 11-4.

© 2004 by CRC Press LLC

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Civil and Environmental Engineering

Mechanical Properties of Common Design Materials

Material Mild steel Medium carbon steel High carbon steel A514 Steel Gray cast iron Malleable cast iron 5056-H18 Aluminum alloy

Yield Strength, sY (ksi)

Ultimate Tensile Strength, su (ksi)

Modulus of Elasticity, E (psi)

Percent Elongation (%)

Absorbed Elastic Energy, s 2Y /2E (psi)

35 45 75 100 6 20 59

60 85 120 115–135 20 50 63

30 ¥ 106 30 ¥ 106 30 ¥ 106 30 ¥ 106 15 ¥ 106 23 ¥ 106 10 ¥ 106

35 25 8 18 5 10 10

20.4 33.7 94.0 166.7 1.2 8.7 174.1

From Blodgett, O.W. and Miller, D.K., Basic principles of shock loading, in Handbook of Structural Engineering, Chen, W.-F., Ed., CRC Press, Boca Raton, FL, 1998, p. 21-7.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Properties of Sections > >

?

D

?

=

D

>

D

?

?

>

D

bh3 I= 12

bh3 3

I bh2 = c 6

bh2 3

h

= 0.289h

12

h 3

6 b2 + h2

(

bh 2 2 h cos a + b2 sin 2 a 12

)

6 b2 + h2

= 0.577h

(

bh

6 b2 + h2

h2 cos2 a + b2 sin 2 a 12

)

H 3 - h3 12( H - h)

H 4 - h4 12

bh3 2 ; c= h 36 3

1 H 4 - h4 6 H

2 H 4 - h4 12 H

bh2 24

H 2 + h2 12

h

?

D

H 2 + h2 12

bh3 12

5 3 4 R 16

3

I bh = c 12 r=

0

H 4 - h4 12

18

4

>

I=

?

D

?

)

>

4

(

b H 3 - h3 12

I b H 3 - h3 = c 6 H r=

0

0

4

I=

D

0

D

0 ?

D >

h 6

5

8

R3

5 3 3 R 16 5 R 24

Square, axis same as first rectangle, side = h; I = h4/12; I/c = h3/6; r = 0.289h. Square, diagonal taken as axis: I = h4/12; I/c = 0.1179h3; r = 0.289h.

© 2004 by CRC Press LLC

)

bh Ê h2 cos2 a + b2 sin3 a ˆ 6 ÁË h cos a + b sin a ˜¯

b2h2

?

r=

(

b3h3

1+ 2 2 4 R 6 0.6906 R3 0.475 R

1587_Book.fm Page 63 Friday, September 26, 2003 12:10 PM

2-63

Civil and Environmental Engineering

Properties of Sections (continued) Equilateral Polygon A = area R = rad circumscribed circle r = rad inscribed circle n = no. sides a = length of side Axis as in preceding section of octagon

>

R cos =

6b2 + 6bb1 + b12 3 h 36(2b + b1 )

c=

1 3b + 2b1 h 3 2b + b1

*

*

>

*

>

D 0

1 3

(Bc

0 3 1

*

BH 3 + bh3 12(BH + bh)

3

BH 3 - bh3 12

- B1h3 + bc 23 - b1h13

BH 3 - bh3 12(BH - bh)

)

I

2 2 1 aH + B1d + b1d1 (2 H - d1 ) c1 = aH + B1d + b1d1 2

D

? @ *

*

I=

6(2b + b1 )

I BH 3 + bh3 = c 6H

?

0 D

D

0 D

@ ?

=

*

h 12b2 + 12bb1 + 2b12

I BH + bh = c 6H

I=

*

12r 2 + a2 48

BH 3 + bh3 12 3

D

0

D

0

0

>

180∞ n

AR (approx ) 4

I=

?

D

>

6R 2 - a 2 R ª 24 2

I 6b2 + 6bb1 + b12 2 = h c 12(3b + 2b1 )

>

>

I

=

I= D

?

*

)

AR 2 = (approx ) 4

>

>

(

I I = c r

)

A 12r 2 + a2 48

=

>

>

(

A 6R 2 - a 2 24

I=

(Bd + bd ) + a(h + h ) 1

1

* I=

=

>

*

0

?

@

> *

c1 =

@ ?

0

0 @

D @

?

?

D

=

>

1 3

H @

= 0.05d

4

(approx )

- bh3 + ac 23

)

1 aH 2 + bd 2 2 aH + bd

r=

pd 4 pr 4 A 2 = = r 64 4 4

3 1

c 2 = H - c1

> *

I=

(Bc

[

I Bd + a( H - d )

I pd 3 pr 3 A = = = r c 32 4 4 = 0.1d (approx ) 2

] r d = 2 4

From Bolz, R.E. and Tuve, G.L., Structures and materials, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, pp. 628–629.

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CRC Handbook of Engineering Tables

Components of the Atmosphere* Average Composition of Dry Air For most engineering applications the following accepted values for the “average” composition of the atmosphere are adequate. These values are for sea level or any land elevation. Proportions remain essentially constant to 50,000 ft (15,240 m) altitude.

Gas

Molecular Weight

Percentage by Volume, mol fraction

Percentage by Weight

Nitrogen Oxygen Argon Carbon dioxide

N2 = 28.016 O2 = 32.000 Ar = 39.944 CO2 = 44.010

78.09 20.95 0.93 0.03

75.55 23.13 1.27 0.05

100.00

100.00

For many engineering purposes the percentages 79% N2–21% O2 by volume and 77% N2–23% O2 by weight are sufficiently accurate, the argon being considered as nitrogen with an adjustment of molecular weight to 28.16. Other gases in the atmosphere constitute less than 0.003% (actually 27.99 parts per million by volume), as given in the following table. Minor Constituents of Dry Air Gas Neon Helium Methane Krypton Nitrous oxide Hydrogen Xenon Ozone Radon

Parts per Million

Molecular Weight

By Volume

By Weight

Ne = 20.183 He = 4.003 CH4 = 16.04 Kr = 83.8 N2O = 44.01 H2 = 2.0160 Xe = 131.3 O3 = 48.000 Rn = 222.

18. 5.2 2.2 1. 1. 0.5 0.08 0.01 (0.06 ¥ 10–12)

12.9 0.74 1.3 3.0 1.6 0.03 0.37 0.02

Minor constituents may also include dust, pollen, bacteria, spores, smoke particles, SO2, H2S, hydrocarbons, and larger amounts of CO2 and ozone, depending on weather, volcanic activity, local industrial activity, and concentration of human, animal, and vehicle population. In certain enclosed spaces the minor constituents will vary considerably with industrial operations and with occupancy by humans, plants, or animals. The above data do not include water vapor, which is an important constituent in all normal atmospheres. * Compiled from several sources. From Bolz, R.E. and Tuve, G.L., Atmosphere, earth, and ocean, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 649.

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Civil and Environmental Engineering

Sound Transmission Through Partition Walls* Dry-Wall Construction The following table presents typical results selected from approximately 100 tests in the National Research Council of Canada Building Research series. The tests were conducted in accordance with ASTM E90–66T, “Recommended Practice for Laboratory Measurement of Airborne Sound Transmission Loss of Building Partitions.” The gypsum board samples represented extremes of density and thickness (as allowed under CSA Standards); they included the fire-resistant and the vinylcovered types, with no significant differences in performance. Transmission Loss, db, at Octave Frequencies ofa

Number

Transmission Loss, Nominal Average

Description of Wall

125

250

500

1000

2000

4000

Single-Leaf or Board on One Side of Studs Only b

1 2 3 4 5

3/8-in. plasterboard 1/2-in. plasterboardb 5/8-in. plasterboardb 22-gage galvanized iron 1/2-in. plasterboard + 3/16-in. plywoodc 1/2-in. plasterboard + 1/2-in. fiberboardd

6

26 28 29 27 28

12 15 16 13 16

17 20 21 17 20

23 25 27 22 25

28 30 31 28 29

33 33 29 34 32

23 27 30 39 31

30

16

22

28

33

32

30

28 33 37 36 25 40 25 36 45

32 35 45 46 34 45 37 47 49

41 43 50 54 41 48 46 50 55

46 47 50 56 36 40 38 42 55

38 40 47 56 42 45 49 52 56

Two-Leaf Walls—Wallboard Both Sides 7 8 9 10 11 12 13 14 15

1/2-in. plasterboard, 3 5/8-in. space 1/2-in. plasterboard, 2-in. fille Staggered studs + 2-in. fillf Plasterboard + plywood + fiberboardg 5/8-in. plasterboard, 3 5/8-in. space 5/8-in. plasterboard, 4-in. fillh Staggered studs + no fillj Staggered studs, 4-in. fillk Multilayer, steel studs, glass fiberm

35 40 46 46 36 45 39 46 53

15 22 26 22 21 28 27 32 36

a

The quoted report included test data on the following additional frequencies: 160, 200, 315, 400, 630, 1,250, 1,600, 2,500, 3,150, and 5,000 hz. b Joints taped for plasterboard walls. c Sheets joined by contact cement on faces. d Plasterboard and wood fiberboard laminated with gypsum joint compound. e Glass fiber batts, 2-in. thick, between studs; 1/2-in. plasterboard. f Staggered wood studs, 2-in. ¥ 4-in., 3 5/8-in. space, 2-in. thick glass fiber batts, 1/2-in. plasterboard, both faces. g 1/2-in. plasterboard and 3/16-in. plywood on both faces; 2-in. ¥ 4-in. wood studs on 16-in. wood fiberboard between studs. h 4-in. low-density glasswool batts, compressed into stud space between 3 5/8-in. steel-channel studs. j 2-in. ¥ 4-in. wood studs, staggered, 3 5/8-in. space, 5/8-in. plasterboard, no fill. k Same as No. 13 but 4-in. low-density glasswool batts in space between 2-in. ¥ 4-in. wood studs. m Three 1/2-in. layers, one 5/8-in. layer plasterboard; 3 5/8-in. steel channel studs, 24-in. centers; 2 1/2-in. glass fiber. General Notes With studs of low torsional rigidity, such as steel channels, sound transmission via the studs appears to be negligible. The simpler constructions have been tested by several laboratories, and results have been found to be reasonably reproducible. The test specimens were mounted and caulked into an opening 10-ft wide by 8-ft high that separated two reverberation rooms. The test signal consisted of third-octave bands of “pink” noise. The test results were not critically sensitive to normal variations in thickness, density, or techniques of erection. Several of the additional tests included multi-layer constructions and the additions of resilient bars, horizontal or vertical. Highest sound attenuation was 53 db (test No. 15 in table). From Bolz, R.E. and Tuve, G.L., Sound and acoustics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 696. Originally from T.D. Northwood, “Transmission Loss of Plasterboard Walls,” Building Research Note 66, Division of Building Research, National Research Council, revised July 1970.

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CRC Handbook of Engineering Tables

Sound-Absorption Coefficients Sound-absorption data on various materials are presented here in terms of the acoustic properties of rooms; these data are also valuable for other applications, such as the acoustic treatments for ducts and tunnels. Architectural applications include the control of noise level in offices, stores, restaurants, and other occupied spaces, and the control of reverberation time and elimination of echoes in concert and lecture halls. Non-absorbent surfaces. Solid walls, floors, or ceilings finished with glazed tile, marble, terrazzo, very smooth concrete, or with linoleum, rubber, cork, or plastic tile cemented directly to concrete, are not sound absorbent. The absorption coefficient (in percentage of incident energy absorbed) is seldom more than 1 or 2 percent at all wavelengths from 125 hz to 4,000 hz. Poor sound absorbers. Brick surfaces, painted concrete blocks, hardwood floors, gypsum board, or smooth nonporous plaster (lime or gypsum) are all poor absorbers. With solid structural backing these finishes seldom afford as much as 10 percent absorption at any wavelength from 125 hz to 4,000 hz. Ordinary window areas may absorb up to 25 percent of the lowfrequency sounds (125 to 250 hz) but much less at the higher frequencies. Sound-absorbing materials. Carpets, drapes, and upholstered seats are fair-to-good sound absorbers. Absorption Coefficients, % (Percentage of Incident Energy Absorbed) Sound Frequency, hz Materials

125

250

500

1000

2000

4000

Heavy carpet on concrete or solid floor Heavy carpet on heavy hairfelt or elastic pad Heavy drapes (1 lb/sq yd) draped 2 to 1 area Light hung fabric Unoccupied wood or metal chairsa Unoccupied upholstered seatinga Full audience, occupying upholstered seatsa

2 8 10 3 15 45 70

6 25 30 4 20 55 75

14 50 50 11 25 65 85

37 60 75 17 40 70 95

60 65 70 24 40 70 90

65 65 65 35 30 60 85

a

Equivalent values based on floor area.

Acoustic Treatments The following data apply mainly to acoustic ceiling treatments, but other surfaces may be similarly treated. These data do not apply to through-transmission of sound. Low sound transmission accompanies high density or weight of material. Absorption Coefficients, % (Percentage of Incident Energy Absorbed) Sound Frequency, hz Class Descriptionb

125

250

500

1000

2000

4000

Porous, lightweight fiber board or tile ¾ in. thick; perforated or fissured; painted; on ¾ in. furring strips Porous fireproof mineral tile, ⅝ in. thick; perforated or fissured; painted; direct solid application to structural surface Porous fireproof mineral tile, ¾ in. thick, drop ceiling or large air space; metal supports Bonded wood or mineral fibers; thickness about 1½ in. Perforated metal pans or hardboard backed with 1½ in. loose pad

20

58

61

80

80

68

10

26

70

89

75

60

70

66

72

92

88

75

41

59

88

85

76

65

36

56

87

94

74

56

b

Data on each class based on five or more commercial products. From Bolz, R.E. and Tuve, G.L., Sound and acoustics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 697.

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1587_Book.fm Page 1 Monday, September 1, 2003 7:17 PM

3 Chemical Engineering, Chemistry, and Materials Science International System of Units (SI) ............................................................................................................3-3 Conversion Factors...................................................................................................................................3-11 Periodic Table of Elements ......................................................................................................................3-23 Properties of Semiconductors .................................................................................................................3-24 Solid State Lasers ......................................................................................................................................3-45 III-V Material Systems with Important Optoelectronic Applications ...................................................3-46 Energy Gap and Lattice Parameters for Cubic Group IV, III-V, and II-VI Semiconductors ...............3-47 Important Parameters of Semiconductors of Interest for Conventional Electronics and Emerging High Temperature Electronics ...........................................................................................3-47 Properties of GaN(a), AIN (b), and InN(c) ...........................................................................................3-48 List of Ferroelectric Materials and Their Crystal Growth Methods ......................................................3-49 General Physical Properties of Ferroelectric Materials ..........................................................................3-50 Applications of the Ferroelectric Thin Films..........................................................................................3-51 The Principal Photometric Units ............................................................................................................3-52 Dielectric Constants of Common Materials ...........................................................................................3-52 Characteristics of Coaxial Cables ............................................................................................................3-52 Dry Saturated Steam: Temperature Table ...............................................................................................3-53 Properties of Superheated Steam ............................................................................................................3-55 Properties of Water at Various Temperatures from 40 to 540°F (4.4 to 282.2°C) ................................3-59 Atomic Mass of Selected Elements..........................................................................................................3-60 Solid Density of Selected Elements .........................................................................................................3-62 Thermal Conductivity of Metals (Part 1) ...............................................................................................3-63 Thermal Conductivity of Metals (Part 2) ...............................................................................................3-64 Thermal Conductivity of Metals (Part 3) ...............................................................................................3-65 Thermal Conductivity of Metals (Part 4) ...............................................................................................3-66 General Properties of Refrigerants ..........................................................................................................3-68 Thermodynamic Properties of Saturated Mercury ................................................................................3-70 Properties of Rare-Earth Metals ..............................................................................................................3-71 Products of Powder Metallurgy ...............................................................................................................3-72

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CRC Handbook of Engineering Tables

Fiber-Reinforced Metals ...........................................................................................................................3-73 Properties of Commercial Plastics ..........................................................................................................3-74 Rubbers and Elastomers ..........................................................................................................................3-85 Electrical Properties of Various Kinds of Glass ......................................................................................3-87 Properties of the Chemical Elements ......................................................................................................3-88 Additional Properties of the Chemical Elements ...................................................................................3-90 Available Stable Isotopes of the Elements ...............................................................................................3-93 Energy Absorption Mass Attenuation Coefficient In cm2/g...................................................................3-96 Gamma-Ray Absorption Cross Section In cm–1 .....................................................................................3-97 Removal Cross Sections for Various Materials .......................................................................................3-98 Diffusion of Gases and Vapors into Air ..................................................................................................3-99 Speed of Sound in Water and Steam (m·s–1) ........................................................................................3-100 Dynamic Viscosity of Water and Steam (mPa·s) ..................................................................................3-101

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Chemical Engineering, Chemistry, and Materials Science

INTERNATIONAL SYSTEM OF UNITS (SI)

1

SI base units

Table 1 gives the seven base quantities, assumed to be mutually independent, on which the SI is founded; and the names and symbols of their respective units, called ``SI base units.' ' Definitions of the SI base units are given in Appendix A. The kelvin and its symbol K are also used to express the value of a temperature interval or a temperature difference.

Table 1. SI base units SI base unit Base quantity length mass time electric current thermodynamic temperature amount of substance luminous intensity

2

Name

Symbol

meter kilogram second ampere kelvin mole candela

m kg s A K mol cd

SI deriived units

Derived units are expressed algebraically in terms of base units or other derived units (including the radian and steradian which are the two supplementary units – see Sec. 3). The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. For example, the derived unit for the derived quantity molar mass (mass divided by amount of substance) is the kilogram per mole, symbol kg/mol. Additional examples of derived units expressed in terms of SI base units are given in Table 2.

Table 2. Examples of SI derived units expressed in terms of SI base units SI derived unit Derived quantity area volume speed, velocity acceleration wave number mass density (density) specific volume current density magnetic field strength amount-of-substance concentration (concentration) luminance

2.1

Name

Symbol

square meter cubic meter meter per second meter per second squared reciprocal meter kilogram per cubic meter cubic meter per kilogram ampere per square meter ampere per meter

m2 m3 m/s m/s 2 m1 kg/m 3 m 3 /kg A/m 2 A/m

mole per cubic meter candela per square meter

mol/m 3 cd/m 2

SI de rived units with special names and symbols

Certain SI derived units have special names and symbols; these are given in Tables 3a and 3b. As discussed in Sec. 3, the radian and steradian, which are the two supplementary units, are included in Table 3a.

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CRC Handbook of Engineering Tables

INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table 3a. SI derived units with special names and symbols, including the radian and steradian SI derived unit Derived quantity

Special name

plane angle solid angle frequency force pressure, stress energy, work, quantity of heat power, radiant flux electric charge, quantity of electricity electric potential, potential difference, electromotive force capacitance electric resistance electric conductance magnetic flux magnetic flux density inductance Celsius temperature(a) luminous flux illuminance (a) (b)

Special symbol

Expression in terms of other SI units

Expression in terms of SI base units

radian steradian hertz newton pascal

rad sr Hz N Pa

N/m2

m m1 = 1 m 2 m2 = 1 s1 m kg s2 m1 kg s2

joule watt

J W

Nm J/s

m2 kg s2 m2 kg s3

coulomb

C

volt farad ohm siemens weber tesla henry degree Celsius lumen lux

V F S Wb T H C lm lx

sA W/A C/V V/A A/V Vs Wb/m2 Wb/A cd sr lm/m2

m2 kg s3 A1 m2 kg1 s4 A2 m2 kg s3 A2 m2 kg1 s3 A2 m2 kg s2 A1 kg s2 A1 m2 kg s2 A2 K cd sr (b) m2 cd sr (b)

See Sec. 2.1.1. The steradian (sr) is not an SI base unit. However, in photometry the steradian (sr) is maintained in expressions for units (see Sec. 3).

Table 3b. SI derived units with special names and symbols admitted for reasons of safeguarding human health (a) SI derived unit Derived quantity

Special name

Special symbol

Expression in terms of other SI units

Expression in terms of SI base units

activity (of a radionuclide)

becquerel

Bq

absorbed dose, specific energy (imparted), kerma

gray

Gy

J/kg

m2 s2

dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent, equivalent dose

sievert

Sv

J/kg

m2 s2

(a)

s1

The derived quantities to be expressed in the gray and the sievert have been revised in accordance with the recommendations of the International Commission on Radiation Units and Measurements (ICRU).

2.1.1 Degree Celsius In addition to the quantity thermodynamic temperature (symbol T ), expressed in the unit kelvin, use is also made of the quantity Celsius temperature (symbol t ) defined by the equation t = TT 0 , where T 0 = 273.15 K by definition. To express Celsius temperature, the unit degree Celsius, symbol C, which is equal in magnitude to the unit kelvin, is used; in this case, ``degree Celsius' ' is a special name used in place of ``kelvin.' ' An interval or difference of Celsius temperature can, however, be expressed in the unit kelvin as well as in the unit degree Celsius. (Note that the thermodynamic temperature T0 is exactly 0.01 K below the thermodynamic temperature of the triple point of water.)

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3-5

Chemical Engineering, Chemistry, and Materials Science

INTERNATIONAL SYSTEM OF UNITS (SI) (continued)

2.2

Use of SI derived units with special names and symbols

Examples of SI derived units that can be expressed with the aid of SI derived units having special names and symbols (including the radian and steradian) are given in Table 4. Table 4. Examples of SI derived units expressed with the aid of SI derived units having special names and symbols SI derived unit Derived quantity angular velocity angular acceleration dynamic viscosity moment of force surface tension heat flux density, irradiance radiant intensity radiance heat capacity, entropy specific heat capacity, specific entropy specific energy thermal conductivity energy density electric field strength electric charge density electric flux density permittivity permeability molar energy molar entropy, molar heat capacity exposure (x and rays) absorbed dose rate (a)

Name

Symbol

Expression in terms of SI base units

radian per second radian per second squared pascal second newton meter newton per meter

rad/s rad/s 2 Pa s Nm N/m

m m 1 s 1 = s 1 m m 1 s 2 = s 2 m1 kg s1 m 2 kg s2 kg s2

watt per square meter watt per steradian watt per square meter steradian joule per kelvin joule per kilogram kelvin joule per kilogram watt per meter kelvin joule per cubic meter volt per meter coulomb per cubic meter coulomb per square meter farad per meter henry per meter joule per mole

W/m 2 W/sr

kg s3 m 2 kg s 3 sr 1

W/(m 2 sr) J/K

kg s 3 sr 1 (a) m 2 kg s2 K1

J/(kg K) J/kg W/(m K) J/m 3 V/m C/m 3 C/m 2 F/m H/m J/mol

m 2 s2 K1 m 2 s2 m kg s3 K1 m1 kg s2 m kg s3 A1 m3 s A m2 s A m3 kg1 s4 A2 m kg s2 A2 m 2 kg s2 mol1

joule per mole kelvin coulomb per kilogram gray per second

J/(mol K) C/kg Gy /s

m 2 kg s2 K1 mol1 kg1 s A m 2 s3

(a)

The steradian (sr) is not an SI base unit. However, in radiometry the steradian (sr) is maintained in expressions for units (see Sec. 3).

The advantages of using the special names and symbols of SI derived units are apparent in Table 4. Consider, for example, the quantity molar entropy: the unit J/(mol K) is obviously more easily understood than its SI base-unit equivalent, m 2 kg s 2 K 1 mol 1. Nevertheless, it should always be recognized that the special names and symbols exist for convenience; either the form in which special names or symbols are used for certain combinations of units or the form in which they are not used is correct. For example, because of the descriptive value implicit in the compound-unit form, communication is sometimes facilitated if magnetic flux (see Table 3a) is expressed in terms of the volt second (V s) instead of the weber (Wb). Tables 3a, 3b, and 4 also show that the values of several different quantities are expressed in the same SI unit. For example, the joule per kelvin (J/K) is the SI unit for heat capacity as well as for entropy. Thus the name of the unit is not sufficient to define the quantity measured. A derived unit can often be expressed in several different ways through the use of base units and derived units with special names. In practice, with certain quantities, preference is given to using certain units with special names, or combinations of units, to facilitate the distinction between quantities whose values have identical expressions in terms of SI base units. For example, the SI unit of frequency is specified as the hertz (Hz) rather than the reciprocal second (s 1 ), and the SI unit of moment of force is specified as the newton meter (N m) rather than the joule (J).

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Similarly, in the field of ionizing radiation, the SI unit of activity is designated as the becquerel (Bq) rather than the reciprocal second (s 1 ), and the SI units of absorbed dose and dose equivalent are designated as the gray (Gy) and the sievert (Sv), respectively, rather than the joule per kilogram (J/kg). 3

SI supplementary units

As previously stated, there are two units in this class: the radian, symbol rad, the SI unit of the quantity plane angle; and the steradian, symbol sr, the SI unit of the quantity solid angle. Definitions of these units are given in Appendix A. The SI supplementary units are now interpreted as so-called dimensionless derived units for which the CGPM allows the freedom of using or not using them in expressions for SI derived units.3 Thus the radian and steradian are not given in a separate table but have been included in Table 3a together with other derived units with special names and symbols (seeSec.2.1). This interpretation of the supplementary units implies that plane angle and solid angle are considered derived quantities of dimension one (so-called dimensionless quantities), each of which has the which has the unit one, symbol 1, as its coherent SI unit. However, in practice, when one expresses the values of derived quantities involving plane angle or solid angle, it often aids understanding if the special names (or symbols) ``radian' ' (rad) or ``steradian' ' (sr) are used in place of the number 1. For example, although values of the derived quantity angular velocity (plane angle divided by time) may be expressed in the unit s1, such values are usually expressed in the unit rad/s. Because the radian and steradian are now viewed as so-called dimensionless derived units, the Consultative Committee for Units (CCU, Comité Consultatif des Unités) of the CIPM as result of a 1993 request it received from ISO/TC12, recommended to the CIPM that it request the CGPM to abolish the class of supplementary units as a separate class in the SI. The CIPM accepted the CCU recommendation, and if the abolishment is approved by the CGPM as is likely (the question will be on the agenda of the 20th CGPM, October 1995), the SI will consist of only two classes of units: base units and derived units, with the radian and steradian subsumed into the class of derived units of the SI. (The option of using or not using them in expressions for SI derived units, as is convenient, would remain unchanged.) 4

Decimal multiples and submultiples of SI units: SI prefixes

Table 5 gives the SI prefixes that are used to form decimal multiples and submultiples of SI units. They allow very large or very small numerical values to be avoided. A prefix attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit. For example, one kilometer, symbol 1 km, is equal to one thousand meters, symbol 1000 m or 103 m. When prefixes are attached to SI units, the units so formed are called ``multiples and submultiples of SI units' ' in order to distinguish them from the coherent system of SI units.

Note:

Alternative definitions of the SI prefixes and their symbols are not permitted. For example, it is unacceptable to use kilo (k) to represent 2 10 = 1024, mega (M) to represent 2 20 = 1 048 576, or giga (G) to represent 2 30 = 1 073 741 824.

3

This interpretation was given in 1980 by the CIPM . It was deemed necessary because Resolution 12 of the 11th CGPM, which established the SI in 1960 , did not specify the nature of the supplementary units. The interpretation is based on two principal considerations: that plane angle is generally expressed as the ratio of two lengths and solid angle as the ratio of an area and the square of a length, and are thus quantities of dimension one (so-called dimensionless quantities); and that treating the radian and steradian as SI base units – a possibility not disallowed by Resolution 12 – could compromise the internal coherence of the SI based on only seven base units. (See ISO 31-0 for a discussion of the concept of dimension.)

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Table 5. SI prefixes Factor

Prefix

10 24 10 21 10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 1

= = = = = = = =

(10 3 ) 8 (10 3 ) 7 (10 3 ) 6 (10 3 ) 5 (10 3 ) 4 (10 3 ) 3 (10 3 ) 2 (10 3 ) 1

5

Units Outside the SI

Symbol

yotta zetta exa peta tera giga mega kilo hecto deka

Y Z E P T G M k h da

Factor 101 102 103 106 109 1012 1015 1018 1021 1024

= = = = = = = =

Prefix

Symbol

deci centi milli micro nano pico femto atto zepto yocto

3 1

(10 ) (10 3 ) 2 (10 3 ) 3 (10 3 ) 4 (10 3 ) 5 (10 3 ) 6 (10 3 ) 7 (10 3 ) 8

d c m n p f a z y

Units that are outside the SI may be divided into three categories: –

those units that are accepted for use with the SI;

–

those units that are temporarily accepted for use with the SI; and

–

those units that are not accepted for use with the SI and thus must strictly be avoided.

5.1

Units accepted for use with the SI The following sections discuss in detail the units that are acceptable for use with the SI.

5.1.1

Hour, degree, liter, and the like

Certain units that are not part of the SI are essential and used so widely that they are accepted by the CIPM for use with the SI. These units are given in Table 6. The combination of units of this table with SI units to form derived units should be restricted to special cases in order not to lose the advantages of the coherence of SI units. Additionally, it is recognized that it may be necessary on occasion to use time-related units other than those given in Table 6; in particular, circumstances may require that intervals of time be expressed in weeks, months, or years. In such cases, if a standardized symbol for the unit is not available, the name of the unit should be written out in full.

Table 6. Units accepted for use with the SI Name

Symbol

冧冧

minute hour time day degree minute plane angle second liter metric ton (c)

min h d ' " l, L (b) t

Value in SI units 1 min 1h 1d 1 1' 1" 1L 1t

= = = = = = = =

60 s 60 min = 3600 s 24 h = 86 400 s (/180) rad (1/60)=(/10 800) rad (1/60)' =(/648 000) rad 1 dm3 = 103 m3 10 3 kg

(b)

The alternative symbol for the liter, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter l and the number 1 . Thus, although both l and L are internationally accepted symbols for the liter, to avoid this risk the symbol to be used in the United States is L . The script letter ᐉ is not an approved symbol for the liter.

(c)

This is the name to be used for this unit in the United States; it is also used in some other English-speaking countries. However, ``tonne' ' is used in many countries.

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5.1.2

Neper, bel, shannon, and the like

There are a few highly specialized units not listed in Table 6 that are given by the International Organization for Standardization (ISO) or the International Electrotechnical Commission (IEC) and which are also acceptable for use with the SI. They include the neper (Np), bel (B), octave, phon, and sone, and units used in information technology, including the baud (Bd), bit (bit), erlang (E), hartley (Hart), and shannon (Sh).4 It is the position of NIST that the only such additional units that may be used with the SI are those given in either the International Standards on quantities and units of ISO or of IEC . 5.1.3

Electronvolt and unified atomic mass unit

The CIPM also finds it necessary to accept for use with the SI the two units given in Table 7. These units are used in specialized fields; their values in SI units must be obtained from experiment and, therefore, are not known exactly.

Note :

In some fields the unified atomic mass unit is called the dalton, symbol Da; however, this name and symbol are not accepted by the CGPM, CIPM, ISO, or IEC for use with the SI. Similarly, AMU is not an acceptable unit symbol for the unified atomic mass unit. The only allowed name is ``unified atomic mass unit' ' and the only allowed symbol is u.

Table 7. Units accepted for use with the SI whose values in SI units are obtained experimentally Name electronvolt unified atomic mass unit (a) (b)

Symbol eV u

Definition (a) (b)

The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum; 1 eV = 1.602 177 331019 J with a combined standard uncertainty of 0.000 000 491019 J . The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide 12 C; 1 u = 1.660 540 2 1027 kg with a combined standard uncertainty of 0.000 001 01027 kg .

5.1.4

Natural and atomic units

In some cases, particularly in basic science, the values of quantities are expressed in terms of fundamental constants of nature or so-called natural units.The use of these units with the SI is permissible when it is necessary for the most effective communication of information. In such cases, the specific natural units that are used must be identified. This requirement applies even to the system of units customarily called ``atomicunits' ' used in theoretical atomic physics and chemistry, inasmuch as there are several different systems that have the appellation ``atomic units.'' Examples of physical quantities used as natural units are given in Table 8.

NIST also takes the position that while theoretical results intended primarily for other theorists may be left in natural units, if they are also intended for experimentalists, they must also be given in acceptable units.

4 The symbol in parentheses following the name of the unit is its internationally accepted unit symbol, but the octave, phon, and sone have no such unit symbols. For additional information on the neper and bel, see Sec. 0.5 of ISO 31-2. The question of the byte (B) is under international consideration.

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INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table 8. Examples of physical quantities sometimes used as natural units Kind of quantity

Physical quantity used as a unit

action electric charge energy length length magnetic flux magnetic moment magnetic moment mass mass speed

Planck constant divided by 2 elementary charge Hartree energy Bohr radius Compton wavelength (electron) magnetic flux quantum Bohr magneton nuclear magneton electron rest mass proton rest mass speed of electromagnetic waves in vacuum

5.2

Symbol

h e Eh a0 C

0 B N me mp c

Units temporarily accepted for use with the SI

Because of existing practice in certain fields or countries, in 1978 the CIPM considered that it was permissible for the units given in Table 9 to continue to be used with the SI until the CIPM considers that their use is no longer necessary. However, these units must not be introduced where they are not presently used. Further, NIST strongly discourages the continued use of these units except for the nautical mile, knot, are, and hectare; and except for the curie, roentgen, rad, and rem until the year 2000 (the cessation date suggested by the Committee for Ineragency Radiation Research and Policy Coordination or CIRRPC, a United States Government interagency group). 5

Table 9. Units temporarily accepted for use with the SI (a) Name nautical mile knot ångström are(b) hectare(b) barn bar gal curie roentgen rad rem (a) (b) (c)

Symbol

Å a ha b bar Gal Ci R rad (c) rem

Value in SI units 1 nautical mile = 1852 m 1 nautical mile per hour = (1852/3600) m/s 1 Å = 0.1 nm = 1010 m 1 a = 1 dam2 = 10 2 m2 1 ha = 1 hm2 = 10 4 m2 1 b = 100 fm2 = 1028 m2 1 bar=0.1 MPa=100 kPa=1000 hPa=10 5 Pa 1 Gal = 1 cm/s 2 = 102 m/s 2 1 Ci = 3.71010 Bq 1 R = 2.58104 C/kg 1 rad = 1 cGy = 102 Gy 1 rem = 1 cSv = 102 Sv

See Sec. 5.2 regarding the continued use of these units. This unit and its symbol are used to express agrarian areas. When there is risk of confusion with the symbol for the radian, rd may be used as the symbol for rad.

5

In 1993 the CCU (see Sec. 3) was requested by ISO/TC 12 to consider asking the CIPM to deprecate the use of the units of Table 9 except for the nautical mile and knot, and possibly the are and hectare. The CCU discussed this request at its February 1995 meeting.

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Appendix A. A.1

Definitions of the SI Base Units and the Radian and Steradian

Introduction

The following definitions of the SI base units are taken from NIST SP 330; the definitions of the SI supplementary units, the radian and steradian, which are now interpreted as SI derived units (see Sec. 3), are those generally accepted and are the same as those given in ANSI/IEEE Std 268-1992. SI derived units are uniquely defined only in terms of SI base units; for example, 1 V = 1 m 2 kg s 3 A 1. A.2

Meter (17th CGPM, 1983)

The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. A.3

Kilogram (3d CGPM, 1901)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. A.4

Second (13th CGPM, 1967)

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium- 133 atom. A.5

Ampere (9th CGPM, 1948)

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 10 7 newton per meter of length. A.6

Kelvin (13th CGPM, 1967)

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. A.7

Mole (14th CGPM, 1971)

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole. A.8

Candela (16th CGPM, 1979)

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 10 12 hertz and that has a radiant intensity in that direction of ( 1/ 683) watt per steradian. A.9

Radian

The radian is the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. A.10

Steradian

The steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. From CRC Handbook of Chemistry and Physics, 83rd ed., Lide, D., Ed., CRC Press, Boca Raton, FL, 2002, pp. 1-25 to 1-32.

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3-11

CONVERSION FACTORS The following table gives conversion factors from various units of measure to SI units. It is reproduced from NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The table gives the factor by which a quantity expressed in a non-SI unit should be multiplied in order to calculate its value in the SI. The SI values are expressed in terms of the base, supplementary, and derived units of SI in order to provide a coherent presentation of the conversion factors and facilitate computations (see the table “International System of Units” in this Section). If desired, powers of ten can be avoided by using SI Prefixes and shifting the decimal point if necessary. Conversion from a non-SI unit to a different non-SI unit may be carried out by using this table in two stages, e.g., 1 calth = 4.184 J 1 BtuIT = 1.055056 E+03 J Thus, 1 BtuIT = (1.055056 E+03 ÷ 4.184) calth = 252.164 calth Conversion factors are presented for ready adaptation to computer readout and electronic data transmission. The factors are written as a number equal to or greater than one and less than ten with six or fewer decimal places. This number is followed by the letter E (for exponent), a plus or a minus sign, and two digits which indicate the power of 10 by which the number must be multiplied to obtain the correct value. For example: 3.523 907 E-02 is 3.523 907 ¥ 10–2 or 0.035 239 07 Similarly:

3.386 389 E+03 is 3.386 389 ¥ 103

or 3 386.389 A factor in boldface is exact; i.e., all subsequent digits are zero. All other conversion factors have been rounded to the figures given in accordance with accepted practice. Where less than six digits after the decimal point are shown, more precision is not warranted. It is often desirable to round a number obtained from a conversion of units in order to retain information on the precision of the value. The following rounding rules may be followed: (1) If the digits to be discarded begin with a digit less than 5, the digit preceding the first discarded digit is not changed. Example: 6.974 951 5 rounded to 3 digits is 6.97 (2) If the digits to be discarded begin with a digit greater than 5, the digit preceding the first discarded digit is increased by one. Example: 6.974 951 5 rounded to 4 digits is 6.975 (3) If the digits to be discarded begin with a 5 and at least one of the following digits is greater than 0, the digit preceding the 5 is increased by 1. Example: 6.974 851 rounded to 5 digits is 6.974 9 (4) If the digits to be discarded begin with a 5 and all of the following digits are 0, the digit preceding the 5 is unchanged if it is even and increased by one if it is odd. (Note that this means that the final digit is always even.) Examples: 6.974 951 5 rounded to 7 digits is 6.974 952 6.974 950 5 rounded to 7 digits is 6.974 950

REFERENCE Taylor, B. N., Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 1995 Edition, Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402, 1995. )

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Factors in boldface are exact To convert from

to

Multiply by

abampere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

E+01

abcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abfarad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . farad (F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

E+01 E+09

abhenry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . henry (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

Eⴚ09

abmho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

E+09 Eⴚ09

abvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

Eⴚ08

acceleration of free fall, standard (g n ). . . . . . . . . . . . . . . meter per second squared (m/s 2 ) . . . . . . . . . . . . . . 9.806 65

E+00

acre (based on U.S. survey foot)9 . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.046 873

E+03

acre foot (based on U.S. survey foot)9 . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.233 489

E+03

ampere hour (A h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 ångstro¨m (Å) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

E+03 Eⴚ10

ångstro¨m (Å) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nanometer (nm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

Eⴚ01

are (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 astronomical unit (AU). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.495 979

E+02 E+11

atmosphere, standard (atm). . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.013 25 atmosphere, standard (atm). . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.013 25 atmosphere, technical (at) 10 . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 atmosphere, technical (at) 10 . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65

E+05 E+02

bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

E+05 E+02

barn (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 barrel [for petroleum, 42 gallons (U.S.)](bbl) . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.589 873 barrel [for petroleum, 42 gallons (U.S.)](bbl) . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.589 873 biot (Bi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 British thermal unit IT (BtuIT )11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 British thermal unit th (Btuth )11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 350

E+04 E+01

Eⴚ28 E01 E+02 E+01 E+03

British thermal unit (mean) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 87

E+03 E+03

British thermal unit (39 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.059 67 British thermal unit (59 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 80

E+03 E+03

British thermal unit (60 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 68 British thermal unitIT foot per hour square foot degree Fahrenheit [BtuIT ft/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.730 735 British thermal unitth foot per hour square foot degree Fahrenheit [Btuth ft/(h ft2 F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.729 577 British thermal unitIT inch per hour square foot degree Fahrenheit [BtuIT in/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.442 279 British thermal unitth inch per hour square foot degree Fahrenheit [Btuth in/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.441 314 British thermal unitIT inch per second square foot degree Fahrenheit [BtuIT in/(s ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 5.192 204

E+03

9

E+00 E+00 E01 E01 E+02

The U.S. survey foot equals (1200/3937) m. 1 international foot = 0.999998 survey foot. One technical atmosphere equals one kilogram-force per square centimeter (1 at = 1 kgf/cm 2 ). The Fifth International Conference on the Properties of Steam (London, July 1956) defined the International Table calorie as 4.1868 J. Therefore the exact conversion factor for the International Table Btu is 1.055 055 852 62 kJ. Note that the notation for International Table used in this listing is subscript ‘‘IT’’. Similarily, the notation for thermochemical is subscript ‘‘th.’’ Further, the thermochemical Btu, Btu th , is based on the thermochemical calorie, cal th , where cal th = 4.184 J exactly.

10

11

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3-13

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to

Multiply by

British thermal unitth inch per second square foot degree Fahrenheit [Btuth in/(s ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 5.188 732

E+02

British thermal unitIT per cubic foot (BtuIT /ft3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3) . . . . . . . . . . . . . . . . . . . 3.725 895

E+04

British thermal unitth per cubic foot (Btuth /ft3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3) . . . . . . . . . . . . . . . . . . . 3.723 403

E+04

British thermal unitIT per degree Fahrenheit (BtuIT / F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101

E+03

British thermal unitth per degree Fahrenheit (Btuth /F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830 British thermal unitIT per degree Rankine (BtuIT /R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101

E+03

British thermal unitth per degree Rankine (Btuth /R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830

E+03

E+03

British thermal unitIT per hour (BtuIT /h) . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.930 711

E01

British thermal unitth per hour (Btuth /h). . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.928 751 British thermal unitIT per hour square foot degree Fahrenheit [BtuIT /(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin [W/(m2 K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.678 263 British thermal unitth per hour square foot degree Fahrenheit [Btuth /(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin [W/(m2 K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.674 466 British thermal unitth per minute (Btuth /min) . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.757 250

E01

British thermal unitIT per pound (BtuIT /lb). . . . . . . . . . joule per kilogram (J/kg) . . . . . . . . . . . . . . . . . . . . . . 2.326 British thermal unitth per pound (Btuth /lb) . . . . . . . . . . joule per kilogram (J/kg) . . . . . . . . . . . . . . . . . . . . . . 2.324 444 British thermal unitIT per pound degree Fahrenheit [BtuIT /(lb F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin (J/(kg K)]. . . . . . . . . . 4.1868 British thermal unitth per pound degree Fahrenheit [Btuth /(lb F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg K)]. . . . . . . . . . 4.184 British thermal unitIT per pound degree Rankine [BtuIT /(lb R)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg K)]. . . . . . . . . . 4.1868 British thermal unitth per pound degree Rankine [Btuth /(lb R)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg K)]. . . . . . . . . . 4.184 British thermal unitIT per second (BtuIT /s) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 British thermal unitth per second (Btuth /s) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unitIT per second square foot degree Fahrenheit [BtuIT /(s ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin [W/(m2 K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unitth per second square foot degree Fahrenheit [Btuth /(s ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin [W/(m2 K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unitIT per square foot (BtuIT /ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2) . . . . . . . . . . . . . . . . . . British thermal unitth per square foot (Btuth /ft2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2) . . . . . . . . . . . . . . . . . . British thermal unitIT per square foot hour [(BtuIT /(ft2 h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . British thermal unitth per square foot hour [Btuth /(ft2 h)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . British thermal unitth per square foot minute [Btuth /(ft2 min)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . British thermal unitIT per square foot second [(BtuIT /(ft2 s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . British thermal unitth per square foot second [Btuth /(ft2 s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . British thermal unitth per square inch second [Btuth /(in2 s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . .

© 2004 by CRC Press LLC

E+00

E+00 E+01 E+03 E+03 E+03 E+03 E+03 E+03 E+03

1.054 350

E+03

2.044 175

E+04

2.042 808

E+04

1.135 653

E+04

1.134 893

E+04

3.154 591

E+00

3.152 481

E+00

1.891 489

E+02

1.135 653

E+04

1.134 893

E+04

1.634 246

E+06

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3-14

CRC Handbook of Engineering Tables

To convert from

to

Multiply by 3

bushel (U.S.) (bu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.523 907 bushel (U.S.) (bu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.523 907

E02 E+01

calorie IT (calIT) 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorie th (calth) 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorie (cal) (mean) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorie (15 C) (cal 15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorie (20 C) (cal 20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorieIT , kilogram (nutrition) 12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorieth , kilogram (nutrition) 12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorie (mean), kilogram (nutrition) 12 . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorieth per centimeter second degree Celsius [calth /(cm s C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . calorieIT per gram (calIT /g). . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) . . . . . . . . . . . . . . . . . . . . . . calorieth per gram (calth /g) . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) . . . . . . . . . . . . . . . . . . . . . . calorieIT per gram degree Celsius [calIT /(g C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg K)]. . . . . . . . . . calorieth per gram degree Celsius [calth /(g C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg K)]. . . . . . . . . . calorieIT per gram kelvin [cal IT /(g K)] . . . . . . . . . . . . . joule per kilogram kelvin [J / (kg K)] . . . . . . . . . calorieth per gram kelvin [cal th / (g K)] . . . . . . . . . . . . . joule per kilogram kelvin [J / (kg K)] . . . . . . . . . calorieth per minute (calth /min). . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorieth per second (calth /s). . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calorieth per square centimeter (calth /cm2). . . . . . . . . . . joule per square meter (J/m2) . . . . . . . . . . . . . . . . . . calorieth per square centimeter minute [calth /(cm2 min)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . calorieth per square centimeter second [calth /(cm2 s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . candela per square inch (cd/in2) . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2). . . . . . . . . . . . . . carat, metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . carat, metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gram (g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of mercury (0 C) 13 . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of mercury (0 C) 13 . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of mercury, conventional (cmHg) 13 . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of mercury, conventional (cmHg) 13 . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of water (4 C) 13 . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter of water, conventional (cmH 2 O) 13 . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centipoise (cP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . centistokes (cSt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2 /s). . . . . . . . . . . . . . . chain (based on U.S. survey foot) (ch)9 . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square millimeter (mm2) . . . . . . . . . . . . . . . . . . . . . . . clo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 K /W). . . . . . . cord (128 ft 3 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m 3 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic foot (ft3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic foot per minute (ft3 /min) . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . . cubic foot per minute (ft3 /min) . . . . . . . . . . . . . . . . . . . . . liter per second (L / s) . . . . . . . . . . . . . . . . . . . . . . . . . . cubic foot per second (ft3 /s) . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . .

4.1868 4.184 4.190 02 4.185 80 4.181 90

E+00 E+00 E+00 E+00 E+00

4.1868 4.184 4.190 02

E+03 E+03 E+03

4.184

E+02

4.1868 4.184

E+03 E+03

4.1868

E+03

4.184 4.1868 4.184 6.973 333 4.184 4.184

E+03 E+03 E+03 E02 E+00 E+04

6.973 333

E+02

4.184 1.550 003 2.0 2.0 1.333 22 1.333 22 1.333 224 1.333 224 9.806 38 9.806 65 1.0 1.0 2.011 684 5.067 075 5.067 075 1.55 3.624 556 2.831 685 4.719 474 4.719 474 2.831 685

E+04 E+03 Eⴚ04 Eⴚ01 E+03 E+00 E+03 E+00 E+01 E+01 Eⴚ03 Eⴚ06 E+01 E10 E04 E01 E+00 E02 E04 E01 E02

12 The kilogram calorie or ‘‘large calorie’’ is an obsolete term used for the kilocalorie, which is the calorie used to express the energy content of foods. However, in practice, the prefix ‘‘kilo’’ is usually omitted. 13 Conversion factors for mercury manometer pressure units are calculated using the standard value for the acceleration of gravity and the density of mercury at the stated temperature. Additional digits are not justified because the definitions of the units do not take into account the compressibility of mercury or the change in density caused by the revised practical temperature scale, ITS-90. Similar comments also apply to water manometer pressure units. Conversion factors for conventional mercury and water manometer pressure units are based on ISO 31-3.

© 2004 by CRC Press LLC

1587_Book.fm Page 15 Monday, September 1, 2003 7:17 PM

3-15

Chemical Engineering, Chemistry, and Materials Science

To convert from 3

14

to

Multiply by 3

cubic inch (in ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic inch per minute (in3 /min). . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . . cubic mile (mi3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic yard (yd3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic yard per minute (yd3 /min) . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . . cup (U.S.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m 3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cup (U.S.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cup (U.S.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . curie (Ci) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . becquerel (Bq) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.638 706 2.731 177

E05 E07

4.168 182 7.645 549 1.274 258 2.365 882 2.365 882 2.365 882 3.7

E+09 E01 E02 E04 E01 E+02 E+10

E13 darcy15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared (m2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.869 233 day (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.64 E+04 day (sidereal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.616 409 E+04 debye (D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb meter (C m) . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 E30 degree (angle) (). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.745 329 E02 degree Celsius (temperature) (C) . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T / K = t / C+273.15 degree Celsius (temperature interval) (C) . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00 degree centigrade (temperature) 16 . . . . . . . . . . . . . . . . . . . degree Celsius (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t / C ª t / deg. cent. E+00 degree centigrade (temperature interval) 16 . . . . . . . . . . degree Celsius (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 degree Fahrenheit (temperature) (F). . . . . . . . . . . . . . . . degree Celsius (C) . . . . . . . . . . . . . . . . . . . . . . . . . . .t / C = (t / F 32) / 1.8 degree Fahrenheit (temperature) (F). . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T / K = (t / F + 459.67)/1.8 degree Fahrenheit (temperature interval)(F) . . . . . . . . degree Celsius (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E01 degree Fahrenheit (temperature interval)(F) . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E01 degree Fahrenheit hour per British thermal unit IT (F h / Btu IT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K / W) . . . . . . . . . . . . . . . . . . . . . . . . . 1.895 634 E+00 degree Fahrenheit hour per British thermal unit th (F h / Btu th). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K / W) . . . . . . . . . . . . . . . . . . . . . . . . . 1.896 903 E+00 degree Fahrenheit hour square foot per British thermal unitIT (F h ft2 /BtuIT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 K /W) . . . . . . 1.761 102 E01 degree Fahrenheit hour square foot per British thermal unitth (F h ft2 /Btuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 K /W) . . . . . . 1.762 280 E01 degree Fahrenheit hour square foot per British thermal unitIT inch [F h ft2 /(BtuIT in)] . . . . . . . . . . . . . . . . . . . . . . . . . . . meter kelvin per watt (m K /W) . . . . . . . . . . . . . . 6.933 472 E+00 degree Fahrenheit hour square foot per British thermal unitth inch 2 E+00 [F h ft /(Btuth in)] . . . . . . . . . . . . . . . . . . . . . . . . . . . meter kelvin per watt (m K /W) . . . . . . . . . . . . . . 6.938 112 degree Fahrenheit second per British thermal unit IT (F s / Btu IT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K / W) . . . . . . . . . . . . . . . . . . . . . . . . . 5.265 651 E04 degree Fahrenheit second per British thermal unit th (F s / Btu th) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K / W) . . . . . . . . . . . . . . . . . . . . . . . . . 5.269 175 E04 degree Rankine (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T / K = (T / R) / 1.8 degree Rankine (temperature interval) (R) . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E01 denier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) . . . . . . . . . . . . . . . . . . . . 1.111 111 E07 denier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gram per meter (g/m) . . . . . . . . . . . . . . . . . . . . . . . . . 1.111 111 E04 dyne (dyn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 Eⴚ05 dyne centimeter (dyn cm). . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 Eⴚ07 Eⴚ01 dyne per square centimeter (dyn/cm2) . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 electronvolt (eV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EMU of capacitance (abfarad) . . . . . . . . . . . . . . . . . . . . . . farad (F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EMU of current (abampere). . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EMU of electric potential (abvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EMU of inductance (abhenry) . . . . . . . . . . . . . . . . . . . . . . henry (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 15 16

1.602 177 1.0 1.0 1.0 1.0

The exact conversion factor is 1.638 706 4 E05. The darcy is a unit for expressing the permeability of porous solids, not area. The centigrade temperature scale is obsolete; the degree centigrade is only approximately equal to the degree Celsius.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

To convert from

to

EMU of resistance (abohm) . . . . . . . . . . . . . . . . . . . . . . . . . ohm () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . erg (erg). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . erg per second (erg/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . erg per square centimeter second |1obrkt㜸1ru|/ (cm2 s)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . ESU of capacitance (statfarad) . . . . . . . . . . . . . . . . . . . . . . farad (F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ESU of current (statampere) . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ESU of electric potential (statvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ESU of inductance (stathenry) . . . . . . . . . . . . . . . . . . . . . . henry (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ESU of resistance (statohm) . . . . . . . . . . . . . . . . . . . . . . . . . ohm () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Multiply by 1.0 1.0 1.0

Eⴚ09 Eⴚ07 Eⴚ07

1.0 1.112 650 3.335 641 2.997 925 8.987 552 8.987 552

Eⴚ03 E12 E10 E+02 E+11 E+11

faraday (based on carbon 12) . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.648 531 fathom (based on U.S. survey foot)9 . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.828 804 fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . femtometer (fm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 fluid ounce (U.S.) (fl oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.957 353 fluid ounce (U.S.) (fl oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.957 353 foot (ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.048 foot (U.S. survey) (ft)9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.048 006 footcandle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.076 391 footlambert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2). . . . . . . . . . . . . . 3.426 259 foot of mercury, conventional (ftHg) 13 . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.063 666 foot of mercury, conventional (ftHg) 13 . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.063 666 foot of water (39.2 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.988 98 foot of water (39.2 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.988 98 foot of water, conventional (ftH 2 O) 13 . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.989 067 foot of water, conventional (ftH 2 O) 13 . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.989 067 foot per hour (ft/h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . 8.466 667 foot per minute (ft/min) . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . 5.08 foot per second (ft/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . 3.048 foot per second squared (ft/s2) . . . . . . . . . . . . . . . . . . . . . . meter per second squared (m/s2). . . . . . . . . . . . . . . 3.048 foot poundal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.214 011 foot pound-force (ft lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 foot pound-force per hour (ft lbf/h). . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.766 161 foot pound-force per minute (ft lbf/min) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.259 697 foot pound-force per second (ft lbf/s) . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 foot to the fourth power (ft 4) 17 . . . . . . . . . . . . . . . . . . . . . . meter to the fourth power (m4) . . . . . . . . . . . . . . . . 8.630 975 franklin (Fr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 gal (Gal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second squared (m/s2). . . . . . . . . . . . . . . gallon [Canadian and U.K. (Imperial)] (gal) . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gallon [Canadian and U.K. (Imperial)] (gal) . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gallon (U.S.) (gal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gallon (U.S.) (gal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gallon (U.S.) per day (gal / d) . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . . gallon (U.S.) per day (gal / d) . . . . . . . . . . . . . . . . . . . . . . . . liter per second (L / s) . . . . . . . . . . . . . . . . . . . . . . . . . . gallon (U.S.) per horsepower hour [gal / (hp h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per joule (m3 /J) . . . . . . . . . . . . . . . . . . . gallon (U.S.) per horsepower hour [gal / (hp h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter per joule (L / J) . . . . . . . . . . . . . . . . . . . . . . . . . . . . gallon (U.S.) per minute (gpm)(gal / min) . . . . . . . . . . . cubic meter per second (m3 /s) . . . . . . . . . . . . . . . . . gallon (U.S.) per minute (gpm) (gal / min) . . . . . . . . . . . liter per second (L / s) . . . . . . . . . . . . . . . . . . . . . . . . . .

E+00 Eⴚ15 E+00 E05 E+01 Eⴚ01 E01 E+01 E+00 E+04 E+01 E+03 E+00 E+03 E+00 E05 Eⴚ03 Eⴚ01 Eⴚ01 E02 E+00 E04 E02 E+00 E03 E10

1.0

Eⴚ02

4.546 09 4.546 09 3.785 412 3.785 412 4.381 264 4.381 264

Eⴚ03 E+00 E03 E+00 E08 E05

1.410 089

E09

1.410 089 6.309 020 6.309 020

E06 E05 E02

17 This is a unit for the quantity second moment of area, which is sometimes called the ‘‘moment of section’’ or ‘‘area moment of inertia’’ of a plane section about a specified axis.

© 2004 by CRC Press LLC

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Chemical Engineering, Chemistry, and Materials Science

To convert from

to

Multiply by

gamma () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tesla (T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gauss (Gs, G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tesla (T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gilbert (Gi). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gill [Canadian and U.K. (Imperial)] (gi) . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gill [Canadian and U.K. (Imperial)] (gi) . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gill (U.S.) (gi). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gill (U.S.) (gi). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gon (also called grade) (gon) . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gon (also called grade) (gon) . . . . . . . . . . . . . . . . . . . . . . . . degree (angle) () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . grain (gr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . grain (gr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milligram (mg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . grain per gallon (U.S.) (gr / gal) . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . .

1.0 1.0 7.957 747 1.420 653 1.420 653 1.182 941 1.182 941 1.570 796 9.0 6.479 891 6.479 891

Eⴚ09 Eⴚ04 E01 E04 E01 E04 E01 E02 Eⴚ01 Eⴚ05 E+01

1.711 806 grain per gallon (U.S.) (gr / gal) . . . . . . . . . . . . . . . . . . . . . milligram per liter (mg / L). . . . . . . . . . . . . . . . . . . . . 1.711 806 gram-force per square centimeter (gf / cm 2). . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 gram per cubic centimeter (g / cm 3) . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . 1.0

E02 E+01 E+01 E+03

hectare (ha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (550 ft lbf/s) (hp) . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (boiler) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (electric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (metric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (U.K.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horsepower (water). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hour (h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hour (sidereal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hundredweight (long, 112 lb). . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hundredweight (short, 100 lb) . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.0 7.456 999 9.809 50 7.46 7.354 988 7.4570 7.460 43 3.6 3.590 170 5.080 235 4.535 924

E+04 E+02 E+03 E+02 E+02 E+02 E+02 E+03 E+03 E+01 E+01

inch (in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch (in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter (cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury (32 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury (32 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury (60 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury (60 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury, conventional (inHg) 13 . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of mercury, conventional (inHg) 13 . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of water (39.2 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of water (60 F) 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch of water, conventional (inH 2 O) 13 . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inch per second (in/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . inch per second squared (in/s2) . . . . . . . . . . . . . . . . . . . . . meter per second squared (m/s2). . . . . . . . . . . . . . . inch to the fourth power (in4) 17 . . . . . . . . . . . . . . . . . . . . . meter to the fourth power (m4) . . . . . . . . . . . . . . . .

2.54 2.54 3.386 38 3.386 38 3.376 85 3.376 85

Eⴚ02 E+00 E+03 E+00 E+03 E+00

3.386 389 3.386 389 2.490 82 2.4884 2.490 889 2.54 2.54 4.162 314

E+03 E+00 E+02 E+02 E+02 Eⴚ02 Eⴚ02 E07

E+02 kayser (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal meter (m 1 ) . . . . . . . . . . . . . . . . . . . . . . . . 1.0 kelvin (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree Celsius (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . .t / C = T / K 273.15 E+03 kilocalorieIT (kcalIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+03 kilocalorieth (kcalth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 kilocalorie (mean) (kcal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+03 E+01 kilocalorieth per minute (kcalth /min) . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.973 333 E+03 kilocalorieth per second (kcalth / s) . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 kilogram-force (kgf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 E+00 kilogram-force meter (kgf m) . . . . . . . . . . . . . . . . . . . . . . newton meter (N m). . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 E+00

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

To convert from

to

kilogram-force per square centimeter (kgf/cm 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram-force per square centimeter (kgf/cm 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram-force per square meter (kgf/m2). . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram-force per square millimeter (kgf/mm 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram-force per square millimeter (kgf/mm 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . megapascal (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram-force second squared per meter (kgf s 2 /m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer per hour (km/h) . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . kilopond (kilogram-force) (kp) . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilowatt hour (kW h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilowatt hour (kW h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . megajoule (MJ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kip per square inch (ksi) (kip/in2). . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Multiply by 9.806 65

E+04

9.806 65 9.806 65

E+01 E+00

9.806 65

E+06

9.806 65

E+00

9.806 65 2.777 778 9.806 65 3.6 3.6 4.448 222 4.448 222

E+00 E01 E+00 E+06 E+00 E+03 E+00

6.894 757 kip per square inch (ksi) (kip/in2). . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.894 757 knot (nautical mile per hour) . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . 5.144 444

E+06 E+03 E01

lambert 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2). . . . . . . . . . . . . . langley (cal th /cm 2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2) . . . . . . . . . . . . . . . . . . light year (l.y.)19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lumen per square foot (lm/ft 2) . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E+03 E+04 E+15 Eⴚ03 E+01

3.183 099 4.184 9.460 73 1.0 1.076 391

maxwell (Mx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . weber (Wb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 Eⴚ08 mho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00 microinch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 Eⴚ08 microinch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . micrometer (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 Eⴚ02 micron () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 Eⴚ06 micron () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . micrometer (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00 mil (0.001 in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 Eⴚ05 mil (0.001 in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 Eⴚ02 mil (angle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.817 477 E04 mil (angle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.625 Eⴚ02 mile (mi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.609 344 E+03 mile (mi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer (km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.609 344 E+00 E+03 mile (based on U.S. survey foot) (mi) 9 . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.609 347 mile (based on U.S. survey foot) (mi) 9 . . . . . . . . . . . . . . kilometer (km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.609 347 E+00 E+03 mile, nautical 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.852 E+05 mile per gallon (U.S.) (mpg) (mi/gal) . . . . . . . . . . . . . . . meter per cubic meter (m/m 3) . . . . . . . . . . . . . . . . . 4.251 437 mile per gallon (U.S.) (mpg) (mi/gal). . . . . . . . . . . . . . . kilometer per liter (km /L) . . . . . . . . . . . . . . . . . . . . . 4.251 437 E01 mile per gallon (U.S.) (mpg) (mi/gal) 22 . . . . . . . . . . . . . liter per 100 kilometer (L/100 km) . . . . . . . .divide 235.215 by number of miles per gallon mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . 4.4704 Eⴚ01 mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer per hour (km/h) . . . . . . . . . . . . . . . . . . . . . 1.609 344 E+00

18

The exact conversion factor is 10 4 /. This conversion factor is based on 1 d = 86 400 s; and 1 Julian century = 36 525 d. (See The Astronomical Almanac for the Year 1995 , page K6, U.S. Government Printing Office, Washington, DC, 1994). 20 In 1964 the General Conference on Weights and Measures reestablished the name ‘‘liter’’ as a special name for the cubic decimeter. Between 1901 and 1964 the liter was slightly larger (1.000 028 dm3); when one uses high-accuracy volume data of that time, this fact must be kept in mind. 21 The value of this unit, 1 nautical mile = 1852 m, was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name ‘‘International nautical mile.’’ 22 For converting fuel economy, as used in the U.S., to fuel consumption. 19

© 2004 by CRC Press LLC

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Chemical Engineering, Chemistry, and Materials Science

To convert from

to

Multiply by

mile per minute (mi/min) . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . mile per second (mi/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) . . . . . . . . . . . . . . . . . . . . . . . . millibar (mbar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millibar (mbar) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter of mercury, conventional (mmHg)13 . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter of water, conventional (mmH 2 O)13 . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minute (angle) (') . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minute (min) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minute (sidereal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.682 24 1.609 344 1.0 1.0 1.333 224 9.806 65 2.908 882 6.0 5.983 617

E+01 E+03 E+02 Eⴚ01 E+02 E+00 E04 E+01 E+01

oersted (Oe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere per meter (A/m). . . . . . . . . . . . . . . . . . . . . . . ohm centimeter ( cm). . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm meter ( m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm circular-mil per foot . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm meter ( m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm circular-mil per foot . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm square millimeter per meter ( mm 2 / m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois) (oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois) (oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . gram (g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (troy or apothecary) (oz) . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (troy or apothecary) (oz) . . . . . . . . . . . . . . . . . . . . . gram (g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce [Canadian and U.K. fluid (Imperial)] (fl oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce [Canadian and U.K. fluid (Imperial)] (fl oz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (U.S. fluid) (fl oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (U.S. fluid) (fl oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois)-force (ozf). . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois)-force inch (ozf in) . . . . . . . . . . . . newton meter (N m). . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois)-force inch (ozf in) . . . . . . . . . . . . millinewton meter (mN m) . . . . . . . . . . . . . . . . . . . ounce (avoirdupois) per cubic inch (oz / in3) . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . ounce (avoirdupois) per gallon [Canadian and U.K. (Imperial)] (oz / gal). . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . ounce (avoirdupois) per gallon [Canadian and U.K. (Imperial)] (oz / gal). . . . . . . . . . . . . . . . . . . . . . . . . gram per liter (g / L) . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois) per gallon (U.S.)(oz / gal) . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . ounce (avoirdupois) per gallon(U.S.)(oz / gal). . . . . . . . gram per liter (g / L) . . . . . . . . . . . . . . . . . . . . . . . . . . . ounce (avoirdupois) per square foot (oz / ft2). . . . . . . . . kilogram per square meter (kg/m2) . . . . . . . . . . . . ounce (avoirdupois) per square inch (oz / in2) . . . . . . . . kilogram per square meter (kg/m2) . . . . . . . . . . . . ounce (avoirdupois) per square yard (oz / yd2) . . . . . . . . kilogram per square meter (kg/m2) . . . . . . . . . . . .

7.957 747 1.0 1.662 426

E+01 Eⴚ02 E09

1.662 426 2.834 952 2.834 952 3.110 348 3.110 348

E03 E02 E+01 E02 E+01

2.841 306

E05

2.841 306 2.957 353 2.957 353 2.780 139 7.061 552 7.061 552 1.729 994

E+01 E05 E+01 E01 E03 E+00 E+03

6.236 023

E+00

6.236 023 7.489 152 7.489 152 3.051 517 4.394 185 3.390 575

E+00 E+00 E+00 E01 E+01 E02

parsec (pc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . peck (U.S.) (pk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . peck (U.S.) (pk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pennyweight (dwt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pennyweight (dwt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gram (g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . perm (0 C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second square meter [kg/(Pa s m2)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . perm (23 C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second square meter [kg/(Pa s m2)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . perm inch (0 C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second meter [kg/(Pa s m)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . perm inch (23 C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second meter [kg/(Pa s m)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.085 678 8.809 768 8.809 768 1.555 174 1.555 174

E+16 E03 E+00 E03 E+00

5.721 35

E11

5.745 25

E11

1.453 22

E12

1.459 29

E12

© 2004 by CRC Press LLC

1587_Book.fm Page 20 Monday, September 1, 2003 7:17 PM

3-20

CRC Handbook of Engineering Tables

To convert from

to

phot (ph) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pica (computer) (1/6 in) . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pica (computer) (1/6 in) . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pica (printer’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pica (printer’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pint (U.S. dry) (dry pt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pint (U.S. dry) (dry pt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pint (U.S. liquid) (liq pt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pint (U.S. liquid) (liq pt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . point (computer) (1/72 in). . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . point (computer) (1/72 in). . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . point (printer’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . point (printer’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . millimeter (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . poise (P) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . pound (avoirdupois) (lb)23 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Multiply by 1.0 4.233 333 4.233 333 4.217 518 4.217 518 5.506 105 5.506 105 4.731 765 4.731 765 3.527 778 3.527 778 3.514 598 3.514 598 1.0

E+04 E03 E+00 E03 E+00 E04 E01 E04 E01 E04 E01 E04 E01 Eⴚ01

4.535 924 3.732 417 1.382 550 1.488 164 1.488 164 4.214 011 4.448 222 1.355 818 5.337 866 1.129 848 4.448 222 1.459 390 1.751 268

E01 E01 E01 E+00 E+00 E02 E+00 E+00 E+01 E01 E+00 E+01 E+02

9.806 65 4.788 026 6.894 757 6.894 757

E+00 E+01 E+03 E+00

4.788 026

E+01

6.894 757 2.926 397 1.601 846 2.767 990 5.932 764

E+03 E04 E+01 E+04 E01

pound per foot (lb/ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) . . . . . . . . . . . . . . . . . . . . 1.488 164 pound per foot hour [lb/(ft h)] . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . 4.133 789

E+00 E04

pound per foot second [lb/(ft s)]. . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . pound per gallon [Canadian and U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . pound per gallon [Canadian and U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) . . . . . . . . . . . . . . . . . . . . . . pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) . . . . . . . . . . . . . . . . . . . . . . pound per horsepower hour [lb/(hp h)] . . . . . . . . . . . . kilogram per joule (kg/J) . . . . . . . . . . . . . . . . . . . . . . pound per hour (lb/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) . . . . . . . . . . . . . . . . . . . .

1.488 164

E+00

9.977 637

E+01

9.977 637 1.198 264 1.198 264 1.689 659 1.259 979

E02 E+02 E01 E07 E04

pound (troy or apothecary) (lb) . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . poundal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . poundal per square foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . poundal second per square foot . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . pound foot squared (lb ft2) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg m2) . . . . . . . . . . . . . . pound-force (lbf)24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pound-force foot (lbf ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N m). . . . . . . . . . . . . . . . . . . . . . . . . . pound-force foot per inch (lbf ft/in) . . . . . . . . . . . . . . . newton meter per meter (N m/m) . . . . . . . . . . . . pound-force inch (lbf in). . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N m). . . . . . . . . . . . . . . . . . . . . . . . . . pound-force inch per inch (lbf in/in) . . . . . . . . . . . . . . newton meter per meter (N m/m) . . . . . . . . . . . . pound-force per foot (lbf/ft) . . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m). . . . . . . . . . . . . . . . . . . . . . . pound-force per inch (lbf/in). . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m). . . . . . . . . . . . . . . . . . . . . . . pound-force per pound (lbf/lb) (thrust to mass ratio) . . . . . . . . . . . . . . . . . . . . . newton per kilogram (N/kg) . . . . . . . . . . . . . . . . . . . pound-force per square foot (lbf/ft2) . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pound-force per square inch (psi) (lbf/in2 ) . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pound-force per square inch (psi) (lbf/in2 ) . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pound-force second per square foot (lbf s/ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . pound-force second per square inch (lbf s/in2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . pound inch squared (lb in2) . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg m2) . . . . . . . . . . . . . . pound per cubic foot (lb/ft3) . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . pound per cubic inch (lb/in3) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . pound per cubic yard (lb/yd3) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . .

23

The exact conversion factor is 4.535 923 7 E01. All units that contain the pound refer to the avoirdupois pound.

24

If the local value of the acceleration of free fall is taken as g n= 9.806 65 m / s 2 (the standard value), the exact conversion factor is 4.448 221 615 260 5 E+00.

© 2004 by CRC Press LLC

1587_Book.fm Page 21 Monday, September 1, 2003 7:17 PM

3-21

Chemical Engineering, Chemistry, and Materials Science

To convert from

to

pound per inch (lb/in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) . . . . . . . . . . . . . . . . . . . . pound per minute (lb/min) . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) . . . . . . . . . . . . . . . . . . . . pound per second (lb/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) . . . . . . . . . . . . . . . . . . . . pound per square foot (lb/ft2) . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2) . . . . . . . . . . . . pound per square inch (not pound-force) (lb/in2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2) . . . . . . . . . . . . pound per yard (lb/yd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) . . . . . . . . . . . . . . . . . . . . psi (pound-force per square inch) (lbf/in 2) . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . psi (pound-force per square inch) (lbf/in 2) . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Multiply by 1.785 797 7.559 873 4.535 924 4.882 428

E+01 E03 E01 E+00

7.030 696 4.960 546 6.894 757

E+02 E01 E+03

6.894 757

E+00

quad (10 15 Btu IT ) 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 quart (U.S. dry) (dry qt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.101 221 quart (U.S. dry) (dry qt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.101 221 quart (U.S. liquid) (liq qt). . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.463 529 quart (U.S. liquid) (liq qt). . . . . . . . . . . . . . . . . . . . . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.463 529

E+18 E03 E+00 E04 E01

rad (absorbed dose) (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . gray (Gy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rem (rem) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sievert (Sv) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . revolution (r) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . revolution per minute (rpm) (r/min). . . . . . . . . . . . . . . . . radian per second (rad/s) . . . . . . . . . . . . . . . . . . . . . . rhe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal pascal second [(Pa s) 1 ]. . . . . . . . . . . rod (based on U.S. survey foot) (rd)9. . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . roentgen (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb per kilogram (C/kg). . . . . . . . . . . . . . . . . . rpm (revolution per minute) (r/min). . . . . . . . . . . . . . . . . radian per second (rad/s) . . . . . . . . . . . . . . . . . . . . . .

1.0 1.0 6.283 185 1.047 198 1.0 5.029 210 2.58 1.047 198

Eⴚ02 Eⴚ02 E+00 E01 E+01 E+00 Eⴚ04 E01

second (angle) (") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (sidereal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nanosecond (ns) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . slug (slug). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . slug per cubic foot (slug/ft 3 ). . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . slug per foot second [slug/(ft s)] . . . . . . . . . . . . . . . . . . pascal second (Pa s) . . . . . . . . . . . . . . . . . . . . . . . . . . square foot (ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square foot per hour (ft2 /h) . . . . . . . . . . . . . . . . . . . . . . . . . square meter per second (m2 /s) . . . . . . . . . . . . . . . . square foot per second (ft2 /s) . . . . . . . . . . . . . . . . . . . . . . . square meter per second (m2 /s) . . . . . . . . . . . . . . . . square inch (in2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square inch (in2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square centimeter (cm2). . . . . . . . . . . . . . . . . . . . . . . . square mile (mi2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square mile (mi2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square kilometer (km2). . . . . . . . . . . . . . . . . . . . . . . . . square mile (based on U.S. survey foot) (mi 2)9 . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square mile (based on U.S. survey foot) (mi 2)9 . . . . . . . . . . . . . . . . square kilometer (km2). . . . . . . . . . . . . . . . . . . . . . . . . square yard (yd2 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statampere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statfarad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . farad (F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . stathenry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . henry (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statmho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . statvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . stere (st) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . stilb (sb). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2). . . . . . . . . . . . . .

4.848 137 9.972 696 1.0 1.0 1.459 390 5.153 788 4.788 026 9.290 304 2.580 64 9.290 304 6.4516 6.4516 2.589 988 2.589 988

E06 E01 Eⴚ08 E+01 E+01 E+02 E+01 Eⴚ02 Eⴚ05 Eⴚ02 Eⴚ04 E+00 E+06 E+00

2.589 998

E+06

2.589 998 8.361 274 3.335 641 3.335 641 1.112 650 8.987 552 1.112 650 8.987 552 2.997 925 1.0

E+00 E01 E10 E10 E12 E+11 E12 E+11 E+02 E+00

1.0 stokes (St) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2 /s). . . . . . . . . . . . . . . 1.0

© 2004 by CRC Press LLC

E+04 Eⴚ04

1587_Book.fm Page 22 Tuesday, September 2, 2003 3:25 PM

3-22

To convert from

CRC Handbook of Engineering Tables

to

tablespoon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tablespoon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . teaspoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m 3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . teaspoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) . . . . . . . . . . . . . . . . . . . . therm (EC)25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . therm (U.S.)25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, assay (AT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, assay (AT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . gram (g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton-force (2000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton-force (2000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, long (2240 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, long, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . .

Multiply by 1.478 676 1.478 676 4.928 922 4.928 922 1.0 1.055 06 1.054 804 2.916 667 2.916 667 8.896 443 8.896 443 1.016 047

E05 E+01 E06 E+00 Eⴚ06 E+08 E+08 E02 E+01 E+03 E+00 E+03

1.328 939 1.0 1.0 3.516 853 4.184 2.831 685 9.071 847 1.186 553 2.519 958 1.333 224

E+03 E+03 E+03 E+03 E+09 E+00 E+02 E+03 E01 E+02

unit pole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . weber (Wb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.256 637

E07

watt hour (W h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square centimeter (W/cm2 ). . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . watt per square inch (W/in2 ). . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2) . . . . . . . . . . . . . . . . . watt second (W s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6 1.0 1.550 003 1.0

E+03 E+04 E+03 E+00

yard (yd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . year (365 days). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . year (sidereal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . year (tropical) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.144 3.1536 3.155 815 3.155 693

Eⴚ01 E+07 E+07 E+07

ton , metric (t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tonne (called ‘‘metric ton’’ in U.S.) (t) . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton of refrigeration (12 000 Btu IT /h) . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton of TNT (energy equivalent) 26 . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, register . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, short (2000 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ton, short, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) . . . . . . . . . . . . . ton, short, per hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) . . . . . . . . . . . . . . . . . . . . torr (Torr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

The therm (EC) is legally defined in the Council Directive of 20 December 1979. Council of the European Communities (now the European Union, EU). The Therm (U.S.) is legally defined in the Federal Register of July 27, 1968. Although the therm (EC), which is based on the International Table Btu, is frequently used by engineers in the United States, the therm (U.S.) is the legal unit used by the U.S. natural gas industry. 26 Defined (not measured) value. From CRC Handbook of Chemistry & Physics, 83rd ed., Lide, D., Ed., CRC Press, Boca Raton, FL, 2002, pp. 1-34 to 1-45.

© 2004 by CRC Press LLC

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References

From CRC Handbook of Chemistry and Physics, 83rd ed., Lide, O., Ed., CRC Press, Boca Raton, FL, 2002.

© 2004 by CRC Press LLC

3-23

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1587_Section_3.fm Page 23 Tuesday, September 2, 2003 4:52 PM

'$/0

Chemical Engineering, Chemistry, and Materials Science

PERIODIC TABLE OF THE ELEMENTS

The term semiconductor is applied to a material in which electric current is carried by electrons or holes and whose electrical conductivity, when extremely pure, rises exponentially with temperature and may be increased from its low “intrinsic” value by many orders of magnitude by “doping” with electrically active impurities. Semiconductors are characterized by an energy gap in the allowed energies of electrons in the material which separates the normally filled energy levels of the valence band (where “missing” electrons behave like positively charged current carriers “holes”) and the conduction band (where electrons behave rather like a gas of free negatively charged carriers with an effective mass dependent on the material and the direction of the electrons’ motion). This energy gap depends on the nature of the material and varies with direction in anisotropic crystals. It is slightly dependent on temperature and pressure, and this dependence is usually almost linear at normal temperatures and pressures. Data are presented in three tables. Table I “General Properties of Semiconductors” lists the main crystallographic and semiconducting properties of a large number of semiconducting materials in three main categories: “Tetrahedral Semiconductors” in which every atom is tetrahedrally co-ordinated to four nearest neighbor atoms (or atomic sites) as for example in the diamond structure; “Octahedral Semiconductors: in which every atom is octahedrally co-ordinated to six nearest neighbor atoms—as for examples the halite structure; and “Other Semiconductors.” Table II gives more detailed information about some better known semiconductors, while Table III gives some information about the electronic energy band structure parameters of the best known materials. Table I. PHYSICO-CHEMICAL PROPERTIES OF SEMICONDUCTORS (LISTED BY CRYSTAL STRUCTURE)

Molecular Mass

Lattice Parameters (Å, Room Temp.)

Density (g/cm3)

Melting Point (K)

Microhardness, N/mm2 Specific Heat, (M-Mohs Scale) J/kg·K (300 K)

Debye Temp. (K)

Coefficient of Thermal Linear Thermal Expansion Conductivity [10–6 K–1 (300K)] [mW/cm·K (300K)]

Part A. Adamantine Semiconductors §A1. Diamond Structure Elements (Strukturbericht symbol A4, Space Group Fd3m-O 7h ) C

Si Ge a-Sn

© 2004 by CRC Press LLC

12.01

3.56683

3.51

28.09 72.59 118.69

5.43072 5.65754 6.4912

2.3283 5.3234 5.765 (281 K)

ª3850 Transition to graphite > 980 1685 ± 2 1231 505.2 (Tr. 286.4)

10 (M)

11270 7644

471.5

2340

702 321.9 213

645 374 230

1.18

2.49 6.1 5.4 (220 K)

9900(I) 23200(IIA) 13600(IIB) 1240 640

CRC Handbook of Engineering Tables

Substance

Average Atomic Mass

1587_Book.fm Page 24 Monday, September 1, 2003 7:17 PM

3-24

Properties of Semiconductors

41.27 49.49 71.73 95.23 93.89 117.39

4.255 5.4057 5.6905 6.60427

41.08 87.97 136.61 (2318) 81.37 97.43 144.34 192.99 (274) 144.46 191.36 240.00 (321) 232.65 279.55 328.19

20.54 43.99 68.31 (109) 40.69 48.72 72.17 96.5 (137) 72.23 95.68 120.00 (161) 116.33 139.78 164.10

4.865 5.139 5.626 5.838 4.63 5.4093 5.6676 6.101 6.309 5.832 6.05 6.477 6.665 5.8517 6.084 6.4623

24.82 41.78 85.73 57.95 101.90 148.73 100.69 144.64 191.47 145.79 189.74 236.57

12.41 20.87 42.87 28.98 50.95 74.37 50.35 72.32 95.74 72.90 94.87 118.29

3.615 4.538 4.777 5.451 5.6622 6.1355 5.4905 5.65315 6.0954 5.86875 6.05838 6.47877

6.502

3.53 4.98 5.63 6.473 5.67

1181 695 770 878 >1570 (Tr. 410) 831

2.3 (M) 2.5 (M) 192 2.5 (M) 2.5 (M)

490 381 276 270 232

240 207 181

12.1 15.4 19.2

8.4 12.5 16.8

134

–2.5

4.2

2.36 4.315 5.090 7.3 5.675 4.079 5.42 6.34

2248 2100 (Tr. 1295) 1790 1568

5.0 (M) 1780 1350 900

494 472 339 264

416 530 400 223

2.9 6.36 7.2 8.19

234 251 140 108

4.826 5.674 5.86

1750 1512 1365

1250 1300 600

330 255 205

219 181 200

4.7 3.8 4.9

200 90 58.5

7.73 8.25 8.17

1820 1070 943

3 (M) 2.5 (M) 300

210 178 164

151 242

5.46 4.6

10 20

3.49 2.9

ª3300 ª2800 ª2300 ª2100 2013 1330 1750 1510 980 1330 1215 798

10 (M) 37000 19000 5.5 (M) 5000 4000 9450 7500 4480 4100 3300 2200

793

2.42 3.81 4.218 4.13 5.316 5.619 4.787 5.66 5.775

320 268 144

ª1900 ª980 ª625 588 417 292 446 344 265 321 249 202

200

3.5 4.2 5.3 5.4 6.1 4.6 4.7 4.7

920 840 600 752 560 270 800 290 160

1587_Book.fm Page 25 Monday, September 1, 2003 7:17 PM

© 2004 by CRC Press LLC

82.54 98.99 143.36 190.46 187.78 234.77

3-25

I VII Compounds CuF CuCl CuBr Cul AgBr AgI II VI Compounds BeS BeSe BeTe BePo ZnO ZnS ZnSe ZnTe ZnPo CdS CdSe CdTe CdPo HgS HgSe HgTe III V Compounds BN BP(L.T.) BAs AIP AIAs AISb GaP GaAs GaSb InP InAs InSb

Chemical Engineering, Chemistry, and Materials Science

–

§A2. Sphalerite (Zinc Blende) Structure Compounds (Strukturbericht symbo1 B3 Space Group F 4 3m-Td2 )

Table I. PHYSICO-CHEMICAL PROPERTIES OF SEMICONDUCTORS (LISTED BY CRYSTAL STRUCTURE) (continued)

Substance

Molecular Mass

Average Atomic Mass

Other sphalerite structure compounds MnS 87.0 43.5 MnSe 133.9 66.95 b-SiC 40.1 20.1 376.32 75.26 Ga2Se3 522.24 104.45 Ga2Te3 In2Te3(H.T.) 608.44 121.7 MgGeP2 158.84 39.71 ZnSnP2 246.00 61.5 333.90 82.38 ZnSnAs2(H.T.) ZnSnSb2 427.56 106.89

Lattice Parameters (Å, Room Temp.)

Density (g/cm3)

5.011 5.82 4.348 5.429 5.899 61.50 5.652 5.65 5.851 6.281

Melting Point (K)

Microhardness, N/mm2 Specific Heat, (M-Mohs Scale) J/kg·K (300 K)

3.21 4.92 5.75 5.8

3070 1020 1063 940

3160 2370 1660

5.53 5.67

1200 1050 870

2500

Debye Temp. (K)

Coefficient of Thermal Linear Thermal Expansion Conductivity [10–6 K–1 (300K)] [mW/cm·K (300K)]

8.9

50 47 69

76 76

§A3. Wurtzite (Zincite) Structure Compounds (Strukturbericht symbol B4, Space Group P 63mc-C46v)

© 2004 by CRC Press LLC

99.0 143.46 190.46 234.80

49.5 71.73 95.23 117.40

3.91 4.06 4.31 4.580

6.42 6.66 7.09 7.494

25.01 151.9 81.37 97.43 192.99 144.46 191.36 240.00

12.51 76.0 40.69 48.72 46.50 72.23 95.68 120.00

2.698 4.54 3.24950 3.8140 4.27 4.1348 4.299 4.57

4.380 7.39 5.2069 6.2576 6.99 6.7490 7.010 7.47

41.79 40.99 83.73 128.83

20.90 20.50 41.87 64.42

3.562 3.111 3.190 3.533

5.900 4.978 5.189 5.693

Tc680K Tc658K

4.82 5.66

2800 ª2800 2250 2100 1568 1748 1512

401 316

3.26 6.10 6.88

ª2500 1500 1200

823 656 556

3.85 5.66 4.1

600 460

CRC Handbook of Engineering Tables

I VII Compounds CuCl CuBr Cul Agl II VI Compounds BeO MgTe Zno ZnS ZnTe Cds CdSe CdTe III V Compounds BP(H.T.) AIN GaN InN

1587_Book.fm Page 26 Monday, September 1, 2003 7:17 PM

3-26

Properties of Semiconductors (continued)

6.45 6.72 5.048 6.701 5.829 6.30

3.248

2.55 3.91

1400 1250 –

§A4. Chalcopyrite Structure Compounds (Strukturbericht symbol E11, Space Group I 4 2d-D12 24 )

© 2004 by CRC Press LLC

154.65 248.45 345.73 197.39 291.19 388.47 242.49 336.29 433.57 322.05 425.85 183.51 277.31 266.58 198.97 292.77 390.05 241.71 335.51 432.79 286.87 380.61 477.89 227.83

38.66 62.11 86.43 49.53 72.80 97.12 60.62 84.07 108.39 83.01 106.46 45.88 69.33 66.65 49.74 73.19 97.51 60.43 83.88 108.2 71.70 95.15 119.47 56.96

5.323 5.617 5.976 5.360 5.618 6.013 5.528 5.785 6.179 5.580 5.844 5.25

10.44 10.92 11.80 10.49 11.01 11.93 11.08 11.56 12.365 11.17 11.65 10.32

3.47 4.70 5.50 4.35 5.56 5.99 4.75 5.77 6.10 6.32 7.11 4.088

2500 2260 2550 2300 1970 2400 1400 1600 1660

5.65 5.707 5.968 6.309 5.755 5.985 6.301 5.828 6.102 6.42 5.66

10.86 10.28 10.77 11.85 10.28 10.90 11.96 11.19 11.69 12.59 10.30

3.94 5.07 6.18 4.72 5.84 6.05 5.00 5.81 6.12 4.53

155.40 199.90 246.00 202.43 246.94

38.85 49.98 61.5 50.61 61.74

5.400 5.465

10.441 10.771

3.39 4.17

1640 1295

5.678 5.741

10.431 10.775

4.00 4.48

ª1470 1049

4200 3500 2550 2050 400

275

195

5.4 6.9

42 27

6.6 7.1

37 49

900 850

1220 1000 1120 990 1053 965

4400 1800 2250 1850

212

10 30 9.49, 0.69

1100 8100 6500 10500 5650

180 282 110

3-27

I III VI2 Compounds CuAlS2 CuAlSe2 CuAlTe2 CuGaS2 CuGaSe2 CuGaTe2 CulnS2 CulnSe2 CulnTe2 CuTlS2 CuTlSe2(L.T.) CuFeS2 CuFeSe2 CuLaS2 AgAlS2 AgAlSe2 AgAlTe2 AgGaS2 AgGaSe2 AgGaTe2 AglnS2(L.T.) AglnSe2 AglnTe2 AgFeS2 II IV V2 Compounds ZnSiP2 ZnGeP2 ZnSnP2 CdSiP2 CdGeP2

1587_Book.fm Page 27 Monday, September 1, 2003 7:17 PM

3.985 4.12 3.076 4.078 3.579 3.890

Chemical Engineering, Chemistry, and Materials Science

Other wurtzite structure compounds MnS 87.0 43.5 MnSe 133.9 66.95 SiC 40.1 20.1 MnTe 182.54 91.27 150.14 30.03 Al2S3 Al2Se3 290.84 58.17

CdSnP2 ZnSiAs2 ZnGeAs2 ZnSnAs2 CdSiAs2 CdGeAs2 CdSnAs2

243.03 242.20 287.80 333.90 290.34 334.83 380.93

73.26 60.55 71.95 83.48 72.58 83.71 95.23

5.900 5.61 5.672 5.8515 5.884 5.9427 6.0944

11.518 10.88 11.153 11.704 10.882 11.2172 11.9182

4.70 5.32 5.53

1311 1150 1048

5.60 5.72

938 880

5000 9200 6800 4550 6850 4700 3450

195

140

263 271

110 150

3-28

Substance

Table I. PHYSICO-CHEMICAL PROPERTIES OF SEMICONDUCTORS (LISTED BY CRYSTAL STRUCTURE) (continued) Lattice Coefficient of Average Parameters Microhardness, Thermal Linear Thermal Molecular Atomic (Å, Room Density Melting Point N/mm2 Specific Heat, Debye Expansion Conductivity Mass Mass Temp.) (g/cm3) (K) (M-Mohs Scale) J/kg·K (300 K) Temp. (K) [10–6 K–1 (300K)] [mW/cm·K (300K)]

48 40

§A5. Other Ternary Semiconductors with Tetrahedral Coordination

© 2004 by CRC Press LLC

251.36

41.89

537.98 295.88

89.66 49.31

3.684 5.290 5.93 5.317 5.327 5.589 5.958 5.436 5.687 6.048

6.004 10.156

6.19 6.14 10.957 16.76 11.256

436.56 582.51 341.98 482.66 628.61 525.21 571.31 671.13 717.23

72.76 97.09 57.00 80.44 104.77 87.54 95.22 111.86 119.54

349.85 393.79 581.37 440.64 628.22

40.73 49.22 72.67 55.08 78.53

7.44 6.43 5.570 5.38 5.654

212.64 301.65 345.97

35.44 50.28 57.66

5.25 5.375

5.215 5.485 5.935

3.81 3.63 5.47 4.45 4.46 5.57 5.92 5.02 5.94 6.51

23

1200

1210

4550

510

254

7.2

12

1030

3840 2890 2770 2510 1970

340

168

8.4

440 310

214 148

7.8 8.9

24 130 28 35 144

169

3.2 9.5

30.2 19

131

12.4

14.6

1110 960 680

4.37 5.61 4.90 6.0

4.318

1113 1015

8500 6150

429

8.21

37.6

CRC Handbook of Engineering Tables

I2 IV VI3 Compounds Cu2SiS3(H.T.) Cu2SiS3(L.T.) Cu2SiTe3 Cu2GeS3(H.T.) Cu2GeS3(L.T.) Cu2GeSe3 Cu2GeTe3 Cu2SnS3 CuSnSe3 Cu2SnTe3 Ag2GeSe3 Ag2SnSe3 Ag2GeTe3 Ag2SnTe3 I3 V VI4 Compounds Cu3PS4 Cu3AsS4 Cu3AsSe4 Cu3SbS4 Cu3SbSe4 I IV2 V3 Compounds CuSi2P3 CuGe2P3 AgGe2P3

1587_Book.fm Page 28 Monday, September 1, 2003 7:17 PM

Properties of Semiconductors (continued)

435.18 629.74 333.06 520.66 715.22 610.86 805.42 294.61 482.21 676.77 380.09 567.69 762.25 852.45 382.79 570.39 764.48 468.27 655.87 746.07 940.63

62.17 84.96 47.58 74.38 102.17 87.27 115.06 42.09 68.89 97.68 54.30 81.10 108.89 121.78 54.68 82.48 109.28 66.90 93.70 106.58 134.38

40.1

20.1

2163.19 2253.39 657.89

144.21 150.23 93.98

5.503 5.904 5.274 5.496 5.937 5.711 6.122 5.564 5.747 6.011 5.577 5.743 6.093 6.205 5.488 5.708 6.004 5.507 5.715 5.764 6.186

10.90 12.05 10.44 10.99 11.87 11.42 12.24 10.32 10.68 12.21 10.08 10.73 11.81 12.41 10.26 10.74 12.11 10.23 10.78 11.80 12.37

4.37 4.95 3.80 5.21 5.67 5.44 5.83 3.06 4.54 5.10 4.03 5.32 5.77 5.9 4.11 5.05 5.81 5.00 6.18 6.3 6.3

Chemical Engineering, Chemistry, and Materials Science

ZnAl2Se4 ZnAl2Te4(?) ZnGa2S4(?) ZnGa2Se4(?) ZnGa2Te4(?) Znln2Se4 Znln2Te4 CdAl2S4 CdAl2Se4 CdAl2Te4(?) CdGa2S4 CdGa2Se4 CdGa2Te4 Cdln2Te4 HgAl2S4 HgAl2Se4 HgAl2Te4(?) HgGa2S4 HgGa2Se4 Hgln2Se4 Hgln2Te4(?)

1250 1075

1060

1100 980

§A7. Other Adamantine Compounds aSiC Hg5Ga2Te8 Hg5ln2Te8 Cdln2Se4

3.0817 15.1183 6.235 6.328 a = c = 5.823

3.21

3070

Part B. Octahedral Semiconductors §B1. Halite Structure Semiconductors (Strukturbericht symbol B1, Space Group Fm3m-O5h )

© 2004 by CRC Press LLC

200.19 197.65 246.29 239.26 286.16 334.8

100.1 98.83 123.15 119.63 143.08 167.4

5.98 6.020 6.313 5.9362 6.1243 6.454

6.14 6.45 7.61 8.15 8.16

1133 1080 (max) 1390 1340 1180

91 23 17 23

3-29

GeTe SnSe SnTe Pbs PbSe PbTe

1587_Book.fm Page 29 Monday, September 1, 2003 7:17 PM

–

§A6. “Defect Chalcopyrite” Structure Compounds (Strukturbericht symbol E3, Space Group I 4-S24 )

Table I. PHYSICO-CHEMICAL PROPERTIES OF SEMICONDUCTORS (LISTED BY CRYSTAL STRUCTURE) (continued)

Substance

Molecular Mass

Average Atomic Mass

Lattice Parameters (Å, Room Temp.)

Density (g/cm3)

Melting Point (K)

Microhardness, N/mm2 Specific Heat, (M-Mohs Scale) J/kg·K (300 K)

Debye Temp. (K)

Coefficient of Thermal Linear Thermal Expansion Conductivity [10–6 K–1 (300K)] [mW/cm·K (300K)]

Selected Other Binary Halites BiSe 287.94 BiTe 336.58 EuSe 230.92 GdSe 236.21 NiD 60.71 CdO 128.41 SrS 119.68 Part C. Other Semiconductors

143.97 168.29 115.46 118.11 30.35 64.21 59.84

5.99 6.47 6.191 5.771 4.1684 4.6953 6.0199

7.98

880

6.6

2300 2400 2260 1700 3000

3.643

2.4

7

§C1. Antifluorite Structure Compounds (Fm3m–O5h ) 76.70 121.20 167.3 225.81

25.57 40.4 55.77 85.27

6.338 6.380 6.765 6.836

1.88 3.08 3.53 5.1

11.5 15.0 9.9 10.0

1375 1388 1051 823

92

5 §C2. Tetradymite Structure Compounds (R3m–D3d )

Sb2Te3 Bi2Se3 Bi2Te3

626.3 654.84 800.76

125.26 130.97 160.15

4.25 4.14 4.38

30.3 28.7 30.45

6.44 7.51 7.73

895 979 858

167 155

24 30

16

§C3. Skutterudite Structure Compounds (Im3–T5h ) CoP3 CoAs3 CoSb3 NiAs3 RhP3 RhAs3

© 2004 by CRC Press LLC

151.85 286.70 424.18 283.45 195.83 327.67

37.96 71.65 106.05 70.86 48.96 81.92

7.7073 8.2060 9.0385 8.330 7.9951 8.4427

6.73

>1270 1230 1123

307

50

6.43 >1470 >1270

100

CRC Handbook of Engineering Tables

Mg2Si Mg2Ge Mg2Sn Mg2Pb

1587_Book.fm Page 30 Monday, September 1, 2003 7:17 PM

3-30

Properties of Semiconductors (continued)

117.04 71.29 104.25 139.37

9.2322 8.0151 8.4673 9.2533

7.36 9.12 9.35

1170 >1470 >1470 1170

AgSbSe2 AgSbTe2 (or Ag19Sb29Te52) AgBiS2(H.T.) AgBiSe2(H.T.) AgBiTe2(H.T.) Cu2CdSnS4

387.54 484.82

96.88 121.2

5.786 6.078

6.60 7.12

380.97 474.77 572.05 486.43

95.24 118.69 143.01 60.80

5.648 5.82 6.155 5.586

10.83

10.81 78.96

4.91 4.36

12.6 4.95

2.34 4.81

2348 493

4.45

5.91

6.23

723

90 303

§C4. Selected Multinary Compounds 10.5 86, 0.3

910 830

§C5. Some Elemental Semiconductors b Se(gray) Te

127.6

9.5 (M) 350

1277 292.6

1370

196.5

8.3 (||C) 17.89 (^C) 74.09 16.8

600 (||C) 45.2 (^C) 13.1 (||C) 33.8 (^C) 19.7

Table II Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance

Heat of Formation Volume [kJ/mole Compressibility (300K)] (10–10m2/N)

Static Dielectric Constant

Atomic Magnetic Susceptibility (10–6 CGS)

Index of Refraction

Miniumum Room Temperature Energy Gap (eV)

Mobility (Room Temp.) (cm2/V·s) Electrons

Holes

Optical Transition

Remarks

Part A. Adamantine Semiconductors §Al. Diamond Structure Elements (Strukturbericht symbol A4, Space Group Fd 3m–O7h)

© 2004 by CRC Press LLC

714.4 324 291 267.5

18 0.306 0.768

5.7 11.8 16 24

–5.88 –3.9 –012

2.419 (589 nm) 3.49 (589 nm) 3.99 (589 nm) 2.75 (589 nm)

5.4 1.107 0.67 0.0; 0.8

1800 1900 3800 2500

1400 500 1820 2400

i* i i

3-31

C Si Ge a-Sn

1587_Book.fm Page 31 Tuesday, September 2, 2003 3:25 PM

468.16 285.14 416.98 557.47

Chemical Engineering, Chemistry, and Materials Science

RhSb3 IrP3 IrAs3 IrSb3

Table II Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance

Heat of Formation Volume [kJ/mole Compressibility (300K)] (10–10m2/N)

Static Dielectric Constant

Atomic Magnetic Susceptibility (10–6 CGS)

Index of Refraction

Miniumum Room Temperature Energy Gap (eV)

Mobility (Room Temp.) (cm2/V·s) Electrons

Optical Transition

Holes

Remarks

2 d

§A2. Sphalerite (Zinc Blende) Structure Compounds (Strukturbericht symbol B3 Space Group F 4 3m–T )

© 2004 by CRC Press LLC

481 481 439 486 389

0.26 0.26 0.27 0.41

7.9 7.9 6.5 12.4 10

1.93 2.12 2.346 2.253 2.22

3.17 2.91 2.95 2.50 2.22

4.17 3.61 1.45

477 422 376

8.9 9.2 10.4

–9.9

2.356 2.89 3.56

3.54 2.58 2.26

4000 30

d d d i d

20

i i d

180 540 340

5(400˚C) 28 100

d d d

Nantokite Marshite Bromirite Miersite

See A3 See also A3

See A3 See A3 339

7.2

2.50

1.44

2.85 247 242

2.10 (a) –0.06

815

4.6 ª2.1

1200

50

d

250 2000 25000

ª1.5 350

d s s

500

70

Metacinnabarite Tiemannite Coloradoite Borazone Ignites 470K

CRC Handbook of Engineering Tables

I VII Compounds CuF CuCl CuBr Cul AgBr Agl II VI Compounds BeS BeSe BeTe BePo ZnO ZnS ZnSe ZnTe ZnP Cds CdSe CdTe CdPo HgS HgSe HgTe III V Compounds BN BP(L.T.)

1587_Book.fm Page 32 Monday, September 1, 2003 7:17 PM

3-32

Properties of Semiconductors (continued)

0.571 0.110 0.771 0.457 0.735 0.549 0.442

10.9 11 11.1 13.2 15.7 12.4 14.6 17.7

–13.8 –16.2 –14.2 –22.8 –27.7 –32.9

3.2 3.2 3.30 3.8 3.1 3.5 3.96

80 1200 200–400 300 8800 4000 4600 33000 78000

420 550 150 400 1400 150 460 750

i i i i d d d d d

* i = indirect, d = direct, s = semimetal. Other sphalerite structure compounds MnS MnSe b-SiC 271 Ga2Te3 198 In2Te3(H.T.) MgGeP2 ZnSnP2 ZnSnAs2(H.T.) ZnSnSb2

See also §A3 See also §A3 2.697 –13.5 –13.6

2.3 1.35 1.04

4000 50 50 El–Td12 Same Same Same

2.1 ª0.7 0.4 §A3. Wurtzite (Zincite) Structure Compounds (Strukturbericht symbol B4, Space Group P 63 mc-C 46v )

© 2004 by CRC Press LLC

2.63

–350 –206 –163 8.45; 9.12

2.32

Iodargirite

3.2 3.67

180

2.42 1.74 1.50

350 900 650

40 50

d d

Greenockide Cadmoselite

3-33

I VII Compounds CuCl CuBr Cul Agl II VI Compounds BeO MgTe ZnO ZnS ZnTe CdS CdSe CdTe

1587_Book.fm Page 33 Monday, September 1, 2003 7:17 PM

627 585 635 535 493 560 477 447

ª1.5 2.45 2.16 1.60 2.24 1.35 0.67 1.27 0.36 0.163

Chemical Engineering, Chemistry, and Materials Science

BAs AlP AlAs AlSb GaP GaAs GaSb InP InAs InSb

Table II Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance

Heat of Formation Volume [kJ/mole Compressibility (300K)] (10–10m2/N)

III V Compounds BP(H.T.) AlN GaN lnN Other wurtzite structure compounds MnS MnSe SiC MnTe 426 Al2S3 Al2Se3 367

Static Dielectric Constant

Atomic Magnetic Susceptibility (10–6 CGS)

Index of Refraction

Miniumum Room Temperature Energy Gap (eV)

Mobility (Room Temp.) (cm2/V·s) Electrons

Holes

Optical Transition

Remarks

6.02 3.34 2.0

2.654 ª1.0 4.1 3.1 §A4. Chalcopyrite Structure Compounds (Strukturbericht symbol E11, Space Group I 4 2d-D 12 2d )

© 2004 by CRC Press LLC

0.106

0.106 0.141 0.227 0.141 0.187 0.278

2.5 1.1 0.88 2.38 0.96, 1.63 0.82, 1.0 1.2 0.86, 0.92 0.95 1.07 0.53 0.16

Chalcopyrite

CRC Handbook of Engineering Tables

I III VI2 Compounds CuAlS2 CuAlSe2 CuAlTe2 CuCaS2 CuGaSe2 CuGaTe2 CulnS2 CulnSe2 CulnTe2 CuTlS2 CuTlSe2(L.T.) CuFeS2 CuFeSe2 CuLaS2 AgAlS2

1587_Book.fm Page 34 Monday, September 1, 2003 7:17 PM

3-34

Properties of Semiconductors (continued)

0.150 0.182 0.280 0.185 0.238 0.338

312 293 275 0.103 289 270 290 271 252

–14.4 –18.4 0.143

266 247

13.7

–23.4 –21.5

2.3 2.2 1.45 2.2 1.8 1.5 1.7 0.85 0.65 1.6 0.53 0.26

1000

1000

50

70 22000

300

Disorders at 910K

25 250

Disorders at 903

§A5. Other Ternary Semiconductors with Tetrahedral Coordination

© 2004 by CRC Press LLC

–18.7 211.5 190.2

–21.3 –23.4 –18.2 –21.0 –28.4 –29.6 –29.5 –31.4 –31.10

0.94

360 238

0.91 0.66

405 870

0.91 (77K) 0.81 0.25 0.08

Wurtzite Tetragonal Cubic Cubic Tetragonal Same Same Cubic Cubic Cubic

3-35

IV VI3 Compounds Cu2SiS3(H.T.) Cu2SiS3(L.T.) Cu2SiTe3 Cu2GeS3(H.T.) Cu2GeS3(L.T.) Cu2GeSe3 Cu2GeTe3 Cu2SnS3 CuSnSe3 Cu2SnTe3 Ag2GeSe3 Ag2SnSe3 Ag2GeTe3 Ag2SnTe3

1587_Book.fm Page 35 Monday, September 1, 2003 7:17 PM

0.7 0.56 1.66 1.1 1.9 1.18 0.96, 0.52

Chemical Engineering, Chemistry, and Materials Science

AgAlSe2 AgAlTe2 AgGaS2 AgGaSe2 AgGaTe2 AglnS2(L.T.) AglnSe2 AglnTe2 AgFeS2 V V2 Compounds ZnSiP2 ZnGeP2 ZnSnP2 CdSiP2 CdGeP2 CdSnP2 ZnSiAs2 ZnGeAs2 ZnSnAs2 CdSiAs2 CdGeAs2 CdSnAs2

Table II Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance V VI4 Compounds Cu3PS4 Cu3AsS4 Cu3AsSe4 Cu3SbS4 Cu3SbSe4 V2 V3 Compounds CuSi2P3 CuGe2P3 AgGe2P3

Heat of Formation Volume [kJ/mole Compressibility (300K)] (10–10m2/N)

Static Dielectric Constant

Atomic Magnetic Susceptibility (10–6 CGS)

Index of Refraction

Miniumum Room Temperature Energy Gap (eV)

Mobility (Room Temp.) (cm2/V·s) Electrons

Holes

Optical Transition

Remarks Enargite

269.6 161.3

–15.8 –13.1 –8.3 –20.5

127.1

0.12

1.24 0.88 0.74 0.31

Famatinite Famatinite

El El

0.90

§A6. “Defect Chalcopyrite” Structure Compounds (Strukturbericht symbol E3, Space Group I 4-S42)

© 2004 by CRC Press LLC

206 198

ª3.4 ª2.2 1.35 1.82 1.2

256 216

3.44 2.43

195

(1.26 or 0.9)

35

60 33 4000

CRC Handbook of Engineering Tables

ZnAl2Se4 ZnAl2Te4(?) ZnGa2S4(?) ZnGa2Se4(?) ZnGa2Te4(?) Znln2Se4 Znln2Te4 CdAl2S4 CdAl2Se4 CdAl2Te4(?) CdGa2S4 CdGa2Se4 CdGa2Te4 Cdln2Te4 HgAl2S4 HgAl2Se4

1587_Book.fm Page 36 Monday, September 1, 2003 7:17 PM

3-36

Properties of Semiconductors (continued)

400 290 200

§A7. Other Adamantine Compounds aSiC Hg5Ga2Te8 Hg5ln2Te8 Cdln2Se4

10.2

–6.4

2.67

2.86

400

0.7 1.55

2000

6H structure B3 with superlattice B3 with superlattice

Part B. Octahedral Semiconductors §B1. Halite Structure Semiconductors (Strukturbericht symbol B1, Space Group Fm3m-O5h) GeTe SnSe SnTe PbS PbSe PbTe

435 393 393

Selected Other Binary Halites BiSe BiTe EuSe GdSe NiD CdO 531 SrSW

161 280 360

0.5 0.37 0.26 0.25

600 1000 1600

600 900 600

Altaite

0.4 1.8 2.0 or 3.7 2.5 4.1

4 100

Part C. Other Semiconductors §C1. Antifluorite Structure Compounds (Fm3m-O5h )

© 2004 by CRC Press LLC

79.08 76.57 52.72

0.77 0.74 0.36 0.1

405 520 320

70 110 260

3-37

Mg2Si Mg2Ge Mg2Sn Mg2Pb

1587_Book.fm Page 37 Monday, September 1, 2003 7:17 PM

2.84 1.95 0.6 0.86

249 204 196 188

Chemical Engineering, Chemistry, and Materials Science

HgAl2Te4(?) HgGa2S4 HgGa2Se4 Hgln2Se4 Hgln2Te4(?)

Table II Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance

Heat of Formation Volume [kJ/mole Compressibility (300K)] (10–10m2/N)

Static Dielectric Constant

Atomic Magnetic Susceptibility (10–6 CGS)

Index of Refraction

Miniumum Room Temperature Energy Gap (eV)

Mobility (Room Temp.) (cm2/V·s) Electrons

Holes

Optical Transition

Remarks

5 3d

§C2. Tetradymite Structure Compounds (R3m-D ) Sb2Te3 Bi2Se3 Bi2Te3

0.3 0.35 0.21

360 600 1140

680

R3m (166)

§C3. Skutterudite Structure Compounds (Im3-T 5h ) 0.43 0.69 0.63

CoP3 CoAs3 CoSb3 RhP3 RhAs3 RhSb3 IrSb3

70

0.85 0.80 1.18

–4000 –3000 700 –3000 –7000 1500

AgSbSe2 AgSbTe2 (or Ag19Sb29Te52) AgBiS2(H.T.) AgBiSe2(H.T.) AgBiTe2(H.T.) Cu2CdSnS4

0.58 0.7, 0.27

1.16

<2

§C5. Some Elemental Semiconductors B Se(gray) Te

© 2004 by CRC Press LLC

397.1 6.6 (0.1 GHz)

–6.7 –22.1

3.4 2.5

1.55 1.5

10

–39.5

3.3

0.33

1700

5 1200

P3121(152) Same

CRC Handbook of Engineering Tables

§C4. Selected Multinary Compounds

1587_Book.fm Page 38 Tuesday, September 2, 2003 3:25 PM

3-38

Properties of Semiconductors (continued)

Substance Si Ge aSn Te

R.T. 1.107 0.67 0.08 0.33

0K

dEg/dT ¥ 104 cV/˚C

1.153 0.744 0.094

–2.3 –3.7 –0.5

dEg/dP ¥ 106 cV·cm2/kg –2.0 +7.3

Density of States Electron Effective Mass mda (mo)

Electron Mobility and Temperature Dependence mn cm2/V·s

1.1 0.55 0.02 0.08

1900 3800 2500 1100

–x

Density of States Hole Effective Mass mdp (mn)

2.6 1.66 1.65

0.56 0.3 0.3 0.19

1.5 1.5 1.0 2.0 2.0 1.2 1.6

0.4 0.5 0.5 0.23

Role Mobility and Temperature Dependence mp cm2/V·s 500 1820 2400 560

–x 2.3 2.33 2.0

III-V Compounds AlAs AlSb GaP GaAs GaSb InP InAs InSb

2.2 1.6 2.24 1.35 0.67 1.27 0.36 0.165

2.3 1.7 2.40 1.53 0.78 1.41 0.43 0.23

–3.5 –5.4 –5.0 –3.5 –4.6 2.8 –2.8

–1.6 –1.17 +9.4 +12 +4.6 +8 +15

0.09 0.35 0.068 0.050 0.067 0.022 0.014

1200 200 300 9000 5000 5000 33,000 78,000

0.41 0.4

420 500 150 500 1400 200 460 750

1.8 1.5 2.1 0.9 2.4 2.3 2.1

II-VI Compounds Zn() ZnS ZnSe ZnTe CdO CdS CdSe GdTe HgSe HgTe

3.2 3.54 2.58 2.26 2.5 ± .1 2.4 1.74 1.44 0.30 0.15

PbS PbSe PbTe

0.37 0.26 0.25

2.80

–0.5 –5.3 –7.2

1.85 1.56

–6 –5 –4.6 –4.1

+0.6 +5.7 +6 +6 +3.3 +8

–1

0.38

0.1 0.165 0.13 0.14 0.030 0.017

180 180 540 340 120 400 650 1200 20,000 25,000

1.5 5(400˚C) 28 100

1.0

0.8 0.6 0.35

50

0.5

350

0.1 0.34 0.14

1000 1500 750

2.0

Halite Structure Compounds +4 +4 +4

–7

0.16 0.3 0.21

800 1500 1600

2.2 2.2 2.2

3-39

© 2004 by CRC Press LLC

0.28 0.16 0.19

1587_Book.fm Page 39 Monday, September 1, 2003 7:17 PM

Minimum Energy Gap (eV)

Chemical Engineering, Chemistry, and Materials Science

Table III Semiconducting Properties of Selected Materials

Table III Semiconducting Properties of Selected Materials Minimum Energy Gap (eV) Substance

R.T.

0K

dEg/dT ¥ 104 cV/˚C

dEg/dP ¥ 106 cV·cm2/kg

Density of States Electron Effective Mass mda (mo)

Electron Mobility and Temperature Dependence mn cm2/V·s

–x

Density of States Hole Effective Mass mdp (mn)

Role Mobility and Temperature Dependence mp cm2/V·s

–x

Others 0.50 0.45 1.3 0.27 0.13

0.21 0.93 0.55 2.05 1.66 1.8 0.57 0.23 1.1 1.1 1.0 0.5

© 2004 by CRC Press LLC

0.56 0.57

0.77 0.74 0.33 0.32

1.80

–5.4

–0.05 –6.4 –9 –3.5

0.046

10 300 200 600 1200 400 280 320 20 10 100,000

0.3 0.05

14 900 30 25,000

0.58 0.46 0.37

1.68 2.5 2

1.07

1.1 0.88

2000 1100 675 510 70 110 260 82 10

1.5 1.5

1.95

20

3.8 –3.6 –3.9

1.55 1.2

0.15 0.15

–5 0.6

20

1.5

50 5 11,000 78

1.1

1.7

–4.8 0.7

CRC Handbook of Engineering Tables

ZnSb CdSb Bi2S3 Bi2Se3 Bi2Te3 Mg2Si Mg2Ge Mg2Sn Mg3Sb2 Zn3As2 Cd3As2 GaSe GaTe InSe TlSe CdSnAs2 Ga2Te2 a-ln2Te2 b-ln2Te2 Hg5ln2Te8 SnO2

1587_Book.fm Page 40 Monday, September 1, 2003 7:17 PM

3-40

Properties of Semiconductors (continued)

Band Curvature Effective Mass (Expressed as Fraction of Free Electron Mass)

Substance

Heavy Holes

Light Holes

“Split-Off ” Band Boles

Energy Separation of “Split-Off ” Band (eV)

Measured (Light) Hole Mobility cm2/V·s

Semiconductors with Valence Band Maximum at the Center of the Brillouin Zone (“F”) Si Ge Sn AlAs AlSb GaP GaAs GaSb InP InAs InSb CdTe HgTe

0.52 0.34 0.3

0.16 0.043

0.25 0.08

0.4 0.8 0.23

0.12 0.06

0.20

0.41 0.4 0.35 0.5

0.025 0.015

0.083

0.044 0.3

500 1820 2400

0.7 0.13 0.34 0.7 0.21 0.43 0.85

550 100 400 1400 150 460 750 50 350

Semiconductors with Multiple Band Maxima Substance PbSe PbTe Bi2Te3

Number of Equivalent Valleys and Direction 4 “L” [111] 4 “L” [111] 6

Band Curvature Effective Masses Longitudinal mL 0.095 0.27 0.207

Transverse mT 0.047 0.02 ~0.045

Anistrophy K = mL/mT 2.0 10 4.5

Measured (Light) Hole Mobility cm2/V·s 1500 750 515

3-41

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1587_Book.fm Page 41 Friday, September 26, 2003 12:10 PM

Part A. Data on Valence Bands of Semiconductors (Room Temperatures)

Chemical Engineering, Chemistry, and Materials Science

Table IV Band Properties of Semiconductors

Table IV Band Properties of Semiconductors Part B. Data on Conduction Bands of Semiconductors (Room temperature Data) Single Valley Semiconductors Substance Energy Gap (eV) Effective Mass (mo) Mobility (cm2/V·s) GaAs

1.35

0.067

8500

InP InAs InSb CdTe

1.27 0.36 0.165 1.44

0.067 0.022 0.014 0.11

5000 33,000 78,000 1000

Comments 3(or 6?) equivalent [100] valleys 0.36 eV above this maximum with a mobility of ~50 3(or 6?) equivalent [100] valleys 0.4 eV above this minimum. Equivalent valleys ~1.0 eV above this minimum. 4(or 8?) equivalent [111] valleys 0.51 eV above this minimum.

Multivalley Semiconductors Energy Gap

Number of Equivalent Valleys and Direction

Si Ge GaSb PbSe PbTe Bi2Te2

1.107 0.6 0.67 0.26 0.25 0.13

6 in [100] “D” 4 in [111] at “L” as Ge (?) 4 in [111] at “L” 4 in [111] at “L” 6

© 2004 by CRC Press LLC

Band Curvature Effective Mass Longitudinal mL

Transverse mT

0.00 1.588 ~1.0 0.085 0.21

0.192 0.0815 ~0.2 0.05 0.029

Anisotropy K = mL/mT 4.7 19.5 ~5 1.7 5.5 ~0.05

Comments

CRC Handbook of Engineering Tables

Substance

1587_Book.fm Page 42 Monday, September 1, 2003 7:17 PM

3-42

Properties of Semiconductors (continued)

Diamond (C) Sulfides Argentite, Ag2S Bismuthinite, Bi2S3 Bornite, Fe2S3 · nCu3S Chalcocite, Cu2S Chalcopyrite, Fe2S1 · Cu1S Covellite, CuS Galena, PbS Haverite, MnS2 Marcasite, FeS2 Metacinnabarite, 4HgS Millerite, NiS Molybdenite, MoS2 Pentlandite, (Fe, Ni)4S4 Pyrrhotite, Fe7S4 Pyrite, FeS2 Sphalerite, ZnS Antimony-sulfur compounds Berthierite, FeSb2S4 Boulangerite, Pb5Sb3S11 Cylindrite, Pb3Sn4Sb2S14 Franckeite, Pb5Sn1Sb2S14 Hauchecornite, Ni4(Bi, Sb)2S4 Jamesonite, Pb4FeSb6S14 Tetrahedrite, Cu3SbS3 Arsenic-sulfur compounds Arsenopyrite, FeAsS Cobaltite, CoAsS Enargite, Cu3AsS4

2.7 1.5 to 2.0 ¥ 10–3 3 to 570 1.6 to 6000 ¥ 10–4 80 to 100 ¥ 10–6 150 to 9000 ¥ 10–6 0.30 to 83 ¥ 10–6 6.8 ¥ 10–6 to 9.0 ¥ 10–2 10 to 20 1 to 150 ¥ 10–2 2 ¥ 10–6 to 1 ¥ 10–3 2 to 4 ¥ 10–7 0.12 to 7.5 1 to 11 ¥ 10–6 2 to 160 ¥ 10–6 1.2 to 600 ¥ 10–3 2.7 ¥ 10–2 to 1.2 ¥ 104 0.0083 to 2.0 2 ¥ 103 to 4 ¥ 104 2.5 to 60 1.2 to 4 1 to 83 ¥ 10–6 0.020 to 0.15 0.30 to 30,000 20 to 300 ¥ 10–6 6.5 to 130 ¥ 10–3 0.2 to 40 ¥ 10–3

Mineral Gersdorfite, NiAsS Glaucodote, (Co, Fe)AsS Antimonide Dyscrasite, Ag3Sb Arsenides Allemonite, SbAs1 Lollingite, FeAs2 Nicollite, NiAs Skutterudite, CoAs3 Smaltite, CoAs2 Tellurides Altaite, PbTe Calavarite, AuTe2 Coloradoite, HgTe Hessite, Ag2Te Nagyagite, Pb6Au(S,Te)14 Sylvanite, AgAuTe4 Oxides Braunite, Mn2O1 Cassiterite, SnO3 Cuprite, Cu2O Hollandite, (Ba, Na, K) Mn8O16 Ilmenite, FeTiO1 Magnetite, Fe1O4 Manganite, MnO · OH Melaconite, CuO Psilomelane, KMnO · MnO1 · nH2O Pyrolusite, MnO2 Rutile, TiO2 Uraninite, UO

r (ohm · m) 1 to 160 ¥ 10–6 5 to 100 ¥ 10–6 0.12 to 1.2 ¥ 10–6 70 to 60,000 2 to 270 ¥ 10–6 0.1 to 2 ¥ 10–6 1 to 400 ¥ 10–6 1 to 12 ¥ 10–6 20 to 200 ¥ 10–6 6 to 12 ¥ 10–6 4 to 100 ¥ 10–6 4 to 100 ¥ 10–6 20 to 80 ¥ 10–6 4 to 20 ¥ 10–6 0.16 to 1.0 4.5 ¥ 10–4 to 10,000 10 to 50 2 to 100 ¥ 10–3 0.001 to 4 52 ¥ 10–6 0.018 to 0.5 6000 0.04 to 6000 0.007 to 30 29 to 910 1.5 to 200

3-43

© 2004 by CRC Press LLC

1587_Book.fm Page 43 Tuesday, September 2, 2003 3:25 PM

r (ohm · m)

Mineral

Chemical Engineering, Chemistry, and Materials Science

Table V Resistivity of Semiconducting Minerals

© 2004 by CRC Press LLC

1587_Book.fm Page 44 Tuesday, September 2, 2003 3:25 PM

From Berger, L.I. and Pamplin, B.R., Properties of semiconductors, in CRC Handbook of Chemistry and Physics, 83rd ed., Lide, D., Ed., CRC Press, Boca Raton, FL, 2002, pp. 12-97 to 12-107. Originally from Carmichael, R.S., ed., Handbook of Physical Properties of Rocks, Vol. I, CRC Press, 1982.

CRC Handbook of Engineering Tables

References 1. Beer, A.C., Galvanomagnetic Effects in Semiconductors, Academic Press, 1963. 2. Goryunova, N.A., The Chemistry of Diamond-Like Semiconductors, The MIT Press, 1965. 3. Abrikosov, N. Kh., Bankina, V.F., Poretskaya, L.E., Shelimova, L.E., and Skudnova, E.V., Semiconducting II-VI, IV-VI, and VVI Compounds, Plenum Press, 1969. 4. Berger, L.I. and Prochukhan, V.D., Ternary Diamond-Like Semiconductors, Cons. Bureau/Plenum Press, 1969. 5. Shay, J.L. and Wernick, J.H., Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties, and Applications, Pergammon Press, 1975. 6. Bergman, R., Thermal Conductivity in Solids, Clarendon, Oxford, 1976. 7. Handbook of Semiconductors, Vol. 1, Moss, T.S. and Paul, W., Eds., Band Theory and Transport Properties; Vol. 2, Moss, T.S. and Balkanski, M., Eds., Optical Properties of Solids; Vol. 3, Moss, T.S. and Keller, S.P., Eds., Materials Properties and Preparation, North Holland Publ. Co., 1980. 8. Böer, K.W., Survey of Semiconductor Physics, Van Nostrand Reinhold, 1990. 9. Rowe, D.M., Ed., CRC Handbook of Thermoelectrics, CRC Press, Boca Raton, FL, 1995. 10. Berger, L.I., Semiconductor Materials, CRC Press, Boca Raton, FL, 1997. 11. Glazov, V.M., Chizhevskaya, S.N., and Glagoleva, N.N., Liquid Semiconductors, Plenum Press, New York, 1969. 12. Phillips, J.C., Bonds and Bands in Semiconductors, Academic Press, New York, 1973. 13. Harrison, W.A., Electronic Structure and the Properties of Solids, Freeman Publ. House, San Francisco, 1980. 14. Balkanski, M., Ed., Optical Properties of Solids, North-Holland, Amsterdam, 1980. 15. Landolt-Börnstein. Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Hellwege, K.-H. and Madelung, O., Eds., Volumes 17 and 22, Springer Verlag, Berlin, 1984 (and further). 16. Shklovskii, B.L. and Efros, A.L., Electronic Processes in Doped Semiconductors, Springer Verlag, Berlin, 1984. 17. Cohen, M.L. and Chelikowsky, J.R., Electronic Structure and Optical Properties of Semiconductors, Springer Verlag, New York, 1988. 18. Glass, J.T., Messier, R.F., and Fujimori, N., Eds., Diamond, Silicon Carbide, and Related Wide Bandgap Semiconductors, MRS Symposia Proc. 1652, Mater. Res. Soc., Pittsburgh, 1990. 19. Palik, E., Ed., Handbook of Optical Constants of Solids II, Academic Press, New York, 1991. 20. Reed, M., Ed., Semiconductors and Semimetals, Volume 35, Academic Press, Boston, 1992. 21. Haug, H. and Koch, S.W., Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd Edition, World Scientific, Singapore, 1993. 22. Lockwood, D.J., Ed., Proc. 22nd Intl. Conf. on the Physics of Semiconductors, Vancouver, 1994, World Scientific, Singapore, 1994. 23. Morelli, D.T., Caillat, T., Fleurial, J.-P., Borschchevsky, A., Vandersande, J., Chen, B., and Uher, C., Phys. Rev., B51, 9622, 1995. 24. Caillat, T., Borshchevsky, A., and Fleurial, J.-P., J. Appl. Phys., 80, 4442, 1996. 25. Fleurial, J.-P.,Caillat, T., and Borshchevsky, A., Proc. XVI Intl. Conf. Thermoelectrics, Dresden, Germany, August 26–29, 1997 (in print). 26. Borshchevsky, A. et al., U.S. Patents 5,610,366 (March 1977) and 5,831,286 (March 1998).

3-44

Properties of Semiconductors (continued)

1587_Book.fm Page 45 Monday, September 1, 2003 7:17 PM

3-45

Chemical Engineering, Chemistry, and Materials Science

Solid State Lasers Solid state lasers include lasers based on paramagnetic ions, organic dye molecules, and color centers in crystalline or amorphous hosts. Semiconductor lasers are included in this section because they are a solid-state device, although the nature of the active center—recombination of electrons and holes—is different from the dopants or defect centers used in other lasers in this category. Conjugated polymer lasers, solid-state excimer lasers, and fiber raman, Brillouin, and soliton lasers are also covered in this section. Reported ranges of output wavelengths for the various types of solid state lasers are shown in the figure. The differences in the ranges of spectral coverage arise in part from the dependence on host properties, in particular the range of transparency and the rate of nonradiative decay due to multiphonon processes. 0.17 mm

7.2 mm Paramagnetic ions (crystal) 0.38 mm

4.0 mm Paramagnetic ions (glass)

0.38 mm

0.87 mm Organic dyes

0.36 mm

5.0 mm Color centers

0.33 mm

0.1

360 mm

Semiconductors

1.0

10

100

Wavelength (mm) Reported ranges of output wavelengths for various types of solid state lasers. Further Reading Cheo, P.K., Ed., Handbook of Solid-State Lasers, Marcel Dekker Inc., New York (1989). Koechner, W., Solid-State Laser Engineering (fourth edition), Springer-Verlag, Berlin (1996). Powell, R.C., Physics of Solid State Laser Materials, Springer-Verlag, Berlin (1997). Powell, R.C., Ed., Selected Papers on Solid State Lasers, SPIE Milestone Series, Vol. MS31, SPIE Optical Engineering Press, Bellingham, WA (1991). From Weber, M.J., Solid state lasers, in Handbook of Lasers, CRC Press, Boca Raton, FL, 2001.

© 2004 by CRC Press LLC

1587_Book.fm Page 46 Monday, September 1, 2003 7:17 PM

3-46

CRC Handbook of Engineering Tables

III-V Material Systems with Important Optoelectronic Applications Material System

Substrate

AlGaAs

GaAs

Lattice-Matched Members GaAs

Important Strained Members Ga1-xInxAs 0 £ x £ 0.25

AlxGa1-xAs 0£x£1 AlAs GaInAsP/InP

InP

AlGaInAs/InP

InP

AlGaInP

GaAs

AlGaAsSb/ GaInAsSb/ GaSb

GaSb

GaAsP

GaAs or GaP

Ga0.47In0.53As GaxIn1-xAsyP1-y x = 0.47 y; 0 £ y £ 1 InP Ga0.47In0.53As (AlxGa1-x)0.47In0.53As 0£x£1 Al0.48In0.52As GaAs Ga0.5In0.5P (AlxGa1-x)0.5In0.5P 0£x£1 Al0.5In0.5P GaSb AlxGa1-xAsysb1-y x = 12 y; 0 £ x £ 1 Ga1-xInxAs1-ySby x = 1.1 y; 0 £ x £ 1 GaAs (on GaAs substrates); GaP (on GaP substrates)

Ga1-xInxAs 0.4 £ x £ 0.6 InAsxP1-x 0 £ x £ 0.2 Ga1-xInxAs 0.4 £ x £ 0.6

Ga1-xInxAs 0 £ x £ 0.25 Ga1-xInxP 0.4 £ x £ 0.6

Main Optoelectronic Applications Emitters and modulators: 0.75 mm £ l £ 1.1 mm, Detectors: 0.4 mm £ l £ 1.1 mm Saturable absorbers: l ~ 0.8–0.9 mm Optoelectronic devices at l = 1.3 mm and 1.55 mm Optoelectronic devices at l = 1.3 mm and 1.55 mm

Red emitters

Emitters and detectors: l ~ 2-3 mm

GaAsP

Visible LED’s

From Wicks, G.W., III-V Semiconductor materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 6.

© 2004 by CRC Press LLC

1587_Book.fm Page 47 Tuesday, September 2, 2003 3:25 PM

3-47

Chemical Engineering, Chemistry, and Materials Science

5.0 MgS

Energy Gap (eV)

4.0

MgSe

3.0 ZnS AlP 2.0

MnTe

MnSe FeSe ZnTe

ZnSe

GaP

AlAs

CdSe AlSb

InP Si

CdTe

GaAs

1.0

GaSb

Ge

InSb InAs

0.0

HgSe -1.0 5.4

5.6

HgTe

5.8 6.0 6.2 Lattice Constant (Å)

6.4

6.6

Energy Gap and lattice parameters for cubic group IV, III-V and II-VI semiconductors. (From Luo, H. and Petrou, A., Optical properties and optoelectronic applications of II-VI semiconductor heterostructures, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 26.)

Important Parameters of Semiconductors of Interest for Conventional Electronics and Emerging High Temperature Electronics Property

Si

GaAs

GaP

3C SiC (6H SiC)

Bandgap (eV) at 300K Maximum operating temperature (K)

1.1 600?

1.4 760?

2.3 1250?

2.2 (2.9) 1200 (1580) sublimes

Melting point (K) Physical stability Electron mobility R.T., cm2/V-s Hole mobility R.T., cm2/V-s Breakdown voltage Eb, 106/V/cm Thermal conductivity K, W/cm-C Sat. elec. drift vel. v(sat), 107 cm/s Dielectric const, K

1690 Good 1400 600 0.3 1.5 1 11.8

1510 Fair 8500 400 0.4 0.5 2 12.8

1740 Fair 350 100 — 0.8 — 11.1

>2100 Excellent 1000 (600) 40 4 5 2 9.7

Diamond

GaN

5.5 1400(?) phase change

3.39

Very good 2200 1600 10 20 2.7 3.5

Good 900 50? 5? 1.3 2.7 9

From Morkoc, H., GaN and silicon carbide as optoelectronic materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 52.

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1587_Book.fm Page 48 Tuesday, September 2, 2003 3:25 PM

3-48

CRC Handbook of Engineering Tables

Properties of GaN(a), AIN(b), and InN(c) Wurtzite Polytype Bandgap energy Temperature coefficient

Eg (300K) = 3.39 eV dEg dT

Pressure coefficient Lattice constants Thermal expansion Thermal conductivity Index of refraction Dielectric constants Zincblende Polytype Bandgap energy Lattice constant Index of refraction Bandgap energy Lattice constants Thermal expansion Thermal conductivity Index of refraction Dielectric constants Zincblende Polytype Bandgap energy Lattice constant Bandgap energy Temperature coefficient Lattice constants Index of refraction Dielectric constants Zincblende Polytype Bandgap energy Lattice constant

Eg (1.6K) = 3.50 eV

= 6.0 ¥ 10 -4 eV K

dEg

= 4.2 ¥ 10 -3 eV kbar dP a = 3.189 ª Å Da = 5.59 ¥ 10 -6 K a k = 1.3 W/cmK n(1 eV) = 2.33 Œr ª 9 Eg (300K) = 3.2–3.3 eV a = 4.52 Å n(3 eV) = 2.5 Eg (300K) = 6.2 eV a = 3.112 Å, c = 4.982 Å Da = 4.2 ¥ 10 -6 K a k = 2\W/cmK n(3eV) = 2.15 ± 0.05 Œr ª 8.5 ± 0.2

Dc = 3.17 ¥ 10 -6 K c n(3.38 eV) = 2.67 Œ• = 5.35

Eg (5K) = 6.28 eV Dc = 5.3 ¥ 10 -6 K c

Œ• = 4.68–4.84

Eg (300K) = 5.11 eV, theory a = 4.38 Å Eg (300K) = 1.89 eV dEg

= 1.8 ¥ 10 -4 eV K dT a = 3.5438 Å n = 2.80–3.05 Œr ª

c = 5.760 Å

Eg (300K) = 2.2 eV, theory a = 4.98 Å

From Morkoc, H., GaN and silicon carbide as optoelectronic materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 65.

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1587_Book.fm Page 49 Monday, September 1, 2003 7:17 PM

3-49

Chemical Engineering, Chemistry, and Materials Science

List of Ferroelectric Materials and Their Crystal Growth Methods Family Perovskite type

Lithium niobate family Tungsten-bronzetype

KDP family

TGS type

Ferroelectric Material

Abbrev.

Growth Method

Barium titanate

BaTiO3

—

Potassium niobate

KNbO3

—

Potassium tantalate Potassium tantalate niobate Lead Ianthanum zirconate titanate (in the form of ceramics) Lithium niobate Lithium tantalate Barium strontium niobate Barium sodium niobate Potassium lithium niobate Potassium sodium strontium niobate Potassium dihydrogen phosphate Potassium dihydrogen arsenate Rubidium dihydrogen phosphate Triglycine sulphate

KTaO3 KTa1-xNbxO3

— KTN

Pb1-x(ZryTi1-y)1-0.25x B V0.25x O3

PLZT

LiNbO3 LiTaO3 Ba5xSr5(1-x)Nb10O30

— — SBN

Remeika method Top seed pulling method Spontaneous nucleation and slow cooling Top seed solution growth Kyropoulos pulling The same as KNbO3 Kyropoulos technique Top seed solution growth Chemical coprecipitation of powder and subsequent hotpressing in oxygen environment Czochralski’s technique Czochralski’s technique Czochralski’s method

Ba5xNa5(1-x)Nb10O30 K3Li2Nb5O15

BNN KLN

Czochralski’s method Kyropoulos method

(KxNa1-x)0.4(SryBa1-y)0.8 Nb2O6 KH2PO4

KNSBN

Czochralski’s technique

KDP

KH2AsO4

KDA

Water solution temperature reduction method The same as KDP

RbH2PO4

RDP

The same as KDP

(NH2CH2COOH)3 · H2SO4 (NH2CH2COOH)3 · H2SeO4 KTiOPO4

TGS

Temperature reduction method

TGSe

The same as TGS

KTP

Top seed flux growth

Bi4Ti3O12 b-Gd2(MoO)3 5PbO · 3GeO2, or Pb5Ge3O11

— GMO —

Flux-growth method Pulling from melt Czochralski’s technique

Triglycine selenate KTP family

Chemical Formula

Bismuth titanate Rare earth molybdate Lead germanium oxide

Potassium titanyl phosphate Bismuth titanate Gadolinium molybdate Lead germanium oxide

Antimony sulphoiodide

Antimony sulphoiodide

SbSI

Bridgman’s technique Vapor phase growth

From Li, C.-Y. and Xu, Y., Ferroelectric materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 93. Originally from Xu, Y., Ferroelectric Materials and Their Applications, Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1991. With permission.

© 2004 by CRC Press LLC

1587_Book.fm Page 50 Tuesday, September 2, 2003 3:25 PM

3-50

CRC Handbook of Engineering Tables

General Physical Properties of Ferroelectric Materials

Chemical Formula

Point Group*

BaTiO3 KNbO3 KTaO3 KTa1-xNbxO3 Pb1-xLax(ZryTi1-y)1-.0.25x B V0.25x O3 LiNbO3 LiTaO3 Ba0.4Sr0.6Nb2O6 Ba2NaNb5O15 K3Li2Nb5O15 (KxNa1-x)0.4 (SryBa1-y)0.8Nb2O6 KH2PO4(KDP)

m3m Æ 4mm Æ mm2 Æ 3m m3m Æ 4mm Æ mm2 Æ 3m m3m Æ 4mm Æ mm2 Æ 3m m3m Æ 4mm Æ mm2 Æ 3m

Phase Transition Temperature (˚C) 120, 5, –90 435, 225, –10

26 30

Density (g/cm3) 6.02

Melting Point (˚C) 1618 1050

7.80 3m Æ 3m 3m Æ 3m (4/m)mm Æ 4mm Æ m (4/m)mm Æ 4mm Æ mm2 (4/m)mm Æ 4mm (4/m)mm Æ 4mm

1210 665 75, –213 560, 300 430

42m Æ mm2

KH2AsO4 RbH2PO4 (NH2CH2COOH)3 · H2SO4 (TGS) (NH2CH2COOH)3 · H2SeO4 KTiOPO4 Bi4Ti3O12 b-Gd2(MoO)3 5PbO · 3GeO2, or Pb5Ge3O11 SbSI *

Spontaneous Polarization (mC/cm2)

71 50 32 40 ~40 ~30

4.64 7.45 ~5.4 5.40

–150

–4.8

2.34

42m Æ mm2 42m Æ mm2 2/m Æ 2

–176 –126 49

2.8

1.69

2/m Æ 2

26

mmm Æ mm2 (4/m)mm Æ m

943 675

42m Æ mm2 6Æ3 mmm Æ mm2

1240 1650 ~1480 ~1450 1250

5.16

159 177

~17 50, a-axis 4, c-axis 0.17 4.8

7.33

22

25 (0˚C)

5.25

Decomposes at 180˚C

6.1 1175 738

Point groups in bold are point groups at room temperature. From Li, C.-Y. and Xu, Y., Ferroelectric materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 94. Originally from Xu, Y., Ferroelectric Materials and Their Applications, Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1991. With permission.

© 2004 by CRC Press LLC

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© 2004 by CRC Press LLC

3-51

Applications of the ferroelectric thin films. (From Li, C.-Y. and Xu, Y., Ferroelectric materials, in Handbook of Photonics, Gupta, M.C., Ed., CRC Press, Boca Raton, FL, 1997, p. 100.)

1587_Book.fm Page 51 Monday, September 1, 2003 7:17 PM

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Chemical Engineering, Chemistry, and Materials Science

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1587_Book.fm Page 52 Tuesday, September 2, 2003 3:25 PM

3-52

CRC Handbook of Engineering Tables

The Principal Photometric Units Quantity Luminous flux Intensity Luminance Illuminance

Defining Equation

SI Unit

F = Km Ú •0 V(l) P(l) dl I = dF/dW L = dI/dAe E = dF/dAi

US Unit

Conversion1 Factor

lumens

lumens

1

candela (lumens/steradian) candela/m2 (Ae is emitting area) lux (lum/m2) (Ai is illumin’d area)

candela ft-lamberts (1 cd/p ft2) Foot-candle (1 lum/ft2)

1 0.2919 0.09294

1

From metric into U.S. units. From Infante, C., Electronic displays, in Handbook of Photonics, Gupta, M.C., ed., CRC Press, Boca Raton, FL, 1997, p. 770.

Dielectric Constants of Common Materials Material

Dielectric Constant (k)

Vacuum Air Water Paper Porcelain Fused quartz Pyrex glass Polyethylene Amber Polystyrene Teflon Transformer oil Titanium dioxide

1 1.00054 78 3.5 6.5 3.8 4.5 2.3 2.7 2.6 2.1 4.5 100

From Morgan, D., Applications, standards, and products for grounding and shielding, in Instrument Engineers’ Handbook: Process Software and Digital Networks, 3rd ed., Liptak, B., Ed., CRC Press, Boca Raton, FL, 2002.

Characteristics of Coaxial Cables Cable Type

Characteristic Impedance

Common Usage

RG-6 RG-8 RG-11 RG-58 RG-59 RG-62

75 50 75 50 75 93

Broadband, Carrier Band Drop Thick Ethernet Broadband, Carrier Band Trunk Thin Ethernet Broadband Drop ARCnet

Note: Some references include the dash in RG-X, others do not. From Barton, C.C., PLC proprietary and open networks, in Instrument Engineers’ Handbook: Process Software and Digital Networks, 3rd ed., Liptak, B., Ed., CRC Press, Boca Raton, FL, 2002.

© 2004 by CRC Press LLC

1587_Book.fm Page 53 Monday, September 1, 2003 7:17 PM

3-53

Chemical Engineering, Chemistry, and Materials Science

Dry Saturated Steam: Temperature Table Specific Volume, ft3/lbm†

Enthalpy, Btu/lbm†

Temp., ºF/ºC

Abs. Press., PSIA P†

32/0 35/1.7 40/4.4 45/7.2 50/10

0.08854 0.09995 0.12170 0.14752 0.17811

0.01602 0.01602 0.01602 0.01602 0.01603

3306 2947 2444 2036.4 1703.2

3306 2947 2444 2036.4 1703.2

0.00 3.02 8.05 13.06 18.07

1075.8 1074.1 1071.3 1068.4 1065.6

1075.8 1077.1 1079.3 1081.5 1083.7

0.0000 0.0061 0.0162 0.0262 0.0361

2.1877 2.1709 2.1435 2.1167 2.0903

2.1877 2.1770 2.1597 2.1429 2.1264

60/15.6 70/21.1 80/26.7 90/32.2 100/37.8

0.2563 0.3631 0.5069 0.6982 0.9492

0.01604 0.01606 0.01608 0.01610 0.01613

1206.6 867.8 633.1 468.0 350.3

1206.7 867.9 633.1 468.0 350.4

28.06 38.04 48.02 57.99 67.97

1059.9 1054.3 1048.6 1042.9 1037.2

1088.0 1092.3 1096.6 1100.9 1105.2

0.0555 0.0745 0.0932 0.1115 0.1295

2.0393 1.9902 1.9428 1.8972 1.8531

2.0948 2.0647 2.0360 2.0087 1.9826

110/43 120/49 130/54 140/60 150/66

1.2748 1.6924 2.2225 2.8886 3.718

0.01617 0.01620 0.01625 0.01629 0.01634

265.3 203.25 157.32 122.99 97.06

265.4 203.27 157.34 123.01 97.07

77.94 87.92 97.90 107.89 117.89

1031.6 1025.8 1020.0 1014.1 1008.2

1109.5 1113.7 1117.9 1122.0 1126.1

0.1471 0.1645 0.1816 0.1984 0.2149

1.8106 1.7694 1.7296 1.6910 1.6537

1.9577 1.9339 1.9112 1.8894 1.8685

Evap. ufg

Sat. Vapor ug

Sat. Liquid hf

Entropy, Btu/lbm R†

Sat. Liquid uf

Evap. hfg

Sat. Vapor hg

Sat. Liquid sf

Evap. sfg

Sat. Vapor sg

160/71 170/77 180/82 190/88 200/93

4.741 5.992 7.510 9.339 11.526

0.01639 0.01645 0.01651 0.01657 0.01663

77.27 62.04 50.21 40.94 33.62

77.29 62.06 50.23 40.96 33.64

127.89 137.90 147.92 157.95 167.99

1002.3 996.3 990.2 984.1 977.9

1130.2 1134.2 1138.1 1142.0 1145.9

0.2311 0.2472 0.2630 0.2785 0.2938

1.6174 1.5822 1.5480 1.5147 1.4824

1.8485 1.8293 1.8109 1.7932 1.7762

210/90 212/100 220/104 230/110 240/116

14.123 14.696 17.186 20.780 24.969

0.01670 0.01672 0.01677 0.01684 0.01692

27.80 26.78 23.13 19.365 16.306

27.82 26.80 23.15 19.382 16.323

178.05 180.07 188.13 198.23 208.34

971.6 970.3 965.2 958.8 952.2

1149.7 1150.4 1153.4 1157.0 1160.5

0.3090 0.3120 0.3239 0.3387 0.3531

1.4508 1.4446 1.4201 1.3901 1.3609

1.7598 1.7566 1.7440 1.7288 1.7140

250/121 260/127 270/132 280/138 290/143

29.825 35.429 41.858 49.203 57.556

0.01700 0.01709 0.01717 0.01726 0.01735

13.804 11.746 10.044 8.628 7.444

13.821 11.763 10.061 8.645 7.461

218.48 228.64 238.84 249.06 259.31

945.5 938.7 931.8 924.7 917.5

1164.0 1167.3 1170.6 1173.8 1176.8

0.3675 0.3817 0.3958 0.4096 0.4234

1.3323 1.3043 1.2769 1.2501 1.2238

1.6998 1.6860 1.6727 1.6597 1.6472

300/149 310/154 320/160 330/166 340/171

67.013 77.68 89.66 103.06 118.01

0.01745 0.01755 0.01765 0.01776 0.01787

6.449 5.609 4.896 4.289 3.770

6.466 5.626 4.914 4.307 3.788

269.59 279.92 290.28 300.68 311.13

910.1 902.6 894.9 887.0 879.0

1179.7 1182.5 1185.2 1187.7 1190.1

0.4369 0.4504 0.4637 0.4769 0.4900

1.1980 1.1727 1.1478 1.1233 1.0992

1.6350 1.6231 1.6115 1.6002 1.5891

350/177 360/182 370/188 380/193 390/199

134.63 153.04 173.37 195.77 220.37

0.01799 0.01811 0.01823 0.01836 0.01850

3.324 2.939 2.606 2.317 2.0651

3.342 2.957 2.625 2.335 2.0836

321.63 332.18 342.79 353.45 364.17

870.7 862.2 853.5 844.6 835.4

1192.3 1194.4 1196.3 1198.1 1199.6

0.5029 0.5158 0.5286 0.5413 0.5539

1.0754 1.0519 1.0287 1.0059 0.9832

1.5783 1.5677 1.5573 1.5471 1.5371

400/204 410/210 420/216 430/221 440/227

247.31 276.75 308.83 343.72 381.59

0.01864 0.01878 0.01894 0.01910 0.01926

1.8447 1.6512 1.4811 1.3308 1.1979

1.8633 1.6700 1.5000 1.3499 1.2171

374.97 385.83 396.77 407.79 418.90

826.0 816.3 806.3 796.0 785.4

1201.0 1202.1 1203.1 1203.8 1204.3

0.5664 0.5788 0.5912 0.6035 0.6158

0.9608 0.9386 0.9166 0.8947 0.8730

1.5272 1.5174 1.5078 1.4982 1.4887

450/232 460/238 470/243

422.6 466.9 514.7

0.0194 0.0196 0.0198

1.0799 0.9748 0.8811

1.0993 0.9944 0.9009

430.1 441.4 452.8

774.5 763.2 751.5

1204.6 1204.6 1204.3

0.6280 0.6402 0.6523

0.8513 0.8298 0.8083

1.4793 1.4700 1.4606

© 2004 by CRC Press LLC

1587_Book.fm Page 54 Monday, September 1, 2003 7:17 PM

3-54

CRC Handbook of Engineering Tables

Dry Saturated Steam: Temperature Table (continued) Specific Volume, ft3/lbm† Temp., ºF/ºC t

Abs. Press., PSIA P†

Sat. Liquid uf

Evap. ufg

Sat. Vapor ug

Enthalpy, Btu/lbm† Sat. Liquid hf

Entropy, Btu/lbm R†

Evap. hfg

Sat. Vapor hg

Sat. Liquid sf

Evap. sfg

Sat. Vapor sg

480/249 490/254

566.1 621.4

0.0200 0.0202

0.7972 0.7221

0.8172 0.7423

464.4 476.0

739.4 726.8

1203.7 1202.8

0.6645 0.6766

0.7868 0.7653

1.4513 1.4419

500/260 520/271 540/282 560/293 580/304

680.8 812.4 962.5 1133.1 1325.8

0.0204 0.0209 0.0215 0.0221 0.0228

0.6545 0.5385 0.4434 0.3647 0.2989

0.6749 0.5594 0.4649 0.3868 0.3217

487.8 511.9 536.6 562.2 588.9

713.9 686.4 656.6 624.2 588.4

1201.7 1198.2 1193.2 1186.4 1177.3

0.6887 0.7130 0.7374 0.7621 0.7872

0.7438 0.7006 0.6568 0.6121 0.5659

1.4325 1.4136 1.3942 1.3742 1.3532

600/316 620/327 640/338 660/349 680/360

1542.9 1786.6 2059.7 2365.4 2708.1

0.0236 0.0247 0.0260 0.0278 0.0305

0.2432 0.1955 0.1538 0.1165 0.0810

0.2668 0.2201 0.1798 0.1442 0.1115

617.0 646.7 678.6 714.2 757.3

548.5 503.6 452.0 390.2 309.9

1165.5 1150.3 1130.5 1104.4 1067.2

0.8131 0.8398 0.8679 0.8987 0.9351

0.5176 0.4664 0.4110 0.3485 0.2719

1.3307 1.3062 1.2789 1.2472 1.2071

700/371 705.4/374.1

3093.7 3206.2

0.0369 0.0503

0.0392 0

0.0761 0.0503

823.3 902.7

172.1 0

995.4 902.7

0.9905 1.0580

0.1484 0

1.1389 1.0580

† PSIA = 0.069 bar (abs); ft3/lbm = 62.4 l/kg; Btu/lbm = 0.556 Kcal/kg From Liptak, B.G., Ed., Instrument Engineers’ Handbook: Process Software and Digital Networks, 3rd ed., CRC Press, Boca Raton, FL, 2002, pp. 817–818. Originally abridged from Thermodynamic Properties of Steam, by Joseph H. Keenan and Fredrick G. Keyes. © 1936, by Joseph H. Keenan and Frederick G. Keyes. Published by John Wiley & Sons, Inc., New York.

© 2004 by CRC Press LLC

200/93

220/104

300/149

350/177

400/204

450/232

500/260

550/288

600/316

700/371

800/427

900/482

1000/538

u 1h (101.74) s

392.6 1150.4 2.0512

404.5 1159.5 2.0647

452.3 1195.8 2.1153

482.2 1218.7 2.1444

512.0 1241.7 2.1720

541.8 1264.9 2.1983

571.6 1288.3 2.2233

601.4 1312.0 2.2468

631.2 1335.7 2.2702

690.8 1383.8 2.3137

750.4 1432.8 2.3542

809.9 1482.7 2.3923

869.5 1533.5 2.4283

u 5h (162.24) s

78.16 1148.8 1.8718

80.59 1158.1 1.8857

90.25 1195.0 1.9370

96.26 1218.1 1.9664

102.26 1241.2 1.9942

108.24 1264.5 2.0205

114.22 1288.0 2.0456

120.19 1311.7 2.0692

126.16 1335.4 2.0927

138.10 1383.6 2.1361

150.03 1432.7 2.1767

161.95 1482.6 2.2148

173.87 1533.4 2.2509

u 10 h (193.21) s

38.85 1146.6 1.7927

40.09 1156.2 1.8071

45.00 1193.9 1.8595

48.03 1217.2 1.8892

51.04 1240.6 1.9172

54.05 1264.0 1.9436

57.05 1287.5 1.9689

60.04 1311.3 1.9924

63.03 1335.1 2.0160

69.01 1383.4 2.0596

74.98 1432.5 2.1002

80.95 1482.4 2.1383

86.92 1533.1 2.1744

27.15 1154.4 1.7624

30.53 1192.8 1.8160

32.62 1216.4 1.8460

34.68 1239.9 1.8743

36.73 1263.5 1.9008

38.78 1287.1 1.9261

40.82 1310.9 1.9498

42.86 1335.8 1.9734

46.94 1383.2 2.0170

51.00 1432.3 2.0576

55.07 1482.3 2.0958

59.13 1533.1 2.1319

u 20 h (227.96) s

22.36 1191.6 1.7808

23.91 1215.6 1.8112

25.43 1239.2 1.8396

26.95 1262.9 1.8664

28.46 1286.6 1.8918

29.97 1310.5 1.9160

31.47 1334.4 1.9392

34.47 1382.9 1.9829

37.46 1432.1 2.0235

40.45 1482.1 2.0618

43.44 1533.0 2.0978

u 40 h (267.25) s

11.040 1186.8 1.6994

11.843 1211.9 1.7314

12.628 1236.5 1.7608

13.401 1260.7 1.7881

14.168 1284.8 1.8140

14.93 1308.9 1.8384

15.688 1333.1 1.8619

17.198 1381.9 1.9058

18.702 1431.3 1.9467

20.20 1481.4 1.9850

21.70 1532.4 2.0214

u 60 h (292.71) s

7.259 1181.6 1.6492

7.818 1208.2 1.6830

8.357 1233.6 1.7135

8.884 1258.5 1.7416

9.403 1283.0 1.7678

9.916 1307.4 1.7926

10.427 1331.8 1.8162

11.441 1380.9 1.8605

12.449 1430.5 1.9015

13.452 1480.8 1.9400

14.454 1531.9 1.9762

u 80 h (312.03) s

5.803 1204.3 1.6475

6.220 1230.7 1.6791

6.624 1256.1 1.7078

7.020 1281.1 1.7346

7.410 1305.8 1.7598

7.797 1330.5 1.7836

8.562 1379.9 1.8281

9.322 1429.7 1.8694

10.077 1480.1 1.9079

10.830 1531.3 1.9442

u 100 h (327.81) s

4.592 1200.1 1.6188

4.937 1227.6 1.6518

5.268 1253.7 1.6813

5.589 1279.1 1.7085

5.905 1304.2 1.7339

6.218 1329.1 1.7581

6.835 1378.9 1.8029

7.446 1428.9 1.8443

8.052 1479.5 1.8829

8.656 1530.8 1.9193

u 120 h (341.25) s

3.783 1195.7 1.5944

4.081 1224.4 1.6287

4.363 1251.3 1.6591

4.636 1277.2 1.6869

4.902 1302.5 1.7127

5.165 1327.7 1.7370

5.683 1377.8 1.7822

6.195 1428.1 1.8237

6.702 1478.8 1.8625

7.207 1530.2 1.8990

3.468 1221.1 1.6087

3.715 1248.7 1.6399

3.954 1275.2 1.6683

4.186 1300.9 1.6945

4.413 1326.4 1.7190

4.861 1376.8 1.7645

5.301 1427.3 1.8063

5.738 1478.2 1.8451

6.172 1529.7 1.8817

u 14.696 h (212.00) s

u 140 h (353.02) s

© 2004 by CRC Press LLC

1587_Book.fm Page 55 Monday, September 1, 2003 7:17 PM

Temperature, ºF/ºC

3-55

Abs. Press., PSIA (Sat. Temp. ºF)

Chemical Engineering, Chemistry, and Materials Science

Properties of Superheated Steam

Abs. Press., PSIA (Sat. Temp. ºF)

Temperature, ºF/ºC 200/93

300/149

350/177

450/232

500/260

550/288

600/316

700/371

800/427

900/482

1000/538

u 160 h (363.53) s

3.008 1217.6 1.5908

3.230 1246.1 1.6230

3.443 1273.1 1.6519

3.648 1299.3 1.6785

3.849 1325.0 1.7033

4.244 1375.7 1.7491

4.631 1426.4 1.7911

5.015 1477.5 1.8301

5.396 1529.1 1.8667

u 180 h (373.06) s

2.649 1214.0 1.5745

2.852 1243.5 1.6077

3.044 1271.0 1.6373

3.229 1297.6 1.6642

3.411 1323.5 1.6894

3.764 1374.7 1.7355

4.110 1425.6 1.7776

4.452 1476.8 1.8167

4.792 1528.6 1.8534

u 200 h (381.79) s

2.361 1210.3 1.5594

2.549 1240.7 1.5937

2.726 1268.9 1.6240

2.895 1295.8 1.6513

3.060 1322.1 1.6767

3.380 1373.6 1.7232

3.693 1424.8 1.7655

4.002 1476.2 1.8048

4.309 1528.0 1.8415

u 220 h (389.86) s

2.125 1206.5 1.5453

2.301 1237.9 1.5808

2.465 1266.7 1.6117

2.621 1294.1 1.6395

2.772 1320.7 1.6652

3.066 1372.6 1.7120

3.352 1424.0 1.7545

3.634 1475.5 1.7939

3.913 1527.5 1.8308

u 240 h (397.37) s

1.9276 1202.5 1.5319

2.094 1234.9 1.5686

2.247 1264.5 1.6003

2.393 1292.4 1.6286

2.533 1319.2 1.6546

2.804 1371.5 1.7017

3.068 1423.2 1.7444

3.327 1474.8 1.7839

3.584 1526.9 1.8209

u 260 h (404.42) s

1.9183 1232.0 1.5573

2.063 1262.3 1.5897

2.199 1290.5 1.6184

2.330 1317.7 1.6447

2.582 1370.4 1.6922

2.827 1422.3 1.7352

3.067 1474.2 1.7748

3.305 1526.3 1.8118

u 280 h (411.05) s

1.7674 1228.9 1.5464

1.9047 1260.0 1.5796

2.033 1288.7 1.6087

2.156 1316.2 1.6354

2.392 1369.4 1.6834

2.621 1421.5 1.7265

2.845 1473.5 1.7662

3.066 1525.8 1.8033

u 300 h (417.33) s

1.6364 1225.8 1.5360

1.7675 1257.6 1.5701

1.8891 1286.8 1.5998

2.005 1314.7 1.6268

2.227 1368.3 1.6751

2.442 1420.6 1.7184

2.652 1427.8 1.7582

2.859 1525.2 1.7954

u 350 h (431.72) s

1.3734 1217.7 1.5119

1.4923 1251.5 1.5481

1.6010 1282.1 1.5792

1.7036 1310.9 1.6070

1.8980 1365.5 1.6563

2.084 1418.5 1.7002

2.266 1471.1 1.7403

2.445 1523.8 1.7777

u 400 h (444.59) s

1.1744 1208.8 1.4892

1.2851 1245.1 1.5281

1.3843 1277.2 1.5607

1.4770 1306.9 1.5894

1.6508 1362.7 1.6398

1.8161 1416.4 1.6842

1.9767 1469.4 1.7247

2.134 1522.4 1.7623

CRC Handbook of Engineering Tables

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3-56

Properties of Superheated Steam (continued)

1000/538 1200/649 1400/760 1600/871

1.1231 1238.4 1.5095

1.2155 1272.0 1.5437

1.3005 1302.8 1.5735

1.3332 1314.6 1.5845

1.3652 1326.2 1.5951

1.3967 1337.5 1.6054

1.4278 1348.8 1.6153

1.4584 1359.9 1.6250

1.6074 1414.3 1.6699

1.7516 1467.7 1.7108

1.8928 1521.0 1.7486

2.170 1628.6 1.8177

2.443 1738.7 1.8803

2.714 1851.9 1.9381

u 500 h (467.01) s

0.9927 1231.3 1.4919

1.0800 1266.8 1.5280

1.1591 1298.6 1.5588

1.1893 1310.7 1.5701

1.2188 1322.6 1.5810

1.2478 1334.2 1.5915

1.2763 1345.7 1.6016

1.3044 1357.0 1.6115

1.4405 1412.1 1.6571

1.5715 1466.0 1.6982

1.6996 1519.6 1.7363

1.9504 1627.6 1.8056

2.197 1737.9 1.8683

2.442 1851.3 1.9262

u 550 h (476.94) s

0.8852 1223.7 1.4751

0.9686 1261.2 1.5131

1.0431 1294.3 1.5451

1.0714 1306.8 1.5568

1.0989 1318.9 1.5680

1.1259 1330.8 1.5787

1.1523 1342.5 1.5890

1.1783 1354.0 1.5991

1.3038 1409.9 1.6452

1.4241 1464.3 1.6868

1.5414 1518.2 1.7250

1.7706 1626.6 1.7946

1.9957 1737.1 1.8575

2.219 1850.6 1.9155

u 600 h (486.21) s

0.7947 1215.7 1.4586

0.8753 1255.5 1.4990

0.9463 1289.9 1.5323

0.9729 1302.7 1.5443

0.9988 1315.2 1.5558

1.0241 1327.4 1.5667

1.0489 1339.3 1.5773

1.0732 1351.1 1.5875

1.1899 1407.7 1.6343

1.3013 1462.5 1.6762

1.4096 1516.7 1.7147

1.6208 1625.5 1.7846

1.8279 1736.3 1.8476

2.033 1850.0 1.9056

u 700 h (503.10) s

0.7277 1243.2 1.4722

0.7934 1280.6 1.5084

0.8177 1294.3 1.5212

0.8411 1307.5 1.5333

0.8639 1320.3 1.5449

0.8860 1332.8 1.5559

0.9077 1345.0 1.5665

1.0108 1403.2 1.6147

1.1082 1459.0 1.6573

1.2024 1513.9 1.6963

1.3853 1623.5 1.7666

1.5641 1734.8 1.8299

1.7405 1848.8 1.8881

u 800 h (518.23) s

0.6154 1229.8 1.4467

0.6779 1270.7 1.4863

0.7006 1285.4 1.5000

0.7223 1299.4 1.5129

0.7433 1312.9 1.5250

0.7635 1325.9 1.5366

0.7833 1338.6 1.5476

0.8763 1398.6 1.5972

0.9633 1455.4 1.6407

1.0470 1511.0 1.6801

1.2088 1621.4 1.7510

1.3662 1733.2 1.8146

1.5214 1847.5 1.8729

u 900 h (531.98) s

0.5264 1215.0 1.4216

0.5873 1260.1 1.4653

0.6089 1275.9 1.4800

0.6294 1290.9 1.4938

0.6491 1305.1 1.5066

0.6680 1318.8 1.5187

0.6863 1332.1 1.5303

0.7716 1393.9 1.5814

0.8506 1451.8 1.6257

0.9262 1508.1 1.6656

1.0714 1619.3 1.7371

1.2124 1731.6 1.8009

1.3509 1846.3 1.8595

u 1000 h (544.61) s

0.4533 1198.3 1.3961

0.5140 1248.8 1.4450

0.5350 1265.9 1.4610

0.5546 1281.9 1.4757

0.5733 1297.0 1.4893

0.5912 1311.4 1.5021

0.6084 1325.3 1.5141

0.6878 1389.2 1.5670

0.7604 1448.2 1.6121

0.8294 1505.1 1.6525

0.9615 1617.3 1.7245

1.0893 1730.0 1.7886

1.2146 1845.0 1.8474

u 1100 h (556.31) s

0.4532 1236.7 1.4251

0.4738 1255.3 1.4425

0.4929 1272.4 1.4583

0.5110 1288.5 1.4728

0.5281 1303.7 1.4862

0.5445 1318.3 1.4989

0.6191 1384.3 1.5535

0.6866 1444.5 1.5995

0.7503 1502.2 1.6405

0.8716 1615.2 1.7130

0.9885 1728.4 1.7775

1.1031 1843.8 1.8363

u 1200 h (567.22) s

0.4016 1223.5 1.4052

0.4222 1243.9 1.4243

0.4410 1262.4 1.4413

0.4586 1279.6 1.4568

0.4752 1295.7 1.4710

0.4909 1311.0 1.4843

0.5617 1379.3 1.5409

0.6250 1440.7 1.5879

0.6843 1499.2 1.6293

0.7967 1613.1 1.7025

0.9046 1726.9 1.7672

1.0101 1842.5 1.8263

u 1400 h (587.10) s

0.3174 1193.0 1.3639

0.3390 1218.4 1.3877

0.3580 1240.4 1.4079

0.3753 1260.3 1.4258

0.3912 1278.5 1.4419

0.4062 1295.5 1.4567

0.4714 1369.1 1.5177

0.5281 1433.1 1.5666

0.5805 1493.2 1.6093

0.6789 1608.9 1.6836

0.7727 1723.7 1.7489

0.8640 1840.0 1.8083

© 2004 by CRC Press LLC

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u 450 h (456.28) s

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Chemical Engineering, Chemistry, and Materials Science

Abs. Press., Temperature, ºF/ºC PSIA (Sat. Temp. ºF) 500/260 550/288 600/316 620/327 640/338 660/349 680/360 700/371 800/427

u 1600 h (604.90) s

900/482

1000/538 1200/649 1400/760 1600/871

0.2936 1215.2 1.3741

0.3112 1238.7 1.3952

0.3271 1259.6 1.4137

0.3417 1278.7 1.4303

0.4034 1358.4 1.4964

0.4553 1425.3 1.5476

0.5027 1487.0 1.5914

0.5906 1604.6 1.6669

0.6738 1720.5 1.7328

0.7545 1837.5 1.7926

u 1800 h (621.03) s

0.2407 1185.1 1.3377

0.2597 1214.0 1.3638

0.2760 1238.5 1.3855

0.2907 1260.3 1.4044

0.3502 1347.2 1.4765

0.3986 1417.4 1.5301

0.4421 1480.8 1.5752

0.5218 1600.4 1.6520

0.5968 1717.3 1.7185

0.6693 1835.0 1.7786

u 2000 h (635.82) s

0.1936 1145.6 1.2945

0.2161 1184.9 1.3300

0.2337 1214.8 1.3564

0.2489 1240.0 1.3783

0.3074 1335.5 1.4576

0.3532 1409.2 1.5139

0.3935 1474.5 1.5603

0.4668 1596.1 1.6384

0.5352 1714.1 1.7055

0.6011 1832.5 1.7660

0.1484 1132.3 1.2687

0.1686 1176.8 1.3073

0.2294 1303.6 1.4127

0.2710 1387.8 1.4772

0.3061 1458.4 1.5273

0.3678 1585.3 1.6088

0.4244 1706.1 1.6775

0.4784 1826.2 1.7389

0.0984 1060.7 1.1966

0.1760 1267.2 1.3690

0.2159 1365.0 1.4439

0.2476 1441.8 1.4984

0.3018 1574.3 1.5837

0.3505 1698.0 1.6540

0.3966 1819.9 1.7163

0.1583 1250.5 1.3508

0.1981 1355.2 1.4309

0.2288 1434.7 1.4874

0.2806 1569.8 1.5742

0.3267 1694.6 1.6452

0.3703 1817.2 1.7080

u 2500 h (668.13) s u 3000 h (695.36) s

0.2733 1187.8 1.3489

3-58

Abs. Press., Temperature, ºF/ºC PSIA (Sat. Temp. ºF) 500/260 550/288 600/316 620/327 640/338 660/349 680/360 700/371 800/427

u 3206.2 h (705.40) s 0.0306 780.5 0.9515

0.1364 1224.9 1.3241

0.1762 1340.7 1.4127

0.2058 1424.5 1.4723

0.2546 1563.3 1.5615

0.2977 1689.8 1.6336

0.3381 1813.6 1.6968

u 4000 h S

0.0287 763.8 0.9347

0.1052 1174.8 1.2757

0.1462 1314.4 1.3827

0.1743 1406.8 1.4482

0.2192 1552.1 1.5417

0.2581 1681.7 1.6154

0.2943 1807.2 1.6795

u 4500 h S

0.0276 753.5 0.9235

0.0798 1113.9 1.2204

0.1226 1286.5 1.3529

0.1500 1388.4 1.4253

0.1917 1540.8 1.5235

0.2273 1673.5 1.5990

0.2602 1800.9 1.6640

u 5000 h S

0.0268 746.4 0.9152

0.0593 1047.1 1.1622

0.1036 1256.5 1.3231

0.1303 1369.5 1.4034

0.1696 1529.5 1.5066

0.2027 1665.3 1.5839

0.2329 1794.5 1.6499

u 5500 h S

0.0262 741.3 0.9090

0.0463 985.0 1.1093

0.0880 1224.1 1.2930

0.1143 1349.3 1.3821

0.1516 1518.2 1.4908

0.1825 1657.0 1.5699

0.2106 1788.1 1.6369

From Liptak, B.G., Ed., Instrument Engineers’ Handbook: Process Software and Digital Networks, 3rd ed., CRC Press, Boca Raton, FL, 2002, pp. 819–822. Originally abridged from Thermodynamic Properties of Steam, by Joseph H. Keenan and Fredrick G. Keyes. © 1936, by Joseph H. Keenan and Frederick G. Keyes. Published by John Wiley & Sons, Inc., New York.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

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Properties of Superheated Steam (continued)

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Chemical Engineering, Chemistry, and Materials Science

Properties of Water at Various Temperatures from 40 to 540ºF (4.4 to 282.2ºC) Temp. ºF

Temp. ºC

Specific Volume* ft3/lb

Specific Gravity

Weight* (lb/ft3)

Vapor Pressure* PSIA

40 50 60 70 80 90 100 120 140 160 180 200 212 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540

4.4 10.0 15.6 21.1 26.7 32.2 37.8 48.9 60.0 71.1 82.2 93.3 100.0 104.4 115.6 126.7 137.8 148.9 160.0 171.1 182.2 193.3 204.4 215.6 226.7 237.8 248.9 260.0 271.1 282.2

.01602 .01603 .01604 .01606 .01608 .01610 .01613 .01620 .01629 .01639 .01651 .01663 .01672 .01677 .01692 .01709 .01726 .01745 .01765 .01787 .01811 .01836 .01864 .01894 .01926 .0196 .0200 .0204 .0209 .0215

1.0013 1.0006 1.0000 0.9987 0.9975 0.9963 0.9944 0.9901 0.9846 0.9786 0.9715 0.9645 0.9593 0.9565 0.9480 0.9386 0.9293 0.9192 0.9088 0.8976 0.8857 0.8736 0.8605 0.8469 0.8328 0.8183 0.8020 0.7863 0.7674 0.7460

62.42 62.38 62.34 62.27 62.19 62.11 62.00 61.73 61.39 61.01 60.57 60.13 59.81 59.63 59.10 58.51 58.00 57.31 56.66 55.96 55.22 54.47 53.65 52.80 51.92 51.02 50.00 49.02 47.85 46.51

0.1217 0.1781 0.2563 0.3631 0.5069 0.6982 0.9492 1.692 2.889 4.741 7.510 11.526 14.696 17.186 24.97 35.43 49.20 67.01 89.66 118.01 153.04 195.77 247.31 308.83 381.59 466.9 566.1 680.8 812.4 962.5

*ft3/lb = 62.4 l/Kg; lb/ft3 = 0.016 Kg/l; PSIA = 0.069 bar (abs). Computed from Keenan & Keyes Steam Table. From Liptak, B.G., Ed., Instrument Engineers’ Handbook: Process Software and Digital Networks, CRC Press, Boca Raton, FL, 2002, p. 823.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Atomic Mass of Selected Elements Atomic Number

Element

Symbol

1 2 3 4

Hydrogen Helium Lithium Beryllium

H He Li Be

5 6 7 8

Boron Carbon Nitrogen Oxygen

9 10 11 12

Atomic Mass

Atomic Number

Element

Symbol

Atomic Mass

1.008 4.003 6.941 9.012

48 49 50 51

Cadmium Indium Tin Antimony

Cd In Sn Sb

112.4 114.82 118.69 121.75

B C N O

10.81 12.01 14.01 16.00

52 53 54 55

Tellurium Iodine Xenon Cesium (–10˚)

Te I Xe Ce

127.6 126.9 131.3 132.91

Fluorine Neon Sodium Magnesium

F N Na Mg

19.00 20.18 22.99 24.31

56 57 58 59

Barium Lantium Cerium Praseodymium

Ba La Ce Pr

137.33 138.91 140.12 140.91

13 14 15

Aluminum Silicon Phosphorus (White)

Al Si P

26.98 28.09 30.97

60 61 62 63

Neodymium Promethium Samarium Europium

Nd Pm Sm Eu

144.24 (145) 150.4 151.96

16 17 18 19

Sulfur Chlorine Argon Potassium

S Cl Ar K

32.06 35.45 39.95 39.1

64 65 66 67

Gadolinium Terbium Dysprosium Holmium

Gd Tb Dy Ho

157.25 158.93 162.5 164.93

20 21 22 23

Calcium Scandium Titanium Vanadium

Ca Sc Ti V

40.08 44.96 47.9 50.94

68 69 70 71

Erbium Thulium Ytterbium Lutetium

Er Tm Yb Lu

167.26 168.93 173.04 174.97

24 25 26 27

Chromium Manganese Iron Cobalt

Cr Mn Fe Co

52.00 54.94 55.85 58.93

72 73 74 75

Hafnium Tantalum Tungsten Rhenium

Hf Ta W Re

178.49 180.95 183.85 186.2

28 29 30 31

Nichel Copper Zinc Gallium

Ni Cu Zn Ga

58.71 63.55 65.38 69.72

76 77 78 79

Osmium Iridium Platinum Gold

Os Ir Pt Au

190.2 192.22 195.09 196.97

32 33 34 35

Germanium Arsenic Selenium Bromine

Ge As Se Br

72.59 74.92 78.96 79.9

80 81 82 83

Mercury Thallium Lead Bismuth

Hg Tl Pb Bi

200.59 204.37 207.2 208.98

36 37 38 39

Krypton Rubidium Strontium Yttrium

Kr Rb Sr Y

83.8 85.47 87.62 88.91

84 85 86 87

Polonium Asatine Radon Francium

Po At Rn Fr

(~210) (210) (222) (223)

40 41 42 43

Zirconium Niobium Molybdenum Technetium

Zr Nb Mo Tc

91.22 92.91 95.94 98.91

88 89 90 91

Radium Actinium Thorium Protoactinium

Ra Ac Th Pa

226.03 (227) 232.04 231.04

44 45 46 47

Ruthenium Rhodium Palladium Silver

Ru Rh Pd Ag

101.07 102.91 106.4 107.87

92 93 94 95

Uranium Neptunium Plutonium Americium

U Np Pu Am

238.03 237.05 (244) (243)

© 2004 by CRC Press LLC

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Chemical Engineering, Chemistry, and Materials Science

Atomic Mass of Selected Elements (continued) Atomic Number 96 97 98 99

Element Curium Berkelium Californium Einsteinium

Symbol Cm Bk Cf Es

Atomic Mass (247) (247) (251) (254)

Atomic Number

Element

Symbol

100 101 102 103

Fermium Mendelevium Nobelium Lawrencium

Fm Md No Lw

Atomic Mass (257) (258) (259) (260)

From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science & Engineering, CRC Press, Boca Raton, FL, 2001, pp. 51–54. Data from James F. Shackelford, Introduction to Materials Science for Engineers, Second Edition, Macmillian Publishing Company, New York, pp. 686–688, (1988).

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Solid Density of Selected Elements

Symbol

Solid Density (Mg/m3)

Atomic Number

Element

Symbol

Solid Density (Mg/m3)

Lithium Beryllium Boron Carbon

Li Be B C

0.533 1.85 2.47 2.27

51 52 53 55

Antimony Tellurium Iodine Cesium (–10˚)

Sb Te I Ce

6.69 6.25 4.95 1.91

11 12 13 14

Sodium Magnesium Aluminum Silicon

Na Mg Al Si

0.966 1.74 2.7 2.33

56 57 58 59

Barium Lantium Cerium Praseodymium

Ba La Ce Pr

3.59 6.17 6.77 6.78

15 16 19 20

Phosphorus (White) Sulfur Potassium Calcium

P S K Ca

1.82 2.09 0.862 1.53

60 62 63 64

Neodymium Samarium Europium Gadolinium

Nd Sm Eu Gd

7.00 7.54 5.25 7.87

21 22 23 24

Scandium Titanium Vanadium Chromium

Sc Ti V Cr

2.99 4.51 6.09 7.19

65 66 67 68

Terbium Dysprosium Holmium Erbium

Tb Dy Ho Er

8.27 8.53 8.80 9.04

25 26 27 28

Manganese Iron Cobalt Nickel

Mn Fe Co Ni

7.47 7.87 8.8 8.91

69 70 71 72

Thulium Ytterbium Lutertium Hafnium

Tm Yb Lu Hf

9.33 6.97 9.84 13.28

29 30 31 32

Copper Zinc Gallium Germanium

Cu Zn Ga Ge

8.93 7.13 5.91 5.32

73 74 75 76

Tantalum Tungsten Rhenium Osmium

Ta W Re Os

16.67 19.25 21.02 22.58

33 34 37 38

Arsenic Selenium Rubidium Strontium

As Se Rb Sr

5.78 4.81 1.53 2.58

77 78 79 81

Iridium Platinum Gold Thallium

Ir Pt Au Tl

22.55 21.44 19.28 11.87

39 40 41 42

Yttrium Zirconium Niobium Molybdenum

Y Zr Nb Mo

4.48 6.51 8.58 10.22

82 83 84 90

Lead Bismuth Polonium Thorium

Pb Bi Po Th

11.34 9.80 9.2 11.72

43 44 45 46

Technetium Ruthenium Rhodium Palladium

Tc Ru Rh Pd

11.5 12.36 12.42 12.00

92 94

Uranium Plutonium

U Pu

19.05 19.81

47 48 49 50

Silver Cadmium Indium Tin

Ag Cd In Sn

10.50 8.65 7.29 7.29

Atomic Number 3 4 5 6

Element

From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science & Engineering, CRC Press, Boca Raton, FL, 2001, pp. 55–57. Data from James F. Shackelford, Introduction to Materials Science for Engineers, Second Edition, Macmillian Publishing Company, New York, pp. 686–688, (1988).

© 2004 by CRC Press LLC

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Chemical Engineering, Chemistry, and Materials Science

Thermal Conductivity of Metals (Part 1) T (K)

Aluminum

Cadmium

Copper

Gold

0.401 0.802 1.20 1.60 1.99

28.7 57.3 85.5 113 138

4.4 8.9 13.1 17.1 20.7

1 2 3 4 5

7.8 15.5 23.2 30.8 38.1

6 7 8 9 10

45.1 51.5 57.3 62.2 66.1

44.2 28.0 18.0 12.2 8.87

2.38 2.77 3.14 3.50 3.85

159 177 189 195 196

23.7 26.0 27.5 28.2 28.2

11 12 13 14 15

69.0 70.8 71.5 71.3 70.2

6.91 5.56 4.67 4.01 3.55

4.18 4.49 4.78 5.04 5.27

193 185 176 166 156

27.7 26.7 25.5 24.1 22.6

16 18 20 25 30

68.4 63.5 56.5 40.0 28.5

3.16 2.62 2.26 1.79 1.56

5.48 5.81 6.01 6.07 5.58

145 124 105 68 43

20.9 17.7 15.0 10.2 7.6

35 40 45 50 60

21.0 16.0 12.5 10.0 6.7

1.41 1.32 1.25 1.20 1.13

5.03 4.30 3.67 3.17 2.48

70 80 90 100

5.0 4.0 3.4 3.0

1.08 1.06 1.04 1.03

2.08 1.82 1.68 1.58

6.7 5.7 5.14 4.83

3.58 3.52 3.48 3.45

200 273 300 400

2.37 2.36 2.37 2.4

0.993 0.975 0.968 0.947

1.11 0.948 0.903 0.873

4.13 4.01 3.98 3.92

3.27 3.18 3.15 3.12

500 600 700 800

2.37 2.32 2.26 2.2

0.92 (0.42) (0.49) (0.559)

0.848 0.805 0.757 0.713

3.88 3.83 3.77 3.71

3.09 3.04 2.98 2.92

900 1000 1100 1200

2.13 (0.93) (0.96) (0.99)

0.678 0.653 0.636 0.624

3.64 3.57 3.5 3.42

2.85 2.78 2.71 2.62

1400

48.7 89.3 104 92.0 69.0

Chromium

29 20.5 15.3 12.2 8.5

6.1 5.2 4.6 4.2 3.8

0.611

Values are in watt · cm–1 · K–1. Note: Values in parentheses are for liquid state. These data apply only to metals of purity of at least 99.9%. The third significant figure may not be accurate. From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science and Engineering, CRC Press, Boca Raton, FL, 2001, pp. 384–385. Data from Ho, C.Y., Powell, R.W., and Liley, P.E., Thermal Conductivity of Selected Materials, NSRDS–NBS–8 and NSRD–NBS–16, Part 2, National Standard Reference Data System–National Bureau of Standards, Part 1, 1966; Part 2, 1968.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Thermal Conductivity of Metals (Part 2) T (K)

Iron

1 2 3 4 5

0.75 1.49 2.24 2.97 3.71

6 7 8 9 10

4.42 5.13 5.80 6.45 7.05

11 12 13 14 15

27.7 42.4 34.0 22.4 13.8

Magnesium

Mercury

Molybdenum

1.30 2.59 3.88 5.15 6.39

0.146 0.292 0.438 0.584 0.730

8.2 4.9 3.2 2.3 1.78

7.60 8.75 9.83 10.8 11.7

0.876 1.02 1.17 1.31 1.45

7.62 8.13 8.58 8.97 9.30

1.46 1.23 1.07 0.94 0.84

12.5 13.1 13.6 14.0 14.3

1.60 1.74 1.88 2.01 2.15

16 18 20 25 30

9.56 9.88 9.97 9.36 8.14

0.77 0.66 0.59 0.507 0.477

14.4 14.3 13.9 12.0 9.5

2.28 2.53 2.77 3.25 3.55

35 40 45 50 60

6.81 5.55 4.50 3.72 2.65

0.462 0.451 0.442 0.435 0.424

7.4 5.7 4.57 3.75 2.74

3.62 3.51 3.26 3.00 2.60

70 80 90 100

2.04 1.68 1.46 1.32

0.415 0.407 0.401 0.396

2.23 1.95 1.78 1.69

2.30 2.09 1.92 1.79

200 273 300 400

0.94 0.835 0.803 0.694

0.366 0.355 0.352 0.338

1.59 1.57 1.56 1.53

(0.078) (0.084) (0.098)

1.43 1.39 1.38 1.34

500 600 700 800

0.613 0.547 0.487 0.433

0.325 0.312 (0.174) (0.19)

1.51 1.49 1.47 1.46

(0.109) (0.12) (0.127) (0.13)

1.3 1.26 1.22 1.18

900 1000 1100 1200

0.38 0.326 0.297 0.282

(0.203) (0.215)

1.45 (0.84) (0.91) (0.98)

1400 1600 1800 2000

0.309 0.327

2200 2600

© 2004 by CRC Press LLC

Lead

1.15 1.12 1.08 1.05 0.996 0.946 0.907 0.88 0.858 0.825

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Chemical Engineering, Chemistry, and Materials Science

Thermal Conductivity of Metals (Part 2) (continued) Values are in watt · cm–1 · K–1. Note: Values in parentheses are for liquid state. These data apply only to metals of purity of at least 99.9%. The third significant figure may not be accurate. From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science and Engineering, CRC Press, Boca Raton, FL, 2001, pp. 386–387.

Thermal Conductivity of Metals (Part 3) T (K)

© 2004 by CRC Press LLC

Nickel

Niobium

1 2 3 4 5

0.64 1.27 1.91 2.54 3.16

0.251 0.501 0.749 0.993 1.23

6 7 8 9 10

3.77 4.36 4.94 5.49 6.00

11 12 13 14 15

Platinum

Silver

Tantalum

2.31 4.60 6.79 8.8 10.5

39.4 78.3 115 147 172

0.115 0.230 0.345 0.459 0.571

1.46 1.67 1.86 2.04 2.18

11.8 12.6 12.9 12.8 12.3

187 193 190 181 168

0.681 0.788 0.891 0.989 1.08

6.48 6.91 7.30 7.64 7.92

2.30 2.39 2.46 2.49 2.50

11.7 10.9 10.1 9.3 8.4

154 139 124 109 96

1.16 1.24 1.30 1.36 1.40

16 18 20 25 30

8.15 8.45 8.56 8.15 6.95

2.49 2.42 2.29 1.87 1.45

7.6 6.1 4.9 3.15 2.28

85 66 51 29.5 19.3

1.44 1.47 1.47 1.36 1.16

35 40 45 50 60

5.62 4.63 3.91 3.36 2.63

1.16 0.97 0.84 0.76 0.66

1.80 1.51 1.32 1.18 1.01

13.7 10.5 8.4 7.0 5.5

0.99 0.87 0.78 0.72 0.651

70 80 90 100

2.21 1.93 1.72 1.58

0.61 0.58 0.563 0.552

0.90 0.84 0.81 0.79

4.97 4.71 4.60 4.50

0.616 0.603 0.596 0.592

200 273 300 400

1.06 0.94 0.905 0.801

0.526 0.533 0.537 0.552

0.748 0.734 0.73 0.722

4.3 4.28 4.27 4.2

0.575 0.574 0.575 0.578

500 600 700 800

0.721 0.655 0.653 0.674

0.567 0.582 0.598 0.613

0.719 0.72 0.723 0.729

4.13 4.05 3.97 3.89

0.582 0.586 0.59 0.594

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CRC Handbook of Engineering Tables

Thermal Conductivity of Metals (Part 3) (continued) T (K)

Nickel

Niobium

Platinum

900 1000 1100 1200

0.696 0.718 0.739 0.761

0.629 0.644 0.659 0.675

0.737 0.748 0.76 0.775

1400 1600 1800 2000

0.804

0.705 0.735 0.764 0.791

0.807 0.842 0.877 0.913

2200 2600 3000

Silver 3.82 3.74 3.66 3.58

Tantalum 0.598 0.602 0.606 0.610 0.618 0.626 0.634 0.640

0.815

0.647 0.658 0.665

From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science and Engineering, CRC Press, Boca Raton, FL, 2001, pp. 388–389.

Thermal Conductivity of Metals (Part 4) T (K) 1 2 3 4 5

© 2004 by CRC Press LLC

Tin

297 181 117

Titanium

Tungsten

Zinc

Zirconium

0.0144 0.0288 0.0432 0.0576 0.0719

14.4 28.7 42.6 55.6 67.1

19.0 37.9 55.5 69.7 77.8

0.111 0.223 0.333 0.442 0.549

6 7 8 9 10

76 52 36 26 19.3

0.0863 0.101 0.115 0.129 0.144

76.2 82.4 85.3 85.1 82.4

78.0 71.7 61.8 51.9 43.2

0.652 0.748 0.837 0.916 0.984

11 12 13 14 15

14.8 11.6 9.3 7.6 6.3

0.158 0.172 0.186 0.200 0.214

77.9 72.4 66.4 60.4 54.8

36.4 30.8 26.1 22.4 19.4

1.04 1.08 1.11 1.13 1.13

49.3 40.0 32.6 20.4 13.1

16.9 13.3 10.7 6.9 4.9

1.12 1.08 1.01 0.85 0.74

16 18 20 25 30

5.3 4.0 3.2 2.22 1.76

0.227 0.254 0.279 0.337 0.382

35 40 45 50 60

1.50 1.35 1.23 1.15 1.04

0.411 0.422 0.416 0.401 0.377

8.9 6.5 5.07 4.17 3.18

3.72 2.97 2.48 2.13 1.71

0.65 0.58 0.535 0.497 0.442

70 80 90 100

0.96 0.91 0.88 0.85

0.356 0.339 0.324 0.312

2.76 2.56 2.44 2.35

1.48 1.38 1.34 1.32

0.403 0.373 0.350 0.332

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Chemical Engineering, Chemistry, and Materials Science

Thermal Conductivity of Metals (Part 4) (continued) T (K)

Tin

Titanium

Tungsten

Zinc

Zirconium

200 273 300 400

0.733 0.682 0.666 0.622

0.245 0.224 0.219 0.204

1.97 1.82 1.78 1.62

1.26 1.22 1.21 1.16

0.252 0.232 0.227 0.216

500 600 700 800

0.596 (0.323) (0.343) (0.364)

0.197 0.194 0.194 0.197

1.49 1.39 1.33 1.28

1.11 1.05 (0.499) (0.557)

0.210 0.207 0.209 0.216

900 1000 1100 1200

(0.384) (0.405) (0.425) (0.446)

0.202 0.207 0.213 0.220

1.24 1.21 1.18 1.15

(0.615) (0.673) (0.73)

0.226 0.237 0.248 0.257

1400 1600 1800 2000

(0.487)

0.236 0.253 0.271

1.11 1.07 1.03 1.00

2200 2600 3000

0.275 0.290 0.302 0.313

0.98 0.94 0.915

Values are in watt · cm–1 · K–1. Note: Values in parentheses are for liquid state. These data apply only to metals of purity of at least 99.9%. The third significant figure may not be accurate. From Shackelford, J.F. and Alexander, W., CRC Handbook of Materials Science and Engineering, CRC Press, Boca Raton, FL, 2001, pp. 390–391.

© 2004 by CRC Press LLC

R-12

R-13

R-22

R-113

R-114

CCl3F 137.38 74.9 –168 388.4 640 4.41 34.6 554 91.39 1 464 12.205 0.7619 0.21 0.878 1.13

CCl2F3 120.93 –21.6 –252 233.6 597 4.12 34.84 558 80.67 1 292 1.458 0.091 02 0.235 0.983 1.139

CCIF3 104.47 –114.6 –294 83.9 561 3.87 36.1 578 81.05–22 1 298–22 0.304 0.018 98 0.247 1.03 1.17

CHClF2 86.48 –41.4 –256 204.8 721.9 4.98 32.8 525 73.28 1 174 1.243 0.077 60 0.305 1.28 1.18

CCl2F-CCIF2 187.39 117.6 –31 417.4 498.9 3.44 36.0 577 96.96 1 553 27.04 1.688 0.218 0.912 1.12

C2Cl2F4 170.94 38.8 –137 294.3 473 3.26 36.3 581 89.95 1 441 4.226 0.263 8 0.246 1.03 1.09

Thermal conductivity Sat liquid, 5˚F Sat liquid, 258.15 K Sat liquid, 86˚F Sat liquid, 303.15 K Vapor at sat press, 5˚F Vapor at sat press, 258.15 K Vapor at 14.7 psia, 86˚F Vapor at 0.101 3 MN/m2, 303.15 K

0.058 100 0.049 85 0.003 4 5.9 0.004 5 7.8

0.052 90 0.040 69 0.004 7 8.1 0.005 9 10

0.06–95 100–95

0.069 120 0.050 86 0.005 1 8.8 0.006 5 11

0.044 76 0.037 64 0.003 5 6.0 0.004 5 7.8

0.041 71 0.033 57 0.004 7 8.1 0.0065 2 11

0.630 0.000 630 0.404 0.000 404 0.008 7 0.000 008 7 0.010 8 0.000 010 8 3.1

0.335 0.000 335 0.254 0.000 254 0.010 8 0.000 010 8 0.012 7 0.000 012 7 2.4

.037–95 0.000 037–95

0.298 0.000 298 0.230 0.000 230 0.011 2 0.000 011 2 0.013 2 0.000 012 3 1.3

1.28 0.001 28 0.638 0.000 638 0.007 9 0.000 007 9 0.009 6 0.000 009 6 3.9

0.614 0.000 614 0.356 0.000 356 0.009 6 0.000 009 6 0.011 4 0.000 011 4

Viscosity, N·s/m2 Sat liquid, 5˚F Sat liquid, 258.15 K Sat liquid, 86˚F Sat liquid, 303.15 K Vapor at sat press, 5˚F Vapor at sat press, 258.15 K Vapor at 14.7 psia, 86˚F Vapor at 0.101 3 MN/m2, 303.15 K Relative dielectric strength of vapor at 73˚F and 14.7 psia (nitrogen = 1)

© 2004 by CRC Press LLC

1.4

R-502

‡ 99.31 –28.3 –254 221.9 641.9 4.43 31.0 496 71.06 1 138 1.501 0.093 7 0.290 1.21 1.14

** 111.6 –50.1 — 194 619 4.27 34.91 559 76.13 1 219 0.825 0.051 50 0.305 1.28 1.135

NH3 17.03 –28.0 –108 271.4 1 657 11.4 14.6 234 37.16 595.2 8.150 0.508 8 1.14 4.77 1.29

0.052 90 0.037 64 0.005 4 9.3 0.006 9 12

0.29 500 0.29 500 0.012 21 0.014 24

0.334 0.000 334 0.240 0.000 240 0.011 2 0.000 011 2 0.013 1 0.000 013 1

0.250 0.000 2 0.207 0.000 2 0.008 5 0.000 000 0.010 2 0.000 00 0.82 (84˚F)

0.292 0.000 292 0.220 0.000 220

R-717

CRC Handbook of Engineering Tables

Chemical formula Molecular weight Boiling temperature at 14.7 psia, ˚F Freezing temperature at 14.7 psia, ˚F Critical temperature, ˚F Critical pressure, psia Critical pressure, MN/m2 Critical density, lb/cu ft Critical density, kg/m3 Density of liquid, 86˚F, lb/cu ft Density of liquid, 303.15 K, kg/m3 Sp vol of sat bvapor, 5˚F, cu ft/lb Sp vol of sat vapor, 258.15 K, m3/kg Sp heat of liquid, 86˚F, Btu/lb ˚F Sp heat of liquid, 303.15 K, kJ/kg·K Sp heat ratio (cp/cv); vapor at 86˚F and 14.7 psia

R-500

1587_Book.fm Page 68 Monday, September 1, 2003 7:17 PM

R-11

3-68

General Properties of Refrigerants*

Group 6

Group 6+

Group 5a

Group 4 1/2

Group 6

Group 5a

Group 5a

† See explanation at end of table. ‡ R-500 is azeotrope 73.8% (by wt) CCl2F2 and 26.2% (by wt) CH3-CHF2. ** R-502 is azeotrope CHClF2 = 48.8% and CClF2CF3 = 51.2%. Fluorocarbons Property

R-13B1

R-14

Chemical formula Molecular weight Boiling point at 14.7 psia, ˚F Freezing point at 14.7 psia, ˚F Critical temperature, ˚F Critical pressure, psia Critical pressure, MN/m2 Critical density, lb/cu ft Critical density, kg/m3 Density of liquid, 86˚F, lb/cu ft Density of liquid, 303.15 K, kg/m3 Sp vol of sat vapor, 5˚F, cu ft/lb Sp vol of sat vapor, 258.15 K, m3/kg Toxicity (Underwriters’ Laboratories Classification)d

CBrF3 148.9 –72.0 –270 152.6 575 3.96 46.5 745 93.58 1 499 0.379 6 0.023 70 Group 6

CF4 88.01 –198.4 –299 –50 543 3.74 39 625 82.2b 1 317b

a b c d

Group 6c

R-40, Methyl Chloride CH3Cl 50.48 –10.8 –144 289.4 968.7 6.68 23.3 373 56.24 900.9 4.471 0.279 1 Group 4

R-50, Methane CH4 16.03 –258.9 –297 –115.8 673.1 4.64 10.1 162

Group 5a

R-170, Ethane C 2H 6 30.04 –127.5 –278 90.1 708.3 4.88 13.2 211 16.57 265.4 0.531 3 0.033 17 Group 5a

R-290, Propane

R-600, nButane

C 3H 8 44.09 –44.2 –309.8 206 617.4 4.26 13.7 219 36.2 579.9 2.509 0.156 6 Group 5a

C4H10 58.12 31.3 –217 306 550.1 3.79 14.2 227 35.62 570.6 9.98 0.623 0 Group 5

At 76.4 psia. At –112˚F (317.59 K). Unofficial. The Underwriters’ Laboratories Classification of toxicity is as follows: Group 1: Lethal concentration 0.5 to 1.0 percent for durations of 5 minutes. Group 2: Lethal concentration 0.5 to 1.0 percent for durations of 30 minutes. Group 3: Lethal concentration 2.0 to 2.5 percent for durations of 1 hour. Group 4: Lethal concentration 2.0 to 2.5 percent for durations of 2 hours. Group 5a: Less toxic than group 4, more toxic than group 6. Group 5b: Available data would classify these as 5a or 6. Group 6: Concentrations up to about 20 percent for 2 hours do not appear to produce injury.

From Bolz, R.E. and Tuve, G.L., Gases and vapors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 68–69.

© 2004 by CRC Press LLC

CO2 44.01 –109.3 subl. –69.9a 87.8 1057.4 7.29 28.6 458

0.266 1 0.016 61 Group 5

3-69

* Based largely on: “ASHRAE Handbook of Fundamentals,” American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1972. Reference “Properties of Commonly-Used Refrigerants,” Air-Conditioning Refrigeration Institute, 1967.

R-744, Carbon Dioxide

1587_Book.fm Page 69 Tuesday, September 2, 2003 3:25 PM

Group 5a

Chemical Engineering, Chemistry, and Materials Science

Toxicity Underwriters’ Laboratories Classification†

1587_Section_3.fm Page 70 Monday, September 1, 2003 8:02 PM

3-70

CRC Handbook of Engineering Tables

Thermodynamic Properties of Saturated Mercury Enthalpy and Entropy Measured from 32˚F 2

For pressures in MN/m , multiply value in lbf/in.2 by 0.006 894 8. For temperature in K, add 459.67 to value in deg F and multiply he result by 5/9. For enthalpy in J/kg, multiplying value in Btu/lb by 2 324.4. For entropy in J/kg·K, multiply value in Btu/lb·deg F by 4 186.8. For specific volume in m3/kg. Multiply value in ft3/lbm by 0.062 420. Enthalpy, Btu/lbm

Entropy, Btu/lbm˚R

Specific Volume, Sat Vapor, ft3/lbm

Temperature, ˚F

Saturated Liquid

Evaporation

Saturated Vapor

Saturated Liquid

Evaporation

Saturated Vapor

0.020 0.040 0.075 0.100 0.200

259.9 288.3 316.2 329.7 364.3

7.532 8.463 9.373 9.814 10.936

127.614 127.486 127.361 127.300 127.144

135.146 135.949 136.734 137.114 138.080

0.01259 0.01386 0.01504 0.01561 0.01699

0.17735 0.17044 0.16415 0.16126 0.15432

0.18994 0.18430 0.17919 0.17687 0.17131

0.400 0.600 0.800 1.00 2.00

402.0 425.8 443.5 457.7 504.9

12.159 12.929 13.500 13.959 15.476

126.975 126.868 126.788 126.724 126.512

139.134 139.797 140.288 140.683 141.988

0.01844 0.01932 0.01994 0.02045 0.02205

0.14736 0.14328 0.14038 0.13814 0.13116

0.16580 0.16260 0.16032 0.15859 0.15321

113.7 77.84 59.58 48.42 25.39

557.9 591.2 616.5 637.0 706.0

17.161 18.233 19.035 19.685 21.864

126.275 126.124 126.011 125.919 125.609

143.436 144.357 145.046 145.604 147.473

0.02373 0.02477 0.02551 0.02610 0.02800

0.12434 0.12002 0.11712 0.11483 0.10779

0.14787 0.14479 0.14264 0.14093 0.13579

13.38 9.26 7.12 5.81 3.09

40 60 80 100 120

784.4 835.7 874.8 906.8 934.3

24.345 25.940 27.159 28.152 29.005

125.255 125.024 124.849 124.706 124.582

149.600 150.964 152.008 152.858 153.587

0.03004 0.03127 0.03218 0.03290 0.03350

0.10068 0.19652 0.09356 0.09127 0.08938

0.13072 0.12779 0.12574 0.12417 0.12288

1.648 1.144 0.885 0.725 0.617

140 160 180 200 225

958.3 979.9 999.5 1017.2 1038.0

29.748 30.415 31.018 31.560 32.204

124.474 124.376 124.288 124.209 124.115

154.222 154.791 155.306 155.769 156.319

0.03401 0.03447 0.03488 0.03523 0.03565

0.08778 0.08640 0.08518 0.08411 0.08287

0.12179 0.12087 0.12006 0.11934 0.11852

0.538 0.478 0.431 0.392 0.354

250 275 300 350 400

1057.2 1074.8 1091.2 1121.4 1148.4

32.784 33.322 33.824 34.747 35.565

124.029 123.950 123.876 123.740 123.620

156.813 157.272 157.700 158.487 159.185

0.03603 0.03637 0.03669 0.03725 0.03775

0.08178 0.08079 0.07989 0.07828 0.07688

0.11871 0.11716 0.11658 0.11553 0.11463

0.322 0.297 0.276 0.241 0.215

500 600 800 1000 1100

1196.0 1236.8 1306.1 1364.0 1390.0

37.006 38.245 40.324 42.056 42.828

123.406 123.221 122.910 122.649 122.533

160.412 161.466 163.234 164.705 165.361

0.03861 0.03932 0.04047 0.04139 0.04179

0.07455 0.07264 0.06961 0.06726 0.06625

0.11316 0.11196 0.11008 0.10865 0.10804

0.177 0.151 0.118 0.098 0.090

Pressure lbf /in.2

4.00 6.00 8.00 10 20

1893 986 545 416 217.3

From Bolz, R.E. and Tuve, G.L., Gases and vapors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 87. Originally abridged from “Thermodynamic Properties of Mercury Vapor,” by L.A. Sheldon. Courtesy of General Electric Company.

© 2004 by CRC Press LLC

Metallic Radius, Å

Electrical Restivity at 298˚K, microhm-cm

Residual Resistivity at 4.2˚K, microhm-cm

15.04 19.95 22.53 20.69 20.81

1.641 1.803 1.877 1.824 1.828

50.9 59.6 79.8 75.3 68.0

3.7 3.2 S.C.‡

7.003 — 7.537 5.253 7.898

20.60 — 19.95 28.93 19.91

1.822 — 1.802 1.983 1.801

93.96 71.2 71.7 74.5 58.3

8.234 8.540 8.781 9.045 9.314

19.30 19.03 18.78 18.49 18.14

38.2 102.16

6.972 9.835

24.82 17.79

Melting Point, ˚C

Boiling Point, ˚C

Heat of Sublimation, kcal/mole DH 298˚K

Scandium Yttrium Lanthanum Cerium Praseodymium

1539 1523 920 798 931

2832 3337 3454 3257 3212

Neodymium Promethium Samarium Europium Gradolinium

1010 1080 1072 822 1311

Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutertium

Element

† ‡

Density, g/cm3 298˚K

Atomic Volume, cm3/mole

91.0 99.6 103.0 111.60 89.09

2.989 4.457 6.166 6.771 6.772

3127 (2460) 1778 1597 3233

77.3 (64) 49.3 42.5 95.75

1360 1409 1470 1522 1545

3041 2335 2720 2510 1727

824 1656

1193 3315

Compresibility, cm2/kg†

Young’s Modulus kg/cm2, Millions

Poisson’s Ratio

0.7

2.26 2.68 4.04 4.10 3.21

0.809 0.663 0.384 0.306 0.332

(0.269) 0.265 0.288 0.248 0.305

64.3 — 105.0 91.0 131.0

6.8 — 6.2 0.6 4.4

3.0 (2.8) 3.34 8.29 2.56

0.387 (0.430) 0.348 0.150 0.573

0.306 (0.278) 0.352 (0.286) 0.259

1.783 1.775 1.767 1.758 1.747

114.5 92.6 81.4 86.0 67.6

3.5 2.4 7.0 4.7 5.6

2.45 2.55 2.47 2.39 2.47

0.586 0.644 0.684 0.748 (0.770)

0.261 0.243 0.255 0.238 (0.235)

1.939 1.735

25.1 58.2

0.29 4.5

7.39 2.38

0.182 (0.860)

0.284 (0.233)

All values in this column should be divided by 106. S.C.–Superconductor. From Spedding, F.H., Solids — Metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 129.

3-71

© 2004 by CRC Press LLC

1587_Book.fm Page 71 Monday, September 1, 2003 7:17 PM

To convert density from g/cm3 to kg/m3, multiply by 1000. To convert Young’s modulus from kg/cm2 to N/m2, multiply by 98,067. Values in parentheses are estimates.

Chemical Engineering, Chemistry, and Materials Science

Properties of Rare-Earth Metals

1587_Section_3.fm Page 72 Wednesday, October 8, 2003 4:37 PM

3-72

CRC Handbook of Engineering Tables

Products of Powder Metallurgy Powder metallurgy refers to the production of parts by a process of molding metal powders and agglomerating the form by heat. The powder mixture is often hot-molded under pressure (10,000–10,000 psi) and is sintered in an inert or a reducing atmosphere, at a temperature between 400–2,000 deg F, depending on the metal mixture. For the refractory metals higher temperatures are necessary. The methods of powder metallurgy provide a close control of the composition and allow use of mixtures that could not be fabricated by any other process. As dimensions are determined by the mold, finish machining or grinding is often eliminated, thereby reducing cost and handling, especially for large lots. Special properties of the finished product, such as porosity, friction coefficient, and electrical conductivity, can be varied somewhat by changing the proportions of the powder components.

Class

Composition or Constituents

Applications and Uses

Small, finished parts Refractory metals

Various ferrous, copper, and nickel alloys

Complex shapes; small parts not requiring high strength or ductility; plain bearings Production of high-purity tungsten, molybdenum, tantalum, niobium, etc.; beryllium; cobalt alloys Porous bearings, oil-impregnated, or with graphite or plastic; friction materials; metal filters; porous electrodes; catalysts; throttle plates Services requiring high strength with lightness, high electrical and thermal conductivities; nuclear reactor components Ceramics with good structural properties; lightweight materials for high temperature (e.g., SAP) High-permeability materials; permanent magnets; ferrite cores; magnetic storage Combustion and rocket nozzles; furnace muffler, tubes, seals, extrusion dies; power-tube cathodes

Pure W, Mo, Ta, Nb, Re, Ti alloys

Porous metals

Copper; copper-lead; bronze; stainless steel

Composite metals

Al, Cu, etc. with W, Mo, Co, or stainless steel reinforcing; reactor fuel elements

Metal– nonmetal composites Magnetic materials

Filament-reinforced ceramics; dispersion strengthening by oxides Nickel-iron; cobalt mixtures; ferrites

Cermets, oxide

Al2O3-Cr; Al2O3-Cr-W; Al2O3-Cr-Mo; ThO2-W

Cermets, carbide

TiC-Ni; TiC-Fe-Cr; TiC-Co-Cr-W; Cr3C2-Ni-W WC-Co; WC-TaC-Co; TiC-Ni; Cr3C2-WC-Ni

Cemented carbides

High-temperature bearings, seals, and dies; gage blocks Tips for cutting tools, lathe centers, gages; wire-drawing dies; rock drills; crushers; blast nozzles

Desirable Properties and Advantages Control of dimensions and finish; two-phase bearing metals; low cost in large production lots Metals used in high-temperature service; electrical, electronic, and nuclear applications Interconnected pores in the size range 5–50 microns; porosity about 20–30% High-strength materials from common metals; durability of nuclear materials Strengthened ceramics; heatresistant aluminum Very high magnetic properties and close control of magnetic properties High-temperature strength (2,000 deg F and above); resistance to thermal shock; high thermal conductivity; corrosion resistance Strength toughness, and corrosion resistance at high temperatures (to 1,700 deg F); hardness Very high hardness, compressive strength, and elastic modulus; war and corrosion resistance; high conductivity; hightemperature strength

From Bolz, R.E. and Tuve, G.L., Solids — Metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 133.

© 2004 by CRC Press LLC

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3-73

Chemical Engineering, Chemistry, and Materials Science

Fiber-Reinforced Metals Ductile and low-strength metals have been reinforced with various fibers. Fiber bundles or mats in molten metals, powder mixtures pressed or extruded, and electroplating are some of the fabrication methods. Copper, aluminum, silver, nickel and titanium are among the matrix materials, with reinforcement by steel, tungsten, boron, molybdenum, silica, glass, oxides, and carbides. The ratio of fiber-strength/matrix-strength determines a certain minimum fiber volume for effective reinforcement, but the fiber–matrix bond and fiber-to-stress alignment are also critical. Increase of strength is almost linear with fiber volume. Short fibers are not fully effective so that the strength is increased much less for a given fiber-volume fraction. Typical test results for fiberreinforced metals are included in the following table. Test Results on Composite Metals* Stress, kpsi Strengthener Matrix Metals

Component

% vol

Matrix Only, No Reinforcement

Composite Material

Metals Strengthened by Fibers Copper Silver Aluminum Aluminum Aluminum Nickel Iron Titanium

W fibers Al2O3 whiskers Glass fibers Al2O3 Steel B Al2O3 Mo

Cobalt Nickel

WC TiC

60 35 50 35 25 8 36 20

20 10b (23%)c 25d 25d 70d 40d 80d

200a 75b (94%)c 161d 173d 384d 237d 96d

Metals Strengthened by Sintered Carbides 90 75

(E = 30)e (E = 31)f

(E = 85)e (E = 55)f

a

Tensile strength with continuous fibers. Tensile strength at 350 deg C; modulus of elasticity: Cu = 17, composite 42 (millions of psi). c Percentage of tensile strength at room temperature retained when tested at 300 deg C. d Tensile strength, room temperature. e Modulus of elasticity, E, measured in compression; hardness, 90 R-A; compressive strength, about 600,000 psi. f Modulus of elasticity, E, measured in compression; hardness about 85 R-A. * Compiled from various sources. b

References “Metals Handbook: Properties and Selection,” Vol. 1, American Society for Metals, 1961. “Modern Composite Materials,” L.J. Broutman and R.H. Krock, Addison-Wesley Publishing Company, 1967. From Bolz, R.E. and Tuve, G.L., Solids — Metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 135.

© 2004 by CRC Press LLC

1587_Book.fm Page 74 Monday, September 1, 2003 7:17 PM

3-74

CRC Handbook of Engineering Tables

Properties of Commercial Plastics Of the many plastics commercially available in each chemical class, only one or a very few examples have been selected for this table as typical of the class. In some cases the range or properties have been expanded to include several grades or types. It is impractical to include a comprehensive list of materials or known properties of these materials in a table of convenient size. Properties vary widely with amount and kind of modifier, such as filler and plasticizer. Within any type of thermoplastic resins, molecular weight is an important variable. This property is controlled to afford the best physical properties available consistent with economical processing properties. The information shown refers in all cases, except for “Forms available” and “Fabrication,” to material in the fabricated form, which in the case of thermosetting materials means commercially cured. Physical and electrical properties will vary, to a greater or lesser degree, with different materials, with humidity conditioning environment and with orientation. Strength values are quoted on the basis of shorttime tests at normal room temperature and are not suitable for engineering design purposes for load-bearing applications. Maximum continuous service temperature refers to unloaded structures. The user of this table is referred to the specifications and test procedures of the American Society for Testing Materials. To convert psi to N/m2, multiply by 6,895. For specific heat in J/kg·K, multiply by 4,184.

Properties

Chemical Class Resin Type

Cellulose Acetate Thermoplastic

Subclass or Modification

Soft

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Cellulose Acetate Cellulose Acetate Butyrate Thermoplastic Thermoplastic Hard

Soft

1010–1013 3.5–7.5 3.2–7.0 0.01–0.06 0.01–0.10

1010–1013 3.5–7.5 3.2–7.0 0.01–0.06 0.01–0.10

1010–1012 3.5–6.4 3.2–6.2 0.01–0.04 0.01–0.04

86–250 1,900–4,700 32–50 2,200–4,200

190–400 4,600–8,500 6–40 4,100–7,600

74–126 1,900–3,800 60–74 1,200–2,600

R 49–R 103 2.0–5.2 1.27–1.34

R 101–R 123 0.4–2.7 1.27–1.34

R 59–R 95 2.5–5.4 1.15–1.22

Medium 44–57 0.3–0.42 8–16

Medium 60–113 0.3–0.42 8–16

Medium 49–58 0.3–0.4 11–17

Fair to good Poor Very poor Poor Very poor Poor Poor Poor Fair to good Poor to fair Fair to good

Fair to good Poor Very poor Poor Very poor Poor Poor Poor Fair to good Poor to fair Fair to good

Good Fair to good

Excellent Pale to colorless 1.46–1.50 D786, D706, D257, D150, D638, D785, D256, D792, D648, D696, D543, D542

Excellent Pale to colorless 1.46–1.50 D786, D706, D257, D150, D638, D785, D256, D792, D648, D696, D543, D542

Good Poor Poor Poor Poor Fair to good Poor Good Good to excellent Pale to colorless 1.46–1.49 D707, D257, D150, D638, D785, D256, D792, D648, D696

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Chemical Engineering, Chemistry, and Materials Science

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

F, Lq, P, R, S

F, Lq, P, R, S

Cs, E, F, MB, MC, MI, Cs, E, F, MB, MC, S MI, S

F, Lq, P, R, S

Cs, E, F, MB, MC, MI, S

Cellulose Acetate Butyrate Thermoplastic

Nylon Thermoplastic

Polycarbonates Thermoplastic

Hard

6/6

Unfilled

1010–1012 3.5–6.4 3.2–6.2 0.01–0.04 0.01–0.04

4.0–4.6 3.4–3.6 0.014–.04 0.04

2 ¥ 1016 3.17 2.96 0.0009 0.001

150–200 5,000–6,800 38–54 3,600–6,100

9,000–12,000 60–300

290–325 8,000–-9,500 20–100 8,000–10,000

R 108–R 117 0.7–2.4 1.19–1.25

R 108–R 120 1.0–2.0 1.13–1.15

M 70–M 180 8–16 1.2

Medium 70–99 0.3–0.4 11–17

Self-extinguishing

Self-extinguishing 135–145 0.3 6.6 138–143

Good Fair to good Good Poor Poor Poor Poor Fair to good Poor Good Good to excellent Pale to colorless 1.46–1.49 D707, D257, D150, D256, D792, D648, D542, D638, D785, D696, D543

0.4 8.0 80–150 Very good Poor Poor No effect No effect Good Good Good Very good Fair to good Good Clear Pale amber to colorless 1.53 D257, D150, D638, D792, D648, D696, D785, D256, D542, D543

Excellent Fair Poor Poor Poor Poor Poor Poor Poor Poor Clear Colorless 1.60 D257, D150, D638, D792, D648, D696, D785, D256, D542, D543

1587_Book.fm Page 76 Monday, September 1, 2003 7:17 PM

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CRC Handbook of Engineering Tables

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

F, Lq, P, R, S

F, Fb, Mf, P, R, S

Cs, E, F, MB, MC, MI, E, F, MB, MC, MI S

F, Fb, Mf, P, R, S

Cs, E, F, MB, MC, MI

To convert psi to N/m2, multiply by 6,895. For specific heat in J/kg·K, multiply by 4,184.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Polyethylene Thermoplastic

Polyethylene Thermoplastic

Polyethylene Thermoplastic

Low Density

Medium Density

High Density

>1015 2.3–2.35 2.3–2.35 <0.0005 <0.0005

>1015 2.3 2.3 <0.0005 <0.0005

>1015 2.3–2.35 2.3–2.35 <0.0005 <0.0005

14–38 1,000–1,400 400–700 1,100–1,700 20–40

35–90 1,200–3,500 50–600 1,500–2,600 10–20

No break 0.91–0.925

0.5–>16 0.926–0.941

85–160 3,100–5,500 15–100 2,400–5,000 5–10 R 30–R 50 1.5–20 0.941–0.965

Very slow

Slow

Slow

0.55 10–20 60–77

0.55 14.16 71–93

0.55 11.13 92–200

Good Good Good to poor Good Good Excellent to poor Excellent to poor Excellent to poor Fair Fair Good

Excellent Excellent Good to poor Excellent Excellent Excellent to poor Excellent to poor Excellent to poor Fair Good Excellent

Excellent Excellent Good to poor Excellent Excellent Excellent to poor Excellent to poor Excellent to poor Fair Fair Good

Translucent Colorless 1.50–1.54 D702, D788, D257, D638, D696, D543, D150, D412, D1248, D542

Translucent Colorless 1.52–1.54 D257, D150, D412, D256, D696, D543, D638, D785, D1248, D542

Translucent Colorless 1.54 D257, D150, D412, D256, D696, D543, D638, D785, D1248, D542

1587_Book.fm Page 77 Monday, September 1, 2003 7:17 PM

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Chemical Engineering, Chemistry, and Materials Science

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

F, Mf, P, R, S

F, Mf, P, R, S

Cl, E, F, MB, MC, MI Cl, E, F, MB, MC, MI

F, Fb, Mf, P, R, S

Cl, E, F, MB, MC, MI

Methylmethacrylate Thermoplastic

Polypropylene Thermoplastic

Polypropylene Thermoplastic

Unmodified

Unmodified

Unmodified

>1014 3.5–4.5 3.0–3.5 0.04–0.06 0.02–0.03

>1015 2.2–2.6 2.2–2.6 <0.0005 0.0005–0.002

350–500 7,000–11,000 2.0–1.0

1.4–1.7 4,300–5,500 >220 4,900 15 93 1.0 0.90

R 30–R 96 1.1–12 0.90

Slow 66–99 0.35 5.0–9.0 60–93

Medium

Medium

0.5 5.8–10

0.5 8–10 190–240

Good Fair to poor Attacked Good Poor

Excellent Excellent Good to poor Excellent to good Excellent to good Excellent to good Excellent to good Excellent to good Good to fair Good to fair Good

Excellent Excellent Poor Excellent Good Good below 80˚C Good below 80˚C Good below 80˚C Good below 80˚C Good below 80˚C

M 80–M 105 0.3–0.6 1.18–1.20

Dissolves Dissolves Good Softens Good Excellent Colorless 1.48–1.50 D257, D150, D638, D792, D648, D696, D785, D256, D543, D542

>1017 2.3 2.3 0.0001–0.0005 0.0001–0.002

2,900–4,500 200–700

Transparent Transparent Colorless to sl. Colorless to sl. yellow yellow 1.49 D257, D150, D412, D257, D150, D412, D256, D256, D648, D648, D543, D638, D785, D543, D638, D542 D785, D542

1587_Book.fm Page 78 Monday, September 1, 2003 7:17 PM

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CRC Handbook of Engineering Tables

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Cs, P, R, S

F, Fb, Mf, P, R, S

F, Fb, Mf, P, R, S

Cs, E, F, Lq, MB, MC, MI

Cl, E, F, MB, MC, MI

Cl, E, F, MB, MC, MI

To convert psi to N/m2, multiply by 6,895. For specific heat in J/kg·K, multiply by 4,184.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Methylmethacrylate Thermoplastic

Polypropylene Thermoplastic

Polypropylene Thermoplastic

Unmodified

Unmodified

Unmodified

>1016 2.5–2.65 2.5–2.65 0.0001–0.0003 0.0001–0.0004

>1013–1017 2.6–3.4 2.5–3.1 0.0006–0.008 0.007–0.01

>1018 2. 2. 0.0002 0.0002

400–600 5,000–10,000 1.0–2.5

>1016 9,000–12,000 1.0–2.5

M 65–M 85 0.25–0.60 1.04–1.08

M 75–M 90 0.3–0.6 1.05–1.1

33–65 2,000–4,500 200–400 1,600–2,000 50–75 D 50–D 65 2.5–4.0 2.1–2.3

Medium to slow 0.32–0.35 6.0–8.0 66–82

Slow 91–104 0.32–0.35 3.6–3.8 77–88

Self-extinguishing 60 0.25 10 260

Excellent Excellent Poor Excellent Excellent Excellent Dissolves Poor Poor Dissolves Fair to poor

Excellent Good to excellent Poor Excellent Good to excellent Good to excellent Dissolves Dissolves Good Fair to good Good to excellent

Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent

Transparent Colorless 1.59–1.60 D257, D150, D638, D792, D648, D696, D785, D256, D543, D542

Transparent Translucent Colorless to amber Colorless to gray 1.56–1.57 1.30–1.40 D257, D150, D638, D792, D648, D696, D785, D256, D543, D542

1587_Book.fm Page 79 Tuesday, September 2, 2003 3:25 PM

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Chemical Engineering, Chemistry, and Materials Science

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

F, Fb, Mf, P, R, S

F, Mf, P, R, S

F, L, P, R, S

E, F, MB, MC, MI

Cl, E, F, MB, MC, MI

E, F, MC, MI

Polytrifluorochloroethylene Thermoplastic Unmodified

Polyvinylchloride and Vinylchloride Acetate Thermoplastic Unmodified, Rigid

Polyvinylchloride and Vinylchloride Acetate Thermoplastic Plasticized, Non-Rigid

1018 2.2–2.8 2.3–2.5 0.001 0.005

1012–1016 3.2–4.0 3.0–4.0 0.01–0.02 0.006–0.02

1011–1014 5.0–9.0 3.0–4.0 0.03–0.05 0.06–0.1

150 4,500–6,000 250 4,200 10 J 75–J 95 2.5–4.0 2.1–2.3

200–600 5,000–9,000 2.0–40

1,500–3,000 200–400

1.0–5.0 R 110–R 120 0.4–2.0 1.36–1.4

1.15–1.35

Self-extinguishing 0.22 7.0 200

Self-extinguishing 60–80 0.2–0.28 5.0–18 70–74

Slow to self-extinguishing 0.36–0.5 7.0–25 80–105

Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent Excellent

Excellent Good to excellent Fair to good Excellent Good Excellent Poor Poor Excellent Poor Excellent

Fair to good Fair to good Poor to fair Fair to good Fair to good Fair Poor Poor Poor Poor Poor

Transparent Colorless to pale 1.43 D1430, D257, D150, D256, D792, D648, D542, D638, D785, D696, D543

Transparent Colorless to amber 1.54 D708, D728, D257, D256, D792, D648, D542, D150, D638, D696, D543

Transparent Colorless to amber 1.50–1.55 D1432, D257, D150, D543, D542

1587_Book.fm Page 80 Monday, September 1, 2003 7:17 PM

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CRC Handbook of Engineering Tables

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

F, Mf, P, R, S

F, Fb, I, Lq, Mf, P, R, S

Cs, E, F, I, MC, MI, S Cl, Cs, E, F, I, MB, MC, MI, S

F, L, P, R, S

Cl, Cs, E, MB, MC, MI, S

To convert psi to N/m2, multiply by 6,895. For specific heat in J/kg·K, multiply by 4,184.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Epoxy Thermosetting Unfilled

MelamineFormaldehyde Thermosetting

Melamine-Formaldehyde Thermosetting

a-Cellulose Filled Mineral-Filled (Electrical)

1012–1014 3.5–5.0 3.4–4.4 0.001–0.005 0.03–0.05

1012–1014 7.9–9.4 7.2–8.4 0.03–0.08 0.03–0.043

1013–1014 10.2 6.1 0.10 0.051

>300 4,000–13,000 2.0–6.0

1,300 7,000–13,000 0.6–0.9

1,950 5,500–6,500

M 75–M 110 0.2–1.0 1.115

M 110–M 124 0.24–0.35 1.47–1.52

E 90 0.3–0.4 1.78

Slow Up to 120 0.25–0.4 4.5–9.0 80

Self-extinguishing 204 0.4 2.0–5.7 99.0

Self-extinguishing 130

Excellent Fair to good Poor Excellent Excellent Excellent Poor

Good Poor Poor Good Poor Good Good Good Good Good Good

Fair Poor Poor Fair Poor Good Good Good Good Good Good

Excellent Excellent Excellent

2.1–4.3 149

Transparent Transparent Opaque Colorless Colorless Dark 1.58 D257, D150, D651, D704, D257, D150, D704, D257, D150, D256, D792, D648, D696, D256, D792, D792, D648, D638, D785, D785, D256, D5432 D648, D638, D543, D696 D785, D543, D696

1587_Book.fm Page 81 Monday, September 1, 2003 7:17 PM

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Chemical Engineering, Chemistry, and Materials Science

Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Properties

P, R, S

P, R, S

Cs, I, S

MC

MC

Chemical Class Resin Type

PhenolFormaldehyde Thermosetting

PhenolFormaldehyde Thermosetting

Subclass or Modification

Cord Filled

Cellulose Filled

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Cs, Lq

Phenol-Formaldehyde Thermosetting Unfilled Cast Phenolic, Mechanical and Chemical Grade

1011–1012 7.0–10.0 5.0–6.0 0.1–0.3 0.04–0.09

1011–1013 5.0–9.0 4.0–7.0 0.0–0.3 0.03–0.07

1.0–7.0 ¥ 1012 6.5–7.5 4.0–5.5 0.10–0.15 0.04–0.05

900–1,300 6,000–9,000 0.5–1.0

800–1,200 6,500–8,500 0.6–1.0

4.0–5.0 6,000–9,000 1.5–2.0

4.0–8.0 1.36–1.43

M 110–M 120 0.24–0.34 1.32–1.55

M 93–M 120 0.25–0.4 1.307–1.318 Self-extinguishing 74–80

121

Self-extinguishing 143–171 0.35–0.40 3.0–4.5 149–177

Variable Poor Poor Variable Poor Good Poor to fair Fair to good Fair to good Fair to good Good

Variable Poor Poor Variable Poor Good to excellent Fair Fair to good Excellent Excellent Excellent

Fair to good Poor to good Poor Poor to good Poor Good to excellent Fair Fair to good Good to excellent Good Excellent

Opaque

Opaque

Clear Colorless to amber

D700, D257, D150, D785, D256, D792, D638, D651, D543, D648

D700, D257, D150, D257, D150, D638, D792, D785, D256, D648, D696, D785, D256, D792, D543, D543 D638, D651, D648, D696

Self-extinguishing 121–127

6.0–8.0

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Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

L, P, S

L, P, S

Cs, R, S

MC

MC

Cs, F

To convert psi to N/m2, multiply by 6,895. For specific heat in J/kg·K, multiply by 4,184.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

Polyester (Styrene-Alkyd) Thermosetting Glassfiber Mat Reinforced

Silicones Thermosetting

Urea Formaldehyde Thermosetting

Mineral Filled

a-Cellulose Filled

1011 4.0–5.5 4.0–5.5 001–0.04 0.01–0.06

>1012 3.5–3.6 3.4–3.6 0.004 0.005–0.007

0.5–5.0 7.7–9.5 6.7–8.0 0.036–0.043 0.025–0.035

500–1,500 30,000–50,000 0.5–1.5

3,000–4,000

1,300–1,400 5,500–13,000 0.6

M 80–M 120 7.0–30 1.5–2.1

M 85–M 95 0.25–0.35 1.8–2.8

E 94–E 97 0.24–0.40 1.47–1.52

Self-extinguishing 93–288 0.2–0.4 1.8–3.0 121–204

Self-extinguishing >260 0.2–0.3 2.0–4.0 288

Self-extinguishing 130 0.6 2.2–3.6 77

Good Poor Poor Good Poor Good Poor Good Good Poor to fair Good

Fair to good Poor to good

Poor Poor Poor Fair Poor Good Good Good Good Good

Translucent Colorless D257, D150, D638, D792, D648, D696, D785, D256, D543

Fair Poor Poor Poor Fair to good Poor Good Opaque Pale to dark

Translucent Colorless 1.54–1.56 D257, D150, D785, D705, D257, D150, D256, D648, D696, D792, D648, D638, D785 D543, D256, D792

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Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

Properties

Chemical Class Resin Type Subclass or Modification

Electrical Properties D.C. resistivity, ohm-cm Dielectric constant, 60 cps Dielectric constant, 106 cps Dissipation factor, 60 cps Dissipation factor, 106 cps Mechanical Properties Modulus of elasticity, 103 psi Tensile strength, psi Ultimate elongation, % Yield stress, psi Yield strain, % Rockwell hardness Notched Izod impact strength, ft lb/in. Specific gravity Thermal Properties Burning rate Heat distortion, 264 psi, ˚C Specific heat, cal/g Linear thermal expansion coefficient, 10–5, ˚C Maximum continuous service temperature, ˚C Chemical Resistance Mineral acids, weak Mineral acids, strong Oxidizing acids, concentrated Alkalies, weak Alkalies, strong Alcohols Ketones Esters Hydrocarbons, aliphatic Hydrocarbons, aromatic Oils: vegetable, animal, mineral Miscellaneous Properties Clarity Color Refractive index, nD Application ASTM specifications and test methods

© 2004 by CRC Press LLC

L, S

P

P, R, S

I

MC

MC

AcrylonitrileButadiene-Styrene (ABS) Thermoplastic

Acetal Thermoplastic

Alkyd Resins Thermosetting

High-Heat Resistant

Homopolymer

Synthetic-Fiber Filled

2.4–5.0 2.4–3.8 0.003–0.008 0.007–0.015

3.7 0.004

3.8–5.0 3.6–4.7 0.012–0.026 0.01–0.016

7,000–8,000 1.0–20 4,000–9,000

10,000–12,000 15–75

R 110–R 115 2.0–4.0 1.06–1.08

M 94, R 120 1.4–2.3 1.43

E 76 0.50–4.5 1.24–2.6

Slow 115–118 0.3–0.4 6.0–6.5 88–110

Slow

Self-extinguishing

0.35 8.1 84

4.0–5.5 149–220

Good Good Poor Good Good Good Poor Poor Fair Fair Good

Fair Poor Poor Poor Poor Good Good Good Good Good Good

Translucent to opaque Colorless

Translucent to Opaque opaque Colorless Colorless 1.48 D638, D150, D792, D638, D150, D792, D256, D256, D758, D758, D543, D651, D648 D696, D651, D648, D543

D638, D150, D792, D256, D758, D696, D651, D648, D543

4,500–6,500 10,000–13,000

Good Fair Good Fair Fair to good Fair to good Fair to good Fair to good Fair to good

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Properties of Commercial Plastics (continued) Forms Available Cs—castings, F—film, Fb—fibers, I—impregnants, L—laminations, Lq—lacquers, Mf—monofilaments, P—powder, pellet, or granules, R—rods, tubes, or other extruded forms, S—sheets. Fabrication Cl—calendering, Cs—casting, E—extrusion, F—hot forming or drawing, I—impregnation, MB—blow molding, MC—compression molding, MI—injection molding, S—spreading.

P, S, L, R

C, R

P

Cl, E, MB, MI

MI, E

Cs, MC, MI

References “Handbook of Common Polymers,” W.J. Roff, J.R. Scott, J. Pacitti, Butterworth & Co., Ltd. (London), 1971; The Chemical Rubber Co., U.S. distributor. ASTM Standards, American Society for Testing and Materials, 1972, Part 26. “Modern Plastics Encyclopedia,” Vol. 44, No. 1A, McGraw-Hill, Inc., 1967. From Bolz, R.E. and Tuve, G.L., Solids — Non-metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 137–147.

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Rubbers and Elastomers Elastomers cannot be classified in any brief and simple manner, nor are they well characterized by the usual mechanical tests. The terms rubber and synthetic rubber are loosely applied to a great variety of elastic materials, from pure gum natural rubber and pure synthetics to cured, compounded, filled, and even reinforced products. ASTM designations (D418) by chemical polymer description are used in the following table; yet within each class the properties can vary widely, depending on the exact composition, heat treatment, service temperature, and application. Typical uses, such as rubber springs and cushioning, permit an almost unlimited number of combinations of design variables. Mechanically, rubbers may be expected to lose strength rapidly with increase in temperature, to show a large hysteresis in stress-strain behavior, to exhibit marked creep and set, and to be greatly affected by rates of load application or frequency of repeated stress. “Heat build-up,” i.e., increase in temperature in service, as well as deterioration from environment (sunlight, oils, ozone, etc.) will reduce the valuable properties of many rubbers, both natural and synthetic. The following data apply to typical samples of commercial elastomers for common uses. Key: A — Acetone B — Benzene C — Carbon tetrachloride D — Carbon disulfide E — Phenol F — Sulfur compounds G — Glycerol or glycol H — Hexane I — Acids

J — Alkalies K — Ketones L — Alcohols M — Ammonia N — Turpentine O — Coal derivatives; bitumens P — Petroleum products R — Aromatics

Chemical Name

Polyisoprene

Other Names

Natural (or Synthetic) Rubber NR (IR)

Chemical and Physical Specific gravity 0.93 Specific heat 0.40 Thermal conductivity W/cm·K 0.001 7 Btu/hr·ft·deg F 0.10 Service temperature, deg C min –25 max 90 Solvents, softeners D,K,P,V Resistant to A,I,J,L Swelled by D,P,V Mechanical and Electrical Tensile strength 300. kg/cm2 (max) kpsi (max) 4.3 Elongation at break, % 600. Vol. resistivity, ohm-cm 1015 Dielectric strength kV/cm 235 V/mil 600. Dielectric constant 3.0 Power factor (50–100 Hz) 0.003 Rebound Good Comparative Ratings — Resistance to Abrasion Good Cold flow (set) Excellent Tearing Good

© 2004 by CRC Press LLC

S — Salts T — Heat of high temperature U — Ultraviolet V — Vegetable oils W — Weathering X — Oxidation Y — Aging Z — Ozone

Butadiene

Styrene-Butadiene

Acrylonitrile Butadiene

BR Cis 4

Buna S Styrene SBR, GR-S

Nitrile, Buna N Hycar NBR, GR-A

1.0 0.45

1.0 0.40

1.0 0.47

0.002 5 0.14

0.002 6 0.15

0.002 5 0.14

–40 90 D,H,N,P G,I,J,W,Y A,P,V

–20 75 K,P,R,V G,I.L,S,X P,V

–20 110 C,K,O.R G,I,K,L,P,S,T,V,W A,E.N

210. 3.0 700. 1015

210. 3.0 600. 1014

295. 4.2 600. 1010

2.3 0.005 Good

235 600. 2.8 0.005 Fair

185 475. 3.0 0.007 Good

Good Good Poor

Excellent Good Fair

Excellent

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CRC Handbook of Engineering Tables

Rubbers and Elastomers Chemical Name

Polyisoprene

Other Names

Natural (or Synthetic) Rubber NR (IR)

Air permeability Oxidation Flame

Fair Fair Poor

Butadiene

Styrene-Butadiene

Acrylonitrile Butadiene

BR Cis 4

Buna S Styrene SBR, GR-S

Nitrile, Buna N Hycar NBR, GR-A

Good Fair

Fair Fair Poor

Excellent Fair Poor

Chemical Name

Polychloroprene

Isobutylene-Isoprene

Polysulfide

Polymethane

Other Names

Neoprenea, CR, GR-M

Butyl, IIR, GR-I

Thiokola, PS, GR-P

Adiprenea, PU

Chemical and Physical Specific gravity 1.25 Specific heat 0.5 Thermal conductivity W/cm·K 0.002 1 Btu/hr·ft·deg F 0.12 Service temperature, deg C min –20 max 100 Solvents, softeners A,B,C,D,I,N,R Resistant to G,L,P,S,T,U,V,W,Y,Z Swelled by C,D,N,R Mechanical and Electrical Tensile strength kg/cm2 (max) 240. kpsi (max) 3,5 Elongation at break, % 800. Vol. resistivity, ohm-cm 1011 Dielectric strength kV/cm 195 V/mil 500 Dielectric constant 7. Power factor (50–100 Hz) .04 Rebound Good Comparative Ratings—Resistance to Abrasion Excellent Cold flow (set) Excellent Tearing Good Air permeability Good Oxidation Good Flame Excellent a

0.95 0.45

1.4 0.31

1.2 0.45

0.001 3 0.075

0.003 0.17

0.001 3 0.075

–40 120 D,P E,G,J,S,U,V,W,X,Y,Z D.H.P

–15 90 C L,P,U,Z C,R

–35 120 P,V,X,Z B,C,K,R

175. 2.5 700. 1017

90. 1.3 500. 108

350. 5.0 550. 1011

295 750 2.4 0.004 Poor

125 325 8. 0.02 Poor

195 500 7. 0.04

Fair Fair Good Excellent Good Poor

Poor Poor Poor Good Good Poor

Excellent Poor Excellent Excellent Good Poor

Proprietary. From Bolz, R.E. and Tuve, G.L., Solids — Non-metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 156–157.

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Chemical Engineering, Chemistry, and Materials Science

Electrical Properties of Various Kinds of Glass Values are for room temperature. In general the volume resistivity is reduced at the higher temperatures, but the dissipation factor increases rapidly above 100–200˚C.

Types of Glass Fused silica 96% silica (7900, 7910–11–12)† Soda lime General-purpose Lamp bulb (0080) Lead alkali silicate Electrical (0010) High lead (8870) Alumino borosilicate (Kimble N51a) Borosilicate Low expansion (7740) Low electrical loss (7070) Tungsten sealing (7050) Aluminosilicate (1710–20) †

Volume Resistivity, ohm-cm

Dielectric Constant, 1 Mhz

Dissipation Factor, 1 Mhz

1012 1010

3.8 3.8

0.0002 0.0005

106–107 107

7.0–7.6 7.2

0.004–0.011 0.009

109 1012

6.6 9.5

0.0016 0.009

107

5.6

0.010

108 1011 109 1011

4.6 4.0 4.9 6.3

0.0046 0.0006 0.0033 0.0037

Numbers in parentheses indicate equivalent Corning glass code numbers. From Bolz, R.E. and Tuve, G.L., Solids — Non-metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 166. Originally from “Electrical Insulating Materials,” Machine Design, 39:161, Sept. 28, 1967.

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CRC Handbook of Engineering Tables

Properties of the Chemical Elements

Name Actinium Aluminum Americium Antimony (Stibium) Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Diamond Graphite Cerium Cesium Chlorine Chromium Cobalt Copper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold (Aurum) Hafnium Helium Holmium Hydrogen Indium Iodine Iridium Iron (Ferrum) Krypton Lanthanum Lawrencium Lead (Plumbum) Lithium Lutetium Magnesium Manganese Mendelevium Mercury (Hydragyrum)

© 2004 by CRC Press LLC

Atomic International Symbol Number at. wt.a Ac Al Am Sb Ar As At Ba Bk Be Bi B Br Cd Ca Cf C

Ce Cs Cl Cr Co Cu Cm Dy Es Er Eu Fm F Fr Gd Ga Ge Au Hf He Ho H In I Ir Fe Kr La Lr Pb Li Lu Mg Mn Md Hg

89 13 95 51 18 33 85 56 97 4 83 5 35 48 20 98 6

58 55 17 24 27 29 96 66 99 68 63 100 9 87 64 31 32 79 72 2 67 1 49 53 77 26 36 57 103 82 3 71 12 25 101 80

(227) 26.9815 (243) 121.75 39.948 74.9216 (210) 137.34 (247) 9.0122 208.980 10.811 79.904 112.40 40.08 (251) 12.01115

140.12 132.905 35.453 51.996 58.9332 63.546 (247) 162.50 (254) 167.26 151.96 (257) 18.9984 (223) 157.25 69.72 72.59 196.967 178.49 4.0026 164.930 1.00797 114.82 126.9044 192.2 55.847 83.80 138.91 (257) 207.19 6.939 174.97 24.312 54.930 (256) 200.59

Specific Gravity (or density)

Melting Point, ˚C

Boiling Point, ˚C

Specific Heat at 25˚C

Thermal Conductivity, watt/cm˚C

(10.02) 2.70 11.7 6.69 1.78 g/l 5.73 (gray) — 3.5 — 1.85 9.75 2.35 3.12 (liq.) 8.65 1.55 —

1050. 660. 994. 630. –189. 815.b 729. 725. — 1285. 271.4 2300. –7.2 321. 840. —

3200. 2441. 2607. 1750. –186. 613. (subl.) 2125. 1630. — 2475. 1560. 2550. 56.8 767. 1485. —

— 0.215 — 0.050 0.125 0.079 — 0.046 — 0.436 0.030 0.245 0.11 0.055 — —

— 2.37 — 0.185 175 ¥ 10–4 — — — — 2.18 0.084 — 0.45 ¥ 10–4 0.92 1.3 —

3.5 2.1 6.77 1.87 3.21 g/l 7.2 8.9 8.96 — 8.54 — 9.05 5.25 — 1.11 (liq.) — 7.90 5.91 5.32 19.32 13.29 0.177 g/l 8.78 0.0899 g/l 7.31 4.93 22.42 7.87 3.73 g/l 6.17 — 11.35 0.53 9.84 1.74 7.21–7.44 — 13.546

>3800. >3500. 798. 28.6 –101. 1860. 1495. 1084. — 1409. — 1522. 822.

4827. 4200. 3257. 678. –34.6 2670. 2870. 2575. — 2335. — 2510. 1597. — –219.6 –188. 27. 677. 1311. 3233. 29.8 2300. 937. 2380. 1063. 2857. 2220. 4700. — –269. 1470. 2720. –259. –253. 156. 2050. 113.5 184.4 2450. 4390. 1536. 2870. –157. –152. 920. 3454. — — 327.5 1750. 180. 1342. 1656. 3315. 650. 1090. 1244. 2060. — — –38.86 356.55

0.124 0.170 0.047 0.057 0.114 0.110 0.10 0.092 — 0.0414 — 0.04 0.042 — 0.197 — 0.055 0.089 0.077 0.031 0.035 1.24 0.039 3.41 0.056 0.102 0.031 0.108 0.059 0.047 — 0.031 0.84 0.037 0.243 0.114 — 0.033

1.5 (0°) 0.24 0.11 — 0.86 ¥ 10–4 0.91 0.69 3.98 — 0.10 — 0.096 — — 2.63 ¥ 10–4 — 0.088 0.29–0.38 0.59 3.15 0.220 14.8 ¥ 10–4 — 18.4 ¥ 10–4 0.24 43.5 ¥ 10–4 1.47 0.803 0.94 ¥ 10–4 0.14 — 0.352 0.71 — 1.56 — — 0.0839

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Chemical Engineering, Chemistry, and Materials Science

Properties of the Chemical Elements (continued)

Name Molybdenum Neodymium Neon Neptunium Nickel Niobium (Columbium) Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus, white Platinum Plutonium Polonium Potassium (Kalium) Praseodymium Promethium Protactnium Radium Radon Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver (Argentum) Sodium (Natrium) Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin (Stannum) Titanium Tungsten (Wolfram) Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium a

Atomic International Symbol Number at. wt.a Mo Nd Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Sm Sc Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr

42 60 10 93 28 41 7 102 76 8 46 15 78 94 84 19 59 61 91 88 86 75 45 37 44 62 21 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 92 23 54 70 39 30 40

95.94 144.24 20.183 (237) 58.71 92.906 14.0067 (254) 190.2 15.9994 106.4 30.9738 195.09 (244) (209) 39.102 140.907 (145) (231) (226) (222) 186.2 102.905 85.47 101.07 150.35 44.956 78.96 28.086 107.868 22.9898 87.62 32.064 180.948 (97) 127.60 158.924 204.37 232.038 168.934 118.69 47.90 183.85 238.03 50.942 131.30 173.04 88.905 65.37 91.22

Specific Gravity (or density)

Melting Point, ˚C

10.22 7.00 0.90 g/l 18.0–20.45 8.90 8.57 1.251 g/l — 22.57 1.43 g/l 12.02 1.82 21.45 19.84 9.32 0.86 6.77 — (15.37) — 9.73 g/l 21.0 12.41 1.532 12.4 7.54 2.99 4.8 2.33 10.50 0.97 2.55 1.96–2.07 16.6 (11.50) 6.24 8.23 11.85 11.7 9.31 7.31 4.54 19.3 18.8 6.1 5.89 g/l 6.97 4.46 7. 6.53

2620. 1010. –249. 640. 1453. 2467. –210. — 3025. –218.4 1550. 44.1 1770. 640. 254. 63.3 931. 1080. — 700. –71. 3180. 1965. 39. 2400. 1072. 1539. 217. 1411. 961. 97.83 770. 113. 2980. 2172. 450. 1360. 304. 1750. 1545. 232. 1670. 3400. 1132. 1900. –112 824. 1523. 419.5 1852.

Boiling Point, ˚C 4651. 3127. –246. 3902. 2914. 4740. –196. — 4225. –183. 2927. 280. 3825. 3230. 962. 760. 3212. 2460. — 1700. –62. 5650. 3700. 700. 4100. 1778. 2832. 700. 3280. 2212. 884. 1375. 445. 5365. 4877. 990. 3041. 1480. 4800. 1727. 2600. 3290. 5550. 4140. 3400. –107. 1193. 3337. 910. 4400.

Specific Heat at 25˚C

Thermal Conductivity, watt/cm˚C

0.060 0.049 0.246 0.296 0.106 0.064 0.249 — 0.031 0.220 0.058 0.18 0.032 0.032 0.030 0.180 0.046 0.044 0.029 0.029 0.0224 0.033 0.058 0.086 0.057 0.047 0.135 0.077 0.17 0.057 0.293 0.072 0.175 0.034 0.058 0.05 0.0435 0.031 0.03 0.0385 0.054 0.125 0.032 0.028 0.116 0.038 0.071 0.0925 0.093 0.067

1.38 0.13 4.77 ¥ 10–4 — 0.905 0.53 2.55 ¥ 10–4 — 0.61 2.61 ¥ 10–4 0.71 — 0.73 0.08 — 0.99 0.12 — — — — 0.71 1.50 — — — — 0.005 0.835 4.27 1.34 — 26.4 ¥ 10–4 0.575 — 0.059 — 0.39 0.41 — 0.67 0.22 1.78 0.25 0.60 5.2 ¥ 10–4 — 0.15 1.21 0.227

Value in parentheses is the mass number of the most stable isotope of the element. At 28 atm. From Bolz, R.E. and Tuve, G.L., Basic chemical data, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 329–330. b

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CRC Handbook of Engineering Tables

Additional Properties of the Chemical Elements

Atomic Number

Latent Heat of Fusion, cal/g

Actinium (227) Aluminum American (243) Antimony Argon

89 13 95 51 18

Arsenic Astatine Barium Berkelium Beryllium

Name

Coef. of Linear Thermal Expansion ¥ 106, K–1

Elasticity Modulus, psi ¥ 10–6

First Ionization Potential, eV

Thermal Neutron Absorption Cross Section, Barnsa

6.9 5.984 — 8.639 15.755

510. 0.24 — 5.7 0.66

100

300

500

11 95 10 38.5 6.7

— 12.5 — 9 —

— 24 — 9.5 —

— 27 — 10.5 —

— 10.0 — 11.3 —

33 85 56 97 4

88.5 — 13.4 — 324

— — — — —

4.7 — 16 — 12

— — 24 — 15

— — — — 40–44

Bismuth Boron Bromine Cadmium Calcium

83 5 35 48 20

12.4 400 16.2 13.2 52

12 — — 26 17.5

13 2 — 30 23

13.5 — — 38 26

4.6 64 — 8 3.2–3.8

Californium (251) Carbon (Graphite) Cerium Cesium Chlorine

98 6 58 55 17

— — 9 3.8 2.16

— — — — —

— — 8 97 —

— — — — —

Chromium Cobalt Columbium See Niobium Copper Curium (247)

24 27

79 66

3.5 —

6 12

9.5 13

36 30

6.764 7.86

3.1 38.

29 96

49 —

10.5 —

16.5 —

18 —

17 —

7.724 —

3.8 —

Dysprosium Einsteinium (254) Erbium Europium Fermium

66 99 68 63 —

26.4 — 24.6 16.9 —

— — — — —

9.0 — 9.0 26 —

— — — — —

9.2 — 10.6 2.1 —

6.8 — 6.08 5.67 —

Fluorine Francium Gadolinium Gallium Germanium

9 87 64 31 32

10.1 — 16.4 19.2 114

— — — — 2.5

— — 4 18 5.6

— — — — 6.5

— — 8.1 — —

17 418 4 6.16 6 7.88

Gold Hafnium Helium Holmium Hydrogen

79 72 2 67 1

15 34 1.2 — 15.0

11.5 — — — —

14 6 — — —

15 — — — —

10.8 20 — 9.7 —

9.22 7 24.481 — 13.595

98.8 105. 0.007 65. 0.33

Indium Iodine Iridium Iron Krypton

49 53 77 26 36

6.8 15 33 65 4.7

25 — 4 6 —

33 93 6.5 12 —

— — 7.5 14.5 —

— — 75 28.5 —

5.785 10.454 9 7.87 13.996

191. 7.0 425. 2.6 31.

57 103

10 —

— —

5 —

6.5 —

5.5 —

5.61 —

Lanthanum Lawrencium

© 2004 by CRC Press LLC

— 0.7 4.4 — —

9.81 9.5 5.21 — 9.32

4.3 — 1.2 — 0.01

7.287 8.296 11.84 8.991 6.111

0.034 755 6.7 2450. 0.44

— 11.256 5.6 3.893 13.01

— 0.004 0.73 30.0 34.

950. — 170. 4300. — 0.01 — 46,000 2.8 2.45

8.9 —

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Additional Properties of the Chemical Elements (continued)

Name

Atomic Number

Latent Heat of Fusion, cal/g

82 3 71

Coef. of Linear Thermal Expansion ¥ 106, K–1

Elasticity Modulus, psi ¥ 10–6

First Ionization Potential, eV

Thermal Neutron Absorption Cross Section, Barnsa

100

300

500

5.5 103 26.4

25 23 —

29 50 —

32 — —

2.0 — 12.2

7.415 5.39 —

0.18 71. 112.

12 25 101 80 42

88.0 64 — 2.7 69

15 11.5 — — 3

25 23 — — 5

29 28 — — 5.5

6.4 23 — — 40

7.644 7.432 — 10.43 7.10

0.07 13.3 — 375. 2.7

60 10 93 28 41

13 4.0 9.7 71 68

— — — 6.5 5

7 — — 13 7

7.5 — — 15.5 7.5

5.5 — — 31 15

5.51 21.559 — 7.633 6.88

46. <2.8 (170) 4.6 1.15

7 102 76 8 46

6.2 — 34 3.3 38

— — — — 8.5

— — 5 — 12

— — 5.5 — 13

— — 80 — 17

14.53 — 8.5 13.614 8.33

Phosphorus Platinum Plutonium (244) Polonium Potassium

15 78 94 84 19

4.8 24 3 11 14.5

— 6.8 — — —

125 8.9 54 — 83

— 9.5 — — —

— 21.3 14 — —

10.484 9.0 5.1 8.43 4.339

Praseodymium Promethium Protactinium (231) Radium (226) Rodon (222)

59 61 91 88 86

17 — 17 10 3.1

— — — — —

5. — — — —

5.3 — — — —

4.7 6.1 — — —

5.46 — — 5.277 10.746

11.3 — (200) (20) (0.7)

Rhenium Rhodium Rubidium Ruthenium Samarium

75 45 37 44 62

42 50 6.3 60 24.7

— 5.0 — — —

7 8.3 90 9 —

— 9.3 — — —

66.7 42 — 60 4.9

7.87 7.46 4.176 7.364 5.6

85. 150. 0.7 2.6 5600.

Scandium Selenium Silicon Silver Sodium

21 34 14 47 11

87 16 430 26.5 27

— — — 14.3 45.7

— 35 2.5 19.0 70.0

— — 3.5 20.6 —

11.5 8.4 16 10.5 —

6.54 9.75 8.149 7.574 5.138

24. 12.3 0.160 63. .53

Strontium Sulfur Tantalum Technetium Tellurium

38 16 73 43 52

25 9.2 41 56.7 33

— 42 5.2 — —

— 63 6.6 — 17

— — 6.9 — —

— — 27 — 17

5.692 10.357 7.88 7.28 9.01

1.21 0.52 21. 22. 4.7

Terbium Thallium Thorium Thulium Tin

65 81 90 69 50

23.6 5.0 17 26.0 14.1

— 24 8.7 — 15.5

7.0 29 11.4 — 21

— 32 12.5 — 27.5

8.3 — 8.5 11.0 6

5.98 6.106 6.95 5.81 7.342

46. 3.4 7.5 127. 0.63

Lead Lithium Lutetium Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium Neon Neptunium (237) Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium

© 2004 by CRC Press LLC

1.9 — 15.3 <0.000 2 8. 0.2 8.8 — — 2.1

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Additional Properties of the Chemical Elements (continued)

Atomic Number

Latent Heat of Fusion, cal/g

Titanium Tungsten Uranium Vanadium Xenon

22 74 92 23 54

Ytterbium Yttrium Zinc Zirconium

70 39 30 40

Name

a

Coef. of Linear Thermal Expansion ¥ 106, K–1

Elasticity Modulus, psi ¥ 10–6

First Ionization Potential, eV

Thermal Neutron Absorption Cross Section, Barnsa

100

300

500

100 46 12 98 4.2

4.4 2.7 10.6 4 —

8.6 4.4 13.5 8 —

9.8 4.6 17 — —

16 50 24 19 —

6.82 7.98 6.08 6.74 12.127

5.8 19. 7.7 5. 35.

12.7 45 27 54

— — 23 3.9

25 — 30 5.5

26.3 — 32 6.2

2.6 9.4 12 13.7

6.2 6.38 9.391 6.84

37. 1.3 1.10 0.18

Values in parentheses apply only to that isotope for which the mass number is given following the name of the element. All other values of neutron cross section apply to the naturally occurring mixture of isotopes. From Bolz, R.E. and Tuve, G.L., Basic chemical data, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 331–332.

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Available Stable Isotopes of the Elements Element and Mass No. Hydrogen 1 2 Helium 3 4 Lithium 6 7

Beryllium 9

Natural Abundance, Percent 99.985 0.015

0.00013 ~100.0

100.0

19.78 80.22

Carbon 12 13

98.99 1.11

Oxygen 16 17 18 Fluorine 19 Neon 20 21 22

Sodium 23 Magnesium 24 25 26 Aluminum 27 Silicon 28 29 30 Phosphorus 31

© 2004 by CRC Press LLC

Natural Abundance, Percent

Sulfur 32 33 34 36

95.0 0.76 4.22 0.014

Chlorine 35 37

75.53 24.47

7.42 92.58

Boron 10 11

Nitrogen 14 15

Element and Mass No.

99.63 0.37

99.76 0.04 0.20 100.0

90.92 0.26 8.82

100.0

78.70 10.13 11.17

Argon 36 38 40

0.34 0.06 99.60

Potassium 39 40a 41

93.1 0.01 6.9

Calcium 40 42 43 44 46 48

96.97 0.64 0.14 2.06 0.003 0.18

Scandium 45 Titanium 46 47 48 49 50

Vanadium 50b 51 Chromium 50 52 53 54

100.0 7.93 7.28 73.94 5.51 5.34

0.24 99.76

4.31 83.76 9.55 2.38

100.0 Manganese 55 92.21 4.70 3.09

100.0

Iron 54 56 57 58

100.0

5.82 91.66 2.19 0.33

Element and Mass No. Cobalt 59

Natural Abundance, Percent 100.0

Nickel 58 60 61 62 64

67.84 26.33 1.19 3.66 1.08

Copper 63 65

69.09 30.91

Zinc 64 66 67 68 70

48.89 27.81 4.11 18.57 0.62

Gallium 69 71

60.4 39.6

Germanium 70 72 73 74 76 Arsenic 75

20.52 27.43 7.76 36.54 7.76 100.0

Selenium 74 76 77 78 80 82

0.87 9.02 7.58 23.52 49.82 9.19

Bromine 79 81

50.54 49.46

Krypton 78 80 82 83 84 86

0.35 2.27 11.56 11.55 56.90 17.37

Rubidium 85 87

72.15 27.85

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CRC Handbook of Engineering Tables

Available Stable Isotopes of the Elements (continued) Element and Mass No. Strontium 84 86 87 88 Yttrium 89 Zirconium 90 91 92 94 96 Niobium 93 Molybdenum 92 94 95 96 97 98 100 Ruthenium 96 98 99 100 101 102 104 Rhodium 103 Palladium 102 104 105 106 108 110 Silver 107 109 Cadmium 106 108 110 111 112

© 2004 by CRC Press LLC

Natural Abundance, Percent 0.56 9.86 7.02 82.56

100.0 51.46 11.23 17.11 17.40 2.80

100.0

15.84 9.04 15.72 16.53 9.46 23.78 9.63

5.51 1.87 12.72 12.62 17.07 31.61 18.60

100.0

0.96 10.97 22.23 27.33 26.71 11.81 51.82 48.18

1.22 0.88 12.39 12.75 24.07

Element and Mass No. Cadmium (cont.) 113 114 116 Indium 113 115c Tin 112 114 115 116 117 118 119 120 122 124

Natural Abundance, Percent 12.26 28.86 7.58

4.28 95.72 0.96 0.66 0.35 14.30 7.61 24.03 8.58 32.85 4.72 5.94

Antimony 121 123

57.25 42.75

Tellurium 120 122 123 124 125 126 128 130

0.09 2.46 0.87 4.61 6.99 18.71 31.79 34.48

Iodine 127 Xenon 124 126 128 129 130 131 132 134 136 Cesium 133 Barium 130 132 134 135

100.0

0.096 0.090 1.92 26.44 4.08 21.18 26.89 10.44 8.87

Element and Mass No. Barium (cont.) 136 137 138 Lanthanum 138 139 Cerium 136 138 140 142d Praseodymium 141

Natural Abundance, Percent 7.81 11.30 71.66

0.09 99.91 0.193 0.250 88.48 11.07

100.0

Neodymium 142 143 144 145 146 148 150 Samarium 144 147e 148f 149g 150 152 154

3.09 14.97 11.24 13.83 7.44 26.72 22.71

Europium 151 153

47.82 52.18

Gadolinium 152h 154 155 156 157 158 160

0.20 2.15 14.73 20.47 15.68 24.87 21.90

Terbium 159

27.11 12.17 23.85 8.30 17.22 5.73 5.62

100.0

100.0

0.101 0.097 2.42 6.59

Dysprosium 156i 158 160 161 162

0.052 0.090 2.29 18.88 25.53

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Available Stable Isotopes of the Elements (continued) Element and Mass No. Dysprosium (cont.) 163 164 Holmium 165

Erbium 162 164 166 167 168 170 Thulium 169 Ytterbium 168 170 171 172 173 174 176 Lutetium 175 176j Hafnium 174k 176 177 178 a b c d e f g h i

Half-life = 1.3 ¥ 109y. Half-life > 1015y. Half-life = 5 ¥ 1014y. Half-life = 5 ¥ 1015y. Half-life = 1.06 ¥ 1011y. Half-life = 1.2 ¥ 1013y. Half-life = 4 ¥ 1014y. Half-life = 1.1 ¥ 1014y. Half-life = 2 ¥ 1014y.

Natural Abundance, Percent 24.97 28.18

100.0

0.136 1.56 33.41 22.94 27.07 14.88

100.0

0.135 3.03 14.31 21.82 16.13 31.84 12.73

97.40 2.60

0.18 5.20 18.50 27.14

Element and Mass No.

Natural Abundance, Percent

Hafnium (cont.) 179 180

13.75 35.24

Tantalum 180 181

0.012 99.988

Element and Mass No. Platinum (cont.) 195 196 198 Gold 197

Natural Abundance, Percent 33.8 25.3 7.2

100.0

Mercury 196 198 199 200 201 202 204

0.146 10.02 16.84 23.13 13.22 29.80 6.85

Tungsten 180 182 183 184 186 Rhenium 185 187l

37.07 62.93

Thallium 203 205

29.50 70.50

Osmium 184 186 187 188 189 190 192

0.018 1.59 1.64 13.3 16.1 26.4 41.0

Lead 204 206 207 208

1.48 23.6 22.6 52.3

0.14 26.41 14.40 30.64 28.41

Bismuth 209

100.0

100.0

Iridium 191 193

37.3 62.7

Thorium 232n†

Platinum 190m 192 194

0.013 0.78 32.9

Uranium 234o† 235p† 238q†

0.0006 0.72 99.27

Half-life = 2.2 ¥ 1010y. Half-life = 4.3 ¥ 1015y. l Half-life = 4 ¥ 1010y. m Half-life = 6 ¥ 1011y. n Half-life = 1.4 ¥ 1010y. o Half-life = 2.5 ¥ 105y. p Half-life = 7.1 ¥ 108y. q Half-life = 4.5 ¥ 109y. † Naturally occurring. j

k

Reference CRC Handbook of Radioactive Nuclides, Y. Wang, Ed., The Chemical Rubber Co., 1969, pp. 25–63. From Bolz, R.E. and Tuve, G.L., Basic chemical data, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 334–336.

© 2004 by CRC Press LLC

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Energy Absorption Mass Attenuation Coefficient In cm2/g Only a fraction of the events represented by the total attenuation cross section actually removes the gamma-ray. In particular, Compton scattering can cause a change in the direction and the energy of a photon without absorbing it. The energy absorption mass attenuation coefficient (me/r) is a measure of the fraction of the gamma-ray energy that is converted from radiant energy into heat. The product of these coefficients and of the density of the material gives the energy absorption cross section. Gamma-Ray Energy, Mev Material

0.1

0.2

0.5

1.0

2

5

10.0

H Be C N O

.0411 .0183 .0215 .0224 .0233

.0531 .0237 .0267 .0267 .0271

.0591 .0264 .0297 .0297 .0297

.0557 .0248 .0280 .0280 .0280

.0467 .0210 .0237 .0236 .0238

.0318 .0151 .0177 .0180 .0183

.0255 .0118 .0145 .0151 .0157

Na Mg Al Si P

.0289 .0335 .0373 .0435 .0501

.0266 .0278 .0275 .0286 .0292

.0284 .0293 .0286 .0290 .0290

.0268 .0276 .0270 .0274 .0271

.0229 .0237 .0232 .0236 .0234

.0185 .0194 .0192 .0198 .0200

.0168 .0180 .0182 .0189 .0195

S A K Ca Fe

.0601 .0729 .0909 .111 .225

.0310 .0302 .0340 .0367 .0489

.0300 .0272 .0295 .0304 .0294

.0279 .0252 .0272 .0279 .0261

.0242 .0220 .0237 .0244 .0231

.0209 .0195 .0214 .0222 .0227

.0206 .0197 .0219 .0231 .0250

Cu Mo Sn I W

.310 .922 1.469 1.726 4.112

.0594 .141 .222 .260 .631

.0296 .0348 .0403 .0433 .0786

.0260 .0263 .0268 .0274 .0353

.0229 .0233 .0233 .0236 .0271

.0231 .0262 .0276 .0283 .0335

.0261 .0316 .0339 .0353 .0426

Pt Tl Pb U Air

4.645 5.057 5.193 9.63 .0233

.719 .791 .821 1.096 .0268

.0892 .0972 .0994 .132 .0297

.0375 .0393 .0402 .0482 .0280

.0280 .0288 .0293 .0324 .0238

.0343 .0349 .0352 .0374 .0181

.0438 .0446 .0450 .0474 .0153

NaI H 2O Concrete Tissue

1.466 .0253 .0416 .0271

.224 .0300 .0289 .0293

.0410 .0330 .0296 .0320

.0273 .0311 .0278 .0300

.0235 .0264 .0239 .0256

.0268 .0198 .0194 .0192

.0325 .0165 .0177 .0160

From Bolz, R.E. and Tuve, G.L., Reactors and materials, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 466. Originally from Reactor Physics Constants, 2nd ed., Argonne National Laboratory, ANL-5800, U.S. Atomic Energy Commission, July 1963.

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Gamma-Ray Absorption Cross Section In cm–1

Material

Density, g/cm3

Gamma-Ray Energy, Mev 0.1

0.2

0.5

1.0

2

5

10.0

Be C Na Mg Al

1.85 2.25 .9712 1.741 2.70

.0339 .0484 .0281 .0583 .1007

.0438 .0601 .0258 .0484 .0743

.0488 .0668 .0276 .0510 .0772

.0459 .0630 .0260 .0481 .0729

.0389 .0533 .0222 .0413 .0626

.0279 .0398 .0180 .0338 .0518

.0218 .0326 .0163 .0313 .0491

Si P S K Ca

2.42 1.83 2.07 0.87 1.55

.1053 .0917 .1244 .0791 .172

.0692 .0534 .0642 .0296 .0569

.0702 .0531 .0621 .0257 .0471

.0663 .0496 .0578 .0237 .0432

.0571 .0428 .0501 .0206 .0378

.0479 .0366 .0433 .0186 .0344

.0457 .0357 .0426 .0191 .0358

Fe Cu Mo Sn I

7.86 8.933 9.01 7.298 4.94

.3844 .5306 1.270 1.620 1.284

.2311 .2644 .3155 .2941 .2139

.2051 .2323 .2370 .1956 .1354

.1816 .2046 .2099 .1700 .1166

.1784 .2064 .2361 .2014 .1398

.1965 .2332 .2847 .2474 .1744

.6813 .8014 .4661 .4559 .9013

.5320 .5984 .3416 .3323 .6059

.6466 .7330 .4139 .3992 .6994

.8222 .9360 .5290 .5103 .8864

.1001 .0311 .0653

.0862 .0264 .0562

.0983 .0198 .0456

.1192 .0165 .0416

W Pt Tl Pb U NaI H 2O Concrete

19.3 21.37 11.86 11.34 18.7 3.667 1.00 2.35

1.769 2.769 8.307 10.721 8.704 79.362 99.264 59.976 58.889 180.08 5.376 .0253 .0978

12.178 15.365 9.381 9.310 20.495 .8214 .0300 .0679

1.517 1.906 1.153 1.127 2.468 .1503 .0330 .0697

From Bolz, R.E. and Tuve, G.L., Reactors and materials, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 467. Originally from Reactor Physics Constants, 2nd ed., Argonne National Laboratory, ANL-5800, U.S. Atomic Energy Commission, July 1963.

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Removal Cross Sections for Various Materials The removal cross section is a measure of the ability of a material to remove fast neutrons for shielding attenuation. It is most often applied to a wall of solid material between the fission source and a layer of water or hydrogenous material. The solid wall reduces the neutron energy to such an extent that it will be thermalized and captued in the water. Symbols: sR = microscopic removal cross section, barns/atom SR = macroscopic removal cross section per cm

Material

sR, Barn

N0 at 20˚C, atom/cm3

SR, cm–1

Material

sR, Barn

N0 at 20˚C, atom/cm3

SR, cm–1

Hydrogen Deuterium Lithium Beryllium Boron

1.00 ± 0.05 — 0.92 ± 0.10a — 1.01 ± 0.04 0.0460 ¥ 1024 1.07 ± 0.06 0.120 0.97 ± 0.10 0.139

— — 0.146 0.128 0.135

Lead Bismuth Uranium Boric Acid (B2O3) Boron carbide (B4C)

3.53 ± 0.30 3.49 ± 0.35 3.6 ± 0.4 4.30 ± 0.41 5.1 ± 0.4

0.0330 0.0282 0.0473 — —

0.116 0.098 0.17 — —

Carbon (graphite) Oxygen Fluorine Aluminum Chlorine

0.72 ± 0.05 0.92 ± 0.05 1.29 ± 0.06 1.31 ± 0.05 1.2 ± 0.8

0.113 — — 0.0603 —

0.081 — — 0.079 —

Fluorothene (C2F3Cl) Heavy water (D2O) Lithium fluoride (LiF) Oil (CH2) Paraffin (C30H62)

6.66 ± 0.8 2.76 ± 0.11 2.43 ± 0.34 2.84 ± 0.11 80.5 ± 5.2

— — — — —

— — — — —

Iron Nickel Copper Zirconium Tungsten

1.98 ± 0.08 1.89 ± 0.10 2.04 ± 0.11 2.36 ± 0.12 3.13 ± 0.25

0.0848 0.0913 0.,0846 0.0423 0.0631

0.168 0.173 0.173 0.10 0.198

Perfluoroheptane (C7F16)

26.3 ± 0.8

—

—

a

Calculated: sR(D2O) = 2.76 b.

Reference “Effective Neutron Removal Cross Sections for Shielding,” G.T. Chapman and C.L. Storrs, AECD-3978 (ORNL-1843), September 19, 1955. From Bolz, R.E. and Tuve, G.L., Reactors and materials, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 467. Originally from Reactor Physics Constants, 2nd ed., Argonne National Laboratory, ANL-5800, U.S. Atomic Energy Commission, July 1963.

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Diffusion of Gases and Vapors into Air Values of Diffusion Constant and Schmidt Number at 1 atm Pressure

Substance

Diffusion Constant, D, sq ft/hr 0˚C 25˚C

H2 NH3 N2 O2 CO2

2.37 0.766 0.691 0.689 0.550

2.76 0.886

CS2 Methyl alcohol Formic acid Acetic acid Ethyl alcohol

Diffusion Constant, D, sq cm/sec 0˚C 25˚C 0.712 0.229

0.80 0.635

0.611 0.198 0.178 0.178 0.142

0.36 0.513 0.509 0.411 0.394

0.414 0.615 0.615 0.515 0.461

Chloroform Diethylamine n-Propyl alcohol Propionic acid Methyl acetate

0.352 0.342 0.329 0.328 0.325

Butylamine Ethyl ether Benzene Ethyl acetate Toluene

(m/rD)† 0˚C 25˚C 0.216 0.673

0.206 0.164

0.217 0.669 0.744 0.744 0.933

0.094 0.132 0.131 0.106 0.102

0.107 0.159 0.159 0.133 0.119

1.41 1.00 1.01 1.25 1.30

1.44 0.969 0.969 1.16 1.29

0.406 0.387 0.383 0.387

0.091 0.0884 0.085 0.0846 0.0840

0.105 0.100 0.099 0.100

1.46 1.50 1.56 1.57 1.58

1.47 1.54 1.56 1.54

0.318 0.304 0.291 0.277 0.274

0.391 0.360 0.341 0.330 0.325

0.0821 0.0786 0.0751 0.0715 0.0709

0.101 0.093 0.088 0.085 0.084

1.61 1.69 1.76 1.85 1.87

1.53 1.66 1.75 1.81 1.83

n-Butyl alcohol i-Butyric acid Chlorobenzene Aniline Xylene

0.272 0.263

0.0703 0.0679 0.0610 0.059

0.090 0.081 0.073 0.072 0.071

1.88 1.95

0.236 0.228

0.348 0.313 0.283 0.279 0.275

2.17 2.25

1.71 1.90 2.11 2.14 2.17

Amyl alcohol n-Octane Naphthalene

0.228 0.195 0.199

0.271 0.232 0.20

0.0589 0.0505 0.0513

0.070 0.060 0.052

2.25 2.62 2.58

2.20 2.57 2.96

0.748 0.940

† Based on m/r = 0.1325 sq cm/sec for air at 0˚C and 0.1541 sq cm/sec for air at 25˚C; applies only when the diffusing gas or vapor is very dilute. From Bolz, R.E. and Tuve, G.L., Heat and mass transfer, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 546.

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Speed of Sound in Water and Steam (m·s–1) Pressure (MPa) t (˚C)

0.01

0.02

0.05

0.1

0.2

0.5

1

2

5

Sat. Liq. 1540.0 1553.8 1556.6 1545.5 1520.7 1462.0 1391.6 1290.6 1088.4 Sat. Vap. 440.5 449.5 462.2 472.1 481.9 493.8 500.9 504.7 498.2

10

20

847.7 472.4

422.2 384.5

50

75

100

0 10 20

1402.3 1402.3 1402.4 1402.4 1402.6 1403.1 1403.8 1405.4 1410.2 1418.2 1434.5 1485.9 1530.6 1447.4 1447.4 1447.5 1447.6 1447.7 1448.2 1449.0 1450.6 1455.3 1463.3 1479.6 1530.0 1573.3 1483.3 1483.3 1483.3 1483.4 1483.6 1484.0 1484.8 1486.4 1491.2 1499.2 1515.3 1564.9 1607.2

1575.5 1616.8 1649.6

25

1498.0 1498.0 1498.1 1498.2 1498.3 1498.8 1499.6 1501.2 1506.0 1514.0 1530.1 1579.5 1621.4

1663.4

30 40 50

1510.8 1510.9 1510.9 1511.0 1511.1 1511.6 1512.4 1514.0 1518.8 1526.8 1543.0 1592.3 1634.1 1531.2 1531.2 1531.2 1531.3 1531.5 1531.9 1532.8 1534.4 1539.2 1547.4 1563.7 1613.3 1655.0 443.7 1545.2 1545.2 1545.3 1545.5 1546.0 1546.8 1548.5 1553.5 1561.8 1578.4 1628.7 1670.8

1675.8 1696.4 1712.2

60 70 80 90 100

450.7 1553.7 1553.8 1553.9 1554.0 1554.5 457.5 456.7 1557.5 1557.6 1557.8 1558.3 464.1 463.4 1557.0 1557.1 1557.2 1557.8 470.5 470.0 468.3 1552.8 1553.0 1553.5 476.9 476.4 475.0 472.3 1545.3 1545.9

110 120 130 140 150

483.1 489.2 495.3 501.2 507.1

482.7 488.9 495.0 500.9 506.8

160 170 180 190 200

512.8 518.5 524.1 529.7 535.1

220 240 260 280 300

1562.3 1566.3 1566.2 1562.3 1555.1

1570.8 1575.2 1575.4 1571.9 1565.1

1587.9 1592.9 1593.7 1591.0 1585.0

1639.3 1645.6 1648.1 1647.2 1643.2

1682.0 1689.1 1692.6 1692.8 1690.1

1723.7 1731.3 1735.4 1736.3 1734.4

481.4 487.8 494.0 500.1 506.0

479.3 1534.6 1535.2 1536.3 1538.4 1544.8 485.9 1521.0 1521.7 1522.8 1525.1 1531.8 492.3 488.8 1505.6 1506.8 1509.2 1516.3 498.6 495.5 1487.0 1488.3 1490.8 1498.4 504.7 502.0 1466.0 1467.4 1470.1 1478.1

1555.4 1543.0 1528.0 1510.7 1491.2

1576.2 1564.7 1550.8 1534.7 1516.5

1636.5 1627.4 1616.0 1602.5 1587.2

1684.8 1677.1 1667.4 1655.6 1642.2

1730.0 1723.4 1714.7 1704.3 1692.1

512.6 518.3 523.9 529.5 535.0

511.9 517.7 523.4 529.0 534.5

510.7 516.6 522.4 528.1 533.7

508.3 514.4 520.4 526.3 532.0

500.2 1444.3 1447.2 1455.7 1469.6 1496.2 507.3 1418.9 1422.0 1431.1 1445.8 1474.0 514.1 501.0 1394.6 1404.3 1420.1 1450.0 520.6 509.7 1365.0 1375.4 1392.2 1424.0 526.8 517.3 1333.2 1344.3 1362.3 1396.2

1570.1 1551.4 1531.0 1509.1 1485.8

1627.1 1610.4 1592.4 1572.9 1552.2

1678.5 1663.6 1647.3 1629.8 1611.2

545.8 556.3 566.0 576.6 586.4

545.7 556.2 566.5 576.5 586.3

545.3 555.9 566.2 576.2 586.1

544.6 555.3 565.6 575.8 585.7

543.2 554.1 564.6 574.9 584.9

538.9 550.4 561.5 572.2 582.6

531.2 544.0 556.1 567.5 578.5

512.6 1275.4 1296.1 1334.8 1434.7 1506.9 529.5 1197.1 1221.1 1265.7 1378.0 1457.1 544.1 1107.7 1136.3 1188.5 1316.0 1402.9 557.4 518.9 1038.9 1102.1 1249.0 1345.1 569.9 538.8 922.8 1004.3 1177.3 1284.3

1570.7 1526.2 1478.1 1426.9 1373.4

320 340 360 380 400

596.0 605.4 614.6 623.7 632.6

595.9 605.3 614.5 623.6 632.5

595.7 605.1 614.4 623.5 632.4

595.4 604.8 614.1 623.2 632.2

594.7 604.2 613.6 622.8 631.8

592.6 602.4 612.0 621.3 630.5

589.1 599.3 609.2 618.9 628.3

581.7 592.9 603.6 613.9 623.9

555.8 570.9 584.8 597.6 609.6

491.7 522.2 545.5 565.0 582.0

890.3 1101.5 1221.3 751.1 1021.7 1157.0 542.7 936.0 1091.6 461.3 846.8 1023.5 507.3 755.1 955.9

1318.5 1263.0 1207.4 1150.7 1093.3

420 440 460 480 500

641.3 649.9 658.4 666.7 674.9

641.3 649.9 658.3 666.6 674.8

641.2 649.8 658.2 666.6 674.8

641.0 649.6 658.1 666.4 674.6

640.6 649.2 657.8 666.1 674.4

639.4 648.2 656.8 665.3 673.6

637.5 646.5 655.3 663.9 672.3

633.5 642.9 652.1 661.0 669.8

620.9 631.7 642.1 652.1 661.8

597.3 611.3 624.2 636.4 647.9

538.7 563.4 584.1 602.3 618.6

666.1 593.6 556.7 554.8 568.9

890.2 828.7 774.3 730.1 698.6

1037.2 983.7 934.4 890.4 852.7

520 540 560 580 600

682.9 690.9 698.7 706.4 714.1

682.9 690.9 698.7 706.4 714.1

682.8 690.8 698.6 706.4 714.0

682.7 690.7 698.6 706.3 713.9

682.5 690.5 698.4 706.1 713.8

681.8 689.9 697.8 705.6 713.3

680.7 688.8 696.9 704.8 712.5

678.3 686.7 694.9 703.0 711.0

671.2 680.3 689.2 697.8 706.3

658.8 669.3 679.4 689.1 698.5

633.5 647.2 660.1 672.2 683.7

588.1 607.7 626.2 643.4 659.2

680.3 673.0 674.1 679.5 687.4

821.9 798.0 781.0 770.0 766.5

620 640 660 680 700

721.6 729.0 736.4 743.6 750.8

721.6 729.0 736.3 743.6 750.7

721.5 729.0 736.3 743.6 750.7

721.5 728.9 736.3 743.5 750.7

721.3 728.8 736.1 743.4 750.6

720.9 728.4 735.8 743.1 750.3

720.2 727.8 735.2 742.6 749.9

718.8 726.5 734.1 741.6 749.0

714.6 722.8 730.7 738.6 746.3

707.7 716.6 725.3 733.7 742.0

694.7 705.2 715.3 725.0 734.5

673.9 687.7 700.7 713.1 725.0

697.2 707.9 718.9 730.0 741.0

762.8 764.7 770.5 777.3 784.1

© 2004 by CRC Press LLC

1555.4 1559.2 1558.7 1554.5 1546.9

1557.1 1561.0 1560.6 1556.5 1549.0

1587_Book.fm Page 101 Monday, September 1, 2003 7:17 PM

3-101

Chemical Engineering, Chemistry, and Materials Science

Speed of Sound in Water and Steam (m·s–1) (continued) Pressure (MPa) t (˚C) 720 740 760 780 800

0.01

0.02

0.05

0.1

0.2

0.5

1

2

5

10

20

50

75

757.8 764.8 771.8 778.6 785.3

757.8 764.8 771.8 778.6 785.3

757.8 764.8 771.7 778.6 785.3

757.8 764.8 771.7 778.6 785.3

757.7 764.7 771.6 778.5 785.2

757.4 764.5 771.4 778.3 785.1

757.0 764.1 771.1 778.1 784.9

756.2 763.4 770.5 777.5 784.4

753.9 761.3 768.7 776.0 783.2

750.1 758.1 765.9 773.6 781.3

743.6 752.6 761.2 769.7 778.0

736.3 747.2 757.7 767.7 777.4

751.9 762.5 772.8 782.6 791.8

2

5

10

20

50

75

126.1 16.1

100.0 18.0

81.8 20.3

56.2 27.5

100 790.9 797.9 805.2 812.8 821.0

From ASME International Steam Tables for Industrial Use.

Dynamic Viscosity of Water and Steam (mPa·s) t (˚C)

0.01

0.02

0.05

0.1

0.2

Sat. Liq. Sat. Vap.

587.6 10.5

466.0 10.9

348.6 11.6

282.9 12.3

231.6 13.0

0 10 20

Pressure (MPa) 0.5 1 180.1 14.1

150.2 15.0

100

1791.8 1791.7 1791.7 1791.5 1791.3 1790.5 1789.3 1786.8 1779.5 1767.9 1746.6 1696.5 1668.8 1652.0 1306.0 1306.0 1305.9 1305.9 1305.8 1305.4 1304.9 1303.8 1300.7 1295.7 1286.6 1266.4 1256.7 1252.7 1001.6 1001.6 1001.6 1001.6 1001.6 1001.4 1001.2 1000.8 999.6 997.7 994.4 988.4 987.2 989.3

25

890.1

890.1

890.1

890.1

890.1

890.0

889.9

889.6

889.0

888.0

886.4

884.5

885.9

889.7

30 40 50

797.4 653.0 10.6

797.4 653.0 546.8

797.4 653.0 546.8

797.3 653.0 546.9

797.3 653.0 546.9

797.3 653.0 546.9

797.3 653.1 547.0

797.2 653.1 547.2

796.9 653.4 547.7

796.6 653.9 548.6

796.2 655.0 550.6

797.2 659.7 557.2

800.4 665.0 563.5

805.4 671.4 570.6

60 70 80 90 100

10.9 11.3 11.6 12.0 12.3

466.4 11.3 11.6 12.0 12.3

466.4 403.9 354.3 11.9 12.3

466.4 403.9 354.4 314.4 12.3

466.4 403.9 354.4 314.4 281.8

466.5 404.0 354.5 314.5 281.9

466.6 404.1 354.6 314.7 282.0

466.8 404.4 354.9 314.9 282.3

467.5 405.1 355.6 315.7 283.1

468.6 406.4 357.0 317.1 284.4

471.0 409.0 359.6 319.7 287.1

478.6 417.0 367.8 327.9 295.1

485.4 423.9 374.7 334.7 301.7

492.6 431.1 381.7 341.5 308.4

110 120 130 140 150

12.7 13.1 13.5 13.8 14.2

12.7 13.1 13.5 13.8 14.2

12.7 13.1 13.4 13.8 14.2

12.6 13.0 13.4 13.8 14.2

254.7 232.1 13.3 13.7 14.1

254.8 232.1 213.0 196.6 182.5

254.9 232.3 213.1 196.7 182.6

255.2 232.5 213.3 197.0 182.8

256.0 233.3 214.1 197.7 183.6

257.3 234.6 215.4 199.0 184.9

260.0 237.2 218.0 201.5 187.3

267.8 244.9 225.5 208.9 194.6

274.3 251.2 231.6 214.8 200.4

280.7 257.4 237.6 220.6 206.0

160 170 180 190 200

14.6 15.0 15.4 15.8 16.2

14.6 15.0 15.4 15.8 16.2

14.6 15.0 15.4 15.8 16.2

14.6 15.0 15.4 15.8 16.2

14.5 14.9 15.3 15.7 16.1

14.4 14.8 15.2 15.6 16.1

170.3 159.6 15.0 15.5 15.9

170.6 159.9 150.4 142.0 134.4

171.3 160.6 151.1 142.7 135.2

172.6 161.8 152.4 143.9 136.4

175.0 164.2 154.8 146.3 138.8

182.1 171.2 161.7 153.2 145.6

187.8 176.8 167.1 158.5 150.9

193.3 182.1 172.3 163.7 155.9

220 240 260 280 300

17.0 17.8 18.6 19.5 20.3

17.0 17.8 18.6 19.5 20.3

17.0 17.8 18.6 19.5 20.3

17.0 17.8 18.6 19.5 20.3

17.0 17.8 18.6 19.4 20.3

16.9 17.7 18.6 19.4 20.2

16.8 17.6 18.5 19.3 20.2

16.5 17.4 18.3 19.2 20.1

122.2 111.3 101.8 18.8 19.8

123.5 112.6 103.2 94.7 86.5

125.9 115.2 105.9 97.7 90.1

132.7 122.1 113.1 105.4 98.5

137.9 127.3 118.4 110.8 104.1

142.8 132.1 123.2 115.6 109.1

320 340 360 380 400

21.1 22.0 22.8 23.6 24.5

21.1 22.0 22.8 23.6 24.5

21.1 22.0 22.8 23.6 24.5

21.1 22.0 22.8 23.6 24.5

21.1 21.9 22.8 23.6 24.4

21.1 21.9 22.8 23.6 24.4

21.0 21.9 22.7 23.6 24.4

21.0 21.8 22.7 23.5 24.4

20.7 21.7 22.6 23.5 24.4

20.7 21.7 22.6 23.6 24.5

82.5 74.2 62.8 25.8 26.0

92.2 86.2 80.3 74.3 68.0

98.2 92.8 87.7 82.8 78.0

103.3 98.2 93.4 89.0 84.8

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Dynamic Viscosity of Water and Steam (mPa·s) (continued) t (˚C)

0.01

0.02

0.05

0.1

0.2

Pressure (MPa) 0.5 1

2

5

10

20

50

75

100

420 440 460 480 500

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.3 26.1 26.9 27.8 28.6

25.2 26.1 27.0 27.8 28.7

25.4 26.3 27.2 28.0 28.9

26.7 27.4 28.2 29.0 29.8

61.2 53.9 47.4 43.0 40.5

73.2 68.5 64.0 59.6 55.8

80.7 76.8 73.0 69.4 66.1

520 540 560 580 600

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.0 31.8 32.6

29.4 30.2 31.1 31.9 32.7

29.5 30.4 31.2 32.0 32.8

29.8 30.6 31.4 32.3 33.1

30.7 31.5 32.3 33.1 33.9

39.3 38.8 38.7 38.8 39.1

52.6 50.2 48.5 47.3 46.6

63.0 60.3 58.0 56.2 54.7

620 640 660 680 700

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.4 34.2 35.0 35.8 36.6

33.5 34.3 35.1 35.9 36.6

33.6 34.4 35.2 36.0 36.8

33.9 34.7 35.5 36.3 37.1

34.7 35.5 36.3 37.1 37.8

39.5 40.0 40.5 41.1 41.6

46.1 46.0 45.9 46.1 46.3

53.6 52.7 52.2 51.8 51.6

720 740 760 780 800

37.3 38.1 38.9 39.6 40.4

37.3 38.1 38.9 39.6 40.4

37.3 38.1 38.9 39.6 40.4

37.3 38.1 38.9 39.6 40.4

37.3 38.1 38.9 39.6 40.4

37.3 38.1 38.9 39.6 40.4

37.4 38.1 38.9 39.7 40.4

37.4 38.2 38.9 39.7 40.5

37.6 38.3 39.1 39.9 40.6

37.8 38.6 39.4 40.1 40.9

38.6 39.4 40.1 40.9 41.6

42.2 42.9 43.5 44.1 44.7

46.6 46.9 47.3 47.8 48.2

51.5 51.5 51.7 51.9 52.1

From ASME International Steam Tables for Industrial Use.

© 2004 by CRC Press LLC

1587_Book.fm Page 1 Monday, September 1, 2003 7:17 PM

4 Mechanical Engineering Basic Mechanical Properties ......................................................................................................................4-3 Symbols and Definitions for Selected Properties .....................................................................................4-4 Heating Values in kJ/kg of Selected Hydrocarbons at 25°C.....................................................................4-4 Some Fuel Properties of Four Different Biomass Types ..........................................................................4-5 Physical Properties of Selected Ceramics ..................................................................................................4-5 Steel Pipe Sizes ...........................................................................................................................................4-6 Commercial Copper Tubing ......................................................................................................................4-7 Summary of Definitions ............................................................................................................................4-8 CAPP System Characteristics and Their Effects .......................................................................................4-9 System's View of the Injection Molding Process ....................................................................................4-10 Magnitude of Process Variation by Machine Input ...............................................................................4-11 Visualization of Accuracy, Repeatability, and Resolution ......................................................................4-11 Anthropomorphic Robot with Frame Assignment ................................................................................4-12 Denavit-Hartenberg Parameters of the Anthropomorphic Robot ........................................................4-12 Basic Grip and Trigger Concepts.............................................................................................................4-13 Examples of Specialization of Robot Designs ........................................................................................4-13 Typical Arm and Wrist Configurations of Industrial Robots ................................................................4-14 From Industrial Robots to Service Robots — The Evolution of Machine Intelligence .......................4-15 Scale of Things, In Meters. Lower Scale Continues in the Upper Bar from Left and Right ................4-16 Metals .......................................................................................................................................................4-17 Molecular and Continuum Flow Models................................................................................................4-17 Knudsen Number Regimes ......................................................................................................................4-18 The Operation Range for Typical MEMS and Nanotechnology Applications Under Standard Conditions Spans the Entire Knudsen Regime ..................................................................................4-18 Classification of Microrobots According to Size and Fabrication Technology .....................................4-19 Classification of Microrobots by Functionality ......................................................................................4-19 Thermal Conductivity, Coefficient of Thermal Expansion, Cost Estimates, and Scaling Trends of Current and Potential Substrate Materials .........................................................................................4-20 Tools for Soft Computing ........................................................................................................................4-20 Saturated Steam, Water, and Ice — SI Units ..........................................................................................4-21 Viscosity and Thermal Conductivity of Steam and Water — SI Units .................................................4-23 Properties of Gases...................................................................................................................................4-24 Mechanical Properties of Metals and Alloys ...........................................................................................4-34 Thermal Properties of Pure Metals — Metric Units ..............................................................................4-46 Terms and Units for Radiant Energy and Illumination .........................................................................4-48

4-1 © 2004 by CRC Press LLC

1587_Book.fm Page 2 Monday, September 1, 2003 7:17 PM

4-2

CRC Handbook of Engineering Tables

Blackbody Radiation ................................................................................................................................4-49 Thermodynamic Nonflow Process Equations ........................................................................................4-50 Thermodynamic Cycle Efficiencies .........................................................................................................4-51 Heat of Fusion of Some Inorganic Compounds ....................................................................................4-52 Conservation Equations of a Viscous, Heat-Conducting Fluid .............................................................4-59 Energy Conversions .................................................................................................................................4-65 Helical Steel Springs.................................................................................................................................4-66 Ultrasonic Energy and Applications .......................................................................................................4-68 Mechanical Components .........................................................................................................................4-69 Pneumatic Compensating Components .................................................................................................4-71 Dynamic Elements and Networks ...........................................................................................................4-73 Properties of Saturated Water and Steam (Temperature) ......................................................................4-76 Properties of Saturated Water and Steam (Pressure) .............................................................................4-81 Thermal Conductivity of Water and Steam (mW·m1·K–1) ....................................................................4-87

© 2004 by CRC Press LLC

1587_Book.fm Page 3 Monday, September 1, 2003 7:17 PM

4-3

Mechanical Engineering

Basic Mechanical Properties Symbol

Definition

Remarks

E

Modulus of elasticity; Young’s modulus; E = s/ee

Hooke’s law; T and ep effects small

G

t Shear modulus of elasticity; G = = E 2(1 + v) ge

T and ep effects small

v

Poisson’s ratio; v =

sPL sy

Proportional limit; at onset of noticeable yielding (or at onset of nonlinear elastic behavior) 0.2% offset yield strength (but yielding can occur at s < sy if sPL < sy)

sf

True fracture strength; s f =

ef

True fracture ductility; e f = ln

% RA

Percent reduction of area; %RA =

n

Strain hardening exponent; s = K e np

Flow property; T and ep effects small to large

Toughness

Area under s vs. ep curve

True toughness or intrinsic toughness; T and ep effects large

su

Ultimate strength;

Mr

Modulus of resilience; M r =

e lateral e longit .

T and ep effects small Flow property; inaccurate; T and ep effects large Flow property; accurate; T and ep effects large

Pf

Fracture property; T and ep effects medium

Af AO 100 = ln Af 100 – %RA AO - A f AO

Max. ep; fracture property; T and ep effects medium Fracture property; T and ep effects medium

¥ 100

Pmax AO

Fracture property; T and ep effects medium s 2PL 2E

Area under original elastic portion of s – e curve

Notes: T is temperature; ep refers to prior plastic strain, especially cyclic plastic strain (fatigue) (these are qualitative indicators here; exceptions are possible) et = ee + e p =

total

elastic

plastic

s Ê sˆ + E Ë K¯

1n

=

Ê s ˆ s +efÁ ˜ E Ësf ¯

1n

From Sandor, B.I., Mechanics of solids, in The CRC Handbook of Mechanical Engineering, Kreith, F., Ed., CRC Press, Boca Raton, FL, 1998, p. 1-75.

© 2004 by CRC Press LLC

1587_Book.fm Page 4 Monday, September 1, 2003 7:17 PM

4-4

CRC Handbook of Engineering Tables

Symbols and Definitions for Selected Properties Property

Symbol

Pressure

Definition

Property

Symbol

Definition

p

Specific heat, constant volume

cv

Temperature

T

Specific heat, constant pressure

cp

Specific volume

v

Volume expansivity

b

Specific internal energy

u

Isothermal compressivity

k

-

1 (∂v ∂p) T v

Specific entropy

s

Isentropic compressibility

a

-

1 (∂v ∂p) s v

Specific enthalpy

h

u + pv

Isothermal bulk modulus

B

- v(∂p ∂v) T

Specific Helmholtz function

y

u – Ts

Isentropic bulk modulus

Bs

Specific Gibbs function

g

h – Ts

Joule-Thomson coefficient

mJ

Compressibility factor

Z

pv/RT

Joule coefficient

h

Specific heat ratio

k

cp /cv

Velocity of sound

c

(∂u ∂T ) v (∂h ∂T ) p 1 (∂v ∂T ) p v

- v(∂p ∂v) s

(∂T ∂p) h (∂T ∂v)u

- v 2 (∂p ∂v) s

From Moran, M.J., Property relations and data, in The CRC Handbook of Mechanical Engineering, Kreith, F., CRC Press, Boca Raton, FL, 1998, p. 2-25.

Heating Values in kJ/kg of Selected Hydrocarbons at 25°C Higher Valuea

Lower Valueb

Hydrocarbon

Formula

Liquid Fuel

Gas. Fuel

Liquid Fuel

Gas. Fuel

Methane Ethane Propane n-Butane n-Octane n-Dodecane Methanol Ethanol

CH4 C 2H 6 C 3H 8 C4H10 C8H18 C12H26 CH3OH C3H5OH

— — 49,973 49,130 47,893 47,470 22,657 29,676

55,496 51,875 50,343 49,500 48,256 47,828 23,840 30,596

— — 45,982 45,344 44,425 44,109 19,910 26,811

50,010 47,484 46,352 45,714 44,788 44,467 21,093 27,731

a

H2O liquid in the products. H2O vapor in the products. From Moran, M. J., Combustion, in The CRC Handbook of Mechanical Engineering, Kreith, F., CRC Press, Boca Raton, FL, 1998, p. 2-62. b

© 2004 by CRC Press LLC

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Mechanical Engineering

Some Fuel Properties of Four Different Biomass Types Property

Pine Shavings

Switchgrass

Rice Hull

Rice Straw

Ash % Carbon Hydrogen Nitrogen Sulfur Oxygen Btu/lb GJ/t

1.43 48.54 5.85 0.47 0.01 43.69 8337 19.38

10.10 47.79 5.76 1.17 0.10 35.07 7741 17.99

18.34 40.96 4.30 0.40 0.02 35.86 6944 16.14

15.90 41.78 4.63 0.70 0.08 36.57 7004 16.28

From Reed, M.C., Wright, L.L., Overend, R.P., and Carlton, W., Biomass energy, in The CRC Handbook of Mechanical Engineering, Kreith, F., CRC Press, Boca Raton, FL, 1998, p. 7-26.

Physical Properties of Selected Ceramics Material Specific gravity Coefficient of linear thermal expansion, ppm/°C, 20–700° Safe operating temperature, °C Thermal conductivity (cal/cm2/cm/sec/°C) Tensile strength (psi) Compressive strength (psi) Flexural strength (psi) Impact strength (ft-lb; 1/2≤ rod) Modulus of elasticity (psi) Thermal shock resistance Dielectric strength, (V/mil; 0.25≤ specimen) Resistivity (W/cm2, 22°C) Power factor at 106 Hz Dielectric constant

Porcelain

Cordierite Refractory

Alumina, Alumina Silicate Refractories

Magnesium Silicate

2.2–2.4 5.0–6.5 ¥ 106

1.6–2.1 2.5–3.0 ¥ 106

2.2–2.4 5.0–7.0 ¥ 106

2.3–2.8 11.5 ¥ 106

~400 0.004–0.005

1,250 0.003–0.004

1,300–1,700 0.004–0.005

1,200 0.003–0.005

1,500–2,500 25,000–50,000 3,500–6,000 0.2–0.3 7–10 ¥ 106 Moderate 40–100

1,000–3,500 20,000–45,000 1,500–7,000 0.2–0.25 2–5 ¥ 106 Excellent 40–100

700–3,000 13,000–60,000 1,500–6,000 0.17–0.25 2–5 ¥ 106 Excellent 40–100

2,500 20,000–30,000 7,000–9,000 0.2–0.3 4–5 ¥ 106 Good 80–100

102–104 0.010–0.020 6.0–7.0

102–104 0.004–0.010 4.5–5.5

102–104 0.002–0.010 4.5–6.5

102–105 0.008–0.010 5.0–6.0

From Lehman, R.L., Strange, D.J., and Fischer, III, W.F., Ceramics and glass, in The CRC Handbook of Mechanical Engineering, Kreith, F., CRC Press, Boca Raton, FL, 1998, p. 12-85.

© 2004 by CRC Press LLC

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4-6

CRC Handbook of Engineering Tables

Steel Pipe Sizes

From Kreith, F., Ed., The CRC Handbook of Mechanical Engineering, CRC Press, Boca Raton, FL, 1998, p. E-81. Originally from Design Properties of Pipe, Chemetron Corporation, 1958.

© 2004 by CRC Press LLC

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Mechanical Engineering

Commercial Copper Tubing*

© 2004 by CRC Press LLC

4-7

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4-8

CRC Handbook of Engineering Tables

Commercial Copper Tubing* (continued)

From Kreith, F., Ed., The CRC Handbook of Mechanical Engineering, CRC Press, Boca Raton, FL, 1998, p. E-82 to E-83.

Summary of Definitions Systems (Machining/Manufacturing) Machining System

Dedicated Machining System (DMS) Flexible Manufacturing System (FMS) Reconfigurable Manufacturing System (RMS)

Definitions One or more machine tools and tooling, and auxiliary equipment (e.g., material handling, control, communications) that operate in a coordinated manner to produce parts at the required volumes and quality. A machining system designed for production of a specific part, and uses transfer line technology with fixed tooling and automation. A machining system configuration with fixed hardware and fixed, but programmable, software to handle changes in work orders, production schedules, part programs, and tooling for several types of parts. A machining system that can be created by incorporating basic process modules, both hardware and software, that can be rearranged or replaced quickly and reliably. Reconfiguration will allow adding, removing, or modifying specific process capabilities, controls, software, or machine structure to adjust production capacity in response to changing market demands or technologies. This type of system will provide customized flexibility for a particular part family, and will be open-ended, so that it can be improved, upgraded, and reconfigured, rather than replaced.

Note: A part family is defined as one or more part types with similar dimensions, geometric features, and tolerances, such that they can be produced on the same, or similar, production equipment. From Mehrabi, M.G., Ulsoy, A.G., and Koren, Y., Manufacturing systems and their design principles, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 4.

© 2004 by CRC Press LLC

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Mechanical Engineering

CAPP System Characteristics and Their Effects Characteristic Complete

Extendable Adaptable User Inclusive User Friendly Teachable

Customizable Modular Robust Efficient Integratable Cost Effective

Effects • Provides a complete manufacturing solution for the part in question. • Meets all the end-user’s requirements. • Facilitates the generation of multiple solutions. • New technologies can be merged into the system. • The system can be extended by the end-user or a third-party software developer. • The system can be used by many different types of end-users. • Utilizes human expertise and computer efficiency in correct proportions. • Promotes synthesis and analysis in addition to automation and simulation. • Easy to implement and maintain. • Easy to use. • Allows the expertise of the end-user to be incorporated into the system. • The system can act as an archiving tool for the end-user’s expertise. • The system can be used to train new process planners. • The system (and its cost) can be tailored to the end-user’s requirements. • Facilitates extendability, adaptability, customizability, and cost effectiveness. • Provides consistently “correct” (by the end-user’s standard) solutions. • Reduces human error. • Solutions are generated in a more timely fashion than by conventional planning. • The work load for a process planner generating a solution is reduced. • Implementation is not computer hardware or software specific. • The system in a customized form suits the budget of a wide range of end-users.

From Yip-Hoi, D., Computer-aided process planning for machining, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 24.

© 2004 by CRC Press LLC

Appearance

Residence Time

Integrity

Melt Front Velocity

Strength

Solidified Layer Development

Flash

Melt Viscosity Clamp Tonnage

Inlet Pressure

Packing Pressure Profile 0.2 Packing Time 0.01

PACKING

Flow Rate

Solidified Layer Development Melt Press. Cycle Time

Melt Density

Solidified Layer Development

Resid. Stress Clarity

Economics Dimensions

Part Temp

Part Strain Ejection Stroke 0.02

EJECTION

Part Stress

Relaxation

Distortion

Ejected Part

Mold Failure

Ejection Velocity 0.01

MACHINE INPUTS

STATE VARIABLES

QUALITY ATTRIBUTES

System’s view of the injection molding process. (From Kazmer, D. and Danai, K., Control of polymer processing, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 141.)

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Mold Coolant Temperature 200 Cooling Time 0.01

COOLING

Melt Temp.

PROCESS/PART QUALITY

Melt Temp. Melt Volume

Injection Velocity Profile 0.02 Maximum Injection Pressure 0.1

Melt Quality

Melt Pressure

INJECTION

Screw Press. 0.02 Shot Size 0.02

PLASTICATION

Barrel Temp 1000 Screw RPM 0.5

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4-10

Thermoplastic Pellets

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Mechanical Engineering

Magnitude of Process Variation by Machine Input Control Quality Melt temperature (C) Mold temperature (C) Injection time (sec) Pack pressure (Mpa) Pack time (sec) Cooling time (sec)

Low (Class 9)

High (Class 1)

5 8 0.17 0.5 0.02 0.86

1 2 0.04 0.1 0.09 0.20

From Kazmer, D. and Danai, K., Control of polymer processing, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 143.

accuracy

repeatibility

resolution

Visualization of accuracy, repeatability, and resolution. (From Kurfess, T.R., Precision manufacturing, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 153. Originally from Dorf, R. and Kusiak, A., Handbook of Design, Manufacturing, and Automation, John Wiley, New York, 1994. With permission.)

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Anthropomorphic robot with frame assignment. (From Siciliano, B., Robot kinematics, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 460.)

Denavit-Hartenberg Parameters of the Anthropomorphic Robot

i 1 2 3 4 5 6

ai 0 p/2 0 - p/2 p/2 - p/2

li 0 0 l3 0 0 0

Ji q1 q2 q3 q4 q5 q6

di 0 0 0 d4 0 0

From Siciliano, B., Robot kinematics, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 460.

© 2004 by CRC Press LLC

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Mechanical Engineering

4-13

Basic grip and trigger concepts. (From Bejczy, A.K., Teleoperation and telerobotics, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 687.)

Examples of specialization of robot designs. (From Hagele, M. and Schraft, R.D., Present state and furture trends in mechanical systems design for robot application, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 781. Originally courtesy of Reis Robotics, ABB Flexible Automation, and CMB Automation. From Warnecke, H.-J. et al., in Handbook of Industrial Robotics, 1999, p. 42. Reprinted with permission of John Wiley & Sons.)

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Typical arm and wrist configurations of industrial robots. (From Hagele, M. and Schraft, R.D., Present state and furture trends in mechanical systems design for robot application, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 784.)

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Mechanical Engineering

4-15

From industrial robots to service robots — the evolution of machine intelligence. (From Hagele, M. and Schraft, R.D., Present state and furture trends in mechanical systems design for robot application, in The Mechanical Systems Design Handbook, Nwokah, O.D.I., and Hurmuzlu, Y., Eds., CRC Press, Boca Raton, FL, 2002, p. 795.)

© 2004 by CRC Press LLC

104

10 -16

10-14

106

108

1010

1012

1014

1016

1018

1020

10-12

10-10

10-8

10-6

10-4

10-2

100

102

Typical Man-Made Devices Scale of things, in meters. Lower scale continues in the upper bar from left to right. One meter is 106 mm, 109 nm, or 1010 Å. (From Gal-el-Hak, M., Introduction, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 1-2.)

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Diameter of Proton

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4-16

102

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Mechanical Engineering

Metals Young’s Modulus (GPa)

Yield Strength (GPa)

Ultimate Strength (GPa)

8–38 40

— —

0.04–0.31 0.15

Tension Tension

110–160 mm thick 1.0 mm thick

69–85 86–137 108–145

— 0.12–0.24 —

— 0.33–0.38 —

Bending Tension Indentation

Various lengths Plated; annealed Various locations

98 ± 4 40–80 57

— — 0.26

— 0.2–0.4 —

Tension Tension Bending

Laser speckle 0.06–16 mm thick ~1 mm thick

74 82 —

— — —

— 0.33–0.36 0.22–0.27

Indentation Tension Bending

~1 mm thick 0.8 mm thick Composite beam

96 ± 12

—

0.95 ± 0.15

Tension

0.5 mm thick

—

0.07–0.12

0.14–0.19

Tension

Composite film

Aluminum; modulus of bulk material = 69 GPa Copper; modulus of bulk material = 117 GPa Gold; modulus of bulk material = 74 GPa

Titanium; modulus of bulk material = 110 GPa Ti–Al–Ti

Method

Comments

From Sharpe, Jr., W.N., Mechanical properties of MEMS materials, in The MEMS Handbook, Gal-

el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 3-19.

Fluid Modeling

Continuum Models

Molecular Models

Deterministic

Statistical

MD

Liouville

DSMC

Euler

Navier–Stokes

Burnett

Chapman–Enskog

Boltzmann

Molecular and continuum flow models. (From Gad-el-Hak, M., Flow physics, in The MEMS Handbook, Gal-elHak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 4-3. Originally from Gad-el-Hak, M. (1999) J. Fluids Eng. 121, pp. 5–33, ASME, New York. With permission.)

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CRC Handbook of Engineering Tables

Kn = 0.0001

0.001

0.01

0.1

1

10

Continuum flow

Transition regime

(ordinary density levels)

(moderately rarefied)

100

Slip-flow regime

Free-molecule flow

(slightly rarefied)

(highly rarefied)

Knudsen number regimes. (From Gad-el-Hak, M., Flow physics, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 4-6. Originally from Gad-el-Hak, M. (1999) J. Fluids Eng. 121, pp. 5–33, ASME, New York. With permission.)

Kn Free Molecular

Hard Disk Drive Micro Channels Micro Pumps Micro Gyroscope Accelerometer

10.

Micro Valves 1.0

Transitional Flow

Micro Nozzles Flow Sensors

0.1 (Helium) Slip Flow 0.01 (Air)

Continuum Flow 0.001

Nano Technology

MEMS h (mm)

0.01 mm

0.1 mm

1.0 mm

10.0 mm

The operation range for typical MEMS and nanotechnology applications under standard conditions spans the entire Knudsen regime (continuum, slip, transition and free molecular flow regimes). (From Bestok, A., Molecular-based microfluidic simulation models, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 8-3.)

© 2004 by CRC Press LLC

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Mechanical Engineering

Classification of Microrobots According to Size and Fabrication Technology Robot Class

Size and Fabrication Technology

Miniature robots or minirobots:

Having a size on the order of a few cubic centimeters and fabricated by assembling conventional miniature components as well as some micromachines (such as MEMS-based microsensors) Defined as a sort of “modified chip” fabricated by silicon MEMS-based technologies (such as batch-compatible bulk or surface micromachining or by micromolding and/or replication method) having features in the micrometer range Operating at a scale similar to the biological cell (on the order of a few hundred nanometers) and fabricated by nonstandard mechanical methods such as protein engineering

MEMS-based microrobots (or microrobotsa)

Nanorobots

a To distinguish a MEMS-based microrobot with micrometer-sized components from the whole class of microrobots (including mini-, micro-, and nanorobots), several more or less confusing notations have been proposed. In this publication, the term MEMS-based microrobot is introduced and used. The term MEMSbased microrobot differs from the notation originally used by Dario et al., but the content is the same. From Ebefors, T. and Stemme, G., Microrobotics, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC

Press, Boca Raton, FL, 2002, p. 28-4.

d)

AM

(PS)

h)

AP

Microrobots physically mounted to positioning system / fixed to external environment

CU + PS

AP

e)

AM

i)

CU + PS

CU + PS

CU + PS + AM

CU (PS)

a)

l) PS + AM

PS

AM

m) CU + PS

AM

CU AP

AP

AP (PS)

b)

f)

AP

AP

AM

j) CU

CU + PS

CU + PS

PS + AM (PS)+ AP

n)

CU + PS + AM CU + PS + AP

(PS) g)

c)

k)

CU + PS

Microrobots without manipulation functions (wire controlled)

PS + AP + AM

AP + AM

AP CU + PS

CU

Microrobots for manipulating operations (wire controlled)

Wireless microrobots for manipulating operations

o) CU+PS + AP + AM

Autonomous microrobots for manipulating operations

Classification of microrobots by functionality (modification of earlier presented classification schemes). CU indicates the control unit; PS, the power source or power supply; AP, the actuators for positioning; AM, the actuators for manipulation. (From Ebefors, T. and Stemme, G., Microrobotics, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 28-5.)

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Thermal Conductivity, Coefficient of Thermal Expansion, Cost Estimates, and Scaling Trends of Current and Potential Substrate Materials

Materials Alumina FR-4 A1N Silicon Heat pipe in silicon A1 Cu Diamond Kovar Heat pipe in Kovar A1SiC

Thermal Conductivity (W/cm-K)

Coefficient of Thermal Expansion (10-6/K)

0.25 Depends on copper 1.00–2.00 1.48 8.00 Æ 20.00 (?) 2.37 3.98 10.00–20.00 0.13 >8.00 2.00 (at 70%)

6.7 13.0 4.1 4.7 4.7 41.8 28.7 1.0–1.5 5.0 5.0 7.0 (?)

Cost of Substrate ($/in2) 0.09 0.07 0.35 1.00 3.00 0.0009 0.0015 1000.00 0.027 0.10 1.00

Scaling with Area Cost Trend 6" limit Constant to 36" 6" limit 6–10" limit 6–10" limit Scales as area Scales as area Scales as area2 Scales as area Scales as area Casting size limited

From Peterson, G.P., Micro heat pipes and micro heat spreaders, in The MEMS Handbook, Gal-el-Hak, M.,

Ed., CRC Press, Boca Raton, FL, 2002, p. 31-17.

Intelligence

Biological

Computing

Artificial

Soft Computing

Hard Computing

(symbolic)

(Computational Intelligence)

(Numeric)

Probabilistic Reasoning

Neurocomputing

Biologically Accurate

Fuzzy Sets

Engineering Oriented Artificial Neural Networks (ANN)

Fuzzy Logic

Membership Function

Genetic Algorithms

Optimization Possibility

Search

Computational Neural Networks (CNN)

Machine Learning

Tools for soft computing. (From Gal-el-Hak, M., Flow control, in The MEMS Handbook, Gal-el-Hak, M., Ed., CRC Press, Boca Raton, FL, 2002, p. 33-36. Originally from Gad-el-Hak, M. (2000) Flow Control: Passive, Active, and Reactive Flow Management. Reprinted with permission of Cambridge University Press, New York.)

© 2004 by CRC Press LLC

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Mechanical Engineering

Saturated Steam, Water, and Ice — SI Units Subscripts: f g i fg ig

refers to a property of liquid in equilibrium with vapor refers to a property of vapor in equilibrium with liquid refers to a property of solid in equilibrium with vapor refers to a change by evaporation refers to a change by sublimation

Temperature C K Solid—Vapor –40 –30 –20 –10 0 0.01

233.15 243.15 253.15 263.15 273.15 273.16

Specific Volume, m3/kg

Pressure, MN/m2

vi 0.000 0.000 0.000 0.000 0.000 0.000

012 038 103 260 610 611

9 1 5 2 8 3

0.000 0.001 0.001 0.001 0.001 0.001

Liquid—Vapor

084 085 087 089 090 090

vg 1 8 4 1 8 8

83.54 29.43 11.286 4.667 2.063 2.061

vf

0 0.01 5.00 6.98 10.00

273.15 273.16 278.15 280.13 283.15

0.000 0.000 0.000 0.001 0.001

610 611 872 000 227

9 3 1 0 6

000 000 000 000 000

2 2 1 2 4

13.03 15.00 17.50 20.00 24.08

286.18 288.15 290.65 293.15 297.23

0.001 0.001 0.002 0.002 0.003

500 705 000 339 000

0 0.001 000 7 1 0.001 000 9 0 0.001 001 3 0.001 001 8 0 0.001 002 7

25.00 28.96 30.00 32.88 35.00

298.15 302.11 303.15 306.03 308.15

0.003 0.004 0.004 0.005 0.005

169 000 246 000 628

0.001 0.001 0.001 0.001 0.001

002 004 004 005 006

36.16 39.00 40.00 41.51 43.76

309.31 312.15 313.15 314.66 316.91

0.006 0.007 0.007 0.008 0.009

000 000 384 000 000

0.001 0.001 0.001 0.001 0.001

45.00 45.81 50.00 53.97 55.00

318.15 318.96 323.15 327.12 328.15

0.009 0.010 0.012 0.015 0.015

593 000 349 000 758

60.00 60.06 65.00 69.10 70.00

333.15 333.21 338.15 342.25 343.15

0.019 0.020 0.025 0.030 0.031

75.00 75.87 80.00 81.33 85.00

348.15 349.02 353.15 354.48 358.15

85.94 89.95 90.00 93.50 95.00

359.09 363.10 363.15 366.65 368.15

ui –411.70 –393.23 –374.03 –354.09 –333.43 –333.40

ug 2 2 2 2 2 2

uf

319.6 333.6 347.5 361.4 375.3 375.3

Specific enhalpy, kJ/kg hi –411.70 –393.23 –374.03 –354.09 –333.43 –333.40

ug

hf

hig 2 2 2 2 2 2

838.9 839.0 838.4 837.0 834.8 834.8

Specific Entropy, kJ/kg·K hg

2 2 2 2 2 2

hfg

427.2 445.8 464.3 482.9 501.3 501.4 hg

si

sg

–1.532 –1.455 –1.377 –1.299 –1.221 –1.221

10.644 10.221 9.835 9.481 9.157 9.156

sf

sg

206.278 206.136 147.120 129.208 106.379

–0.03 0 +20.97 29.30 42.00

2 2 2 2 2

375.3 375.3 382.3 385.0 389.2

–0.02 +0.01 20.98 29.30 42.01

2 2 2 2 2

501.4 501.3 489.6 484.9 477.7

2 2 2 2 2

501.3 –0.000 1 501.4 0 510.6 +0.076 1 514.2 0.105 9 519.8 0.151 0

9.156 9.156 9.025 8.975 8.900

5 2 7

87.980 77.926 67.004 57.791 45.665

54.71 62.99 73.48 83.95 101.04

2 2 2 2 2

393.3 396.1 399.5 402.9 408.5

54.71 62.99 73.48 83.96 101.05

2 2 2 2 2

470.6 465.9 460.0 454.1 444.5

2 2 2 2 2

525.3 528.9 533.5 538.1 545.5

0.195 0.224 0.260 0.296 0.354

7 5 7 6 5

8.827 8.781 8.723 8.667 8.577

9 4 7 2 6

9 0 3 3 0

43.360 34.800 32.894 28.192 25.216

104.88 121.45 125.78 137.81 146.67

2 2 2 2 2

409.8 415.2 416.6 420.5 423.4

104.89 121.46 125.79 137.82 146.68

2 2 2 2 2

442.3 432.9 430.5 423.7 418.6

2 2 2 2 2

547.2 554.4 556.3 561.5 565.3

0.367 0.422 0.436 0.476 0.505

4 6 9 4 3

8.558 8.474 8.453 8.395 8.353

0 6 3 1 1

006 007 007 008 009

4 4 8 4 4

23.739 20.530 19.523 18.103 16.203

151.53 163.39 167.56 173.87 183.27

2 2 2 2 2

425.0 428.8 430.1 432.2 435.2

151.53 163.40 167.57 173.88 183.29

2 2 2 2 2

415.9 409.1 406.7 403.1 397.7

2 2 2 2 2

567.4 572.5 574.3 577.0 581.0

0.521 0.559 0.572 0.592 0.622

0 2 5 6 4

8.330 8.275 8.257 8.228 8.187

4 8 0 7 2

0.001 0.001 0.001 0.001 0.001

009 010 012 014 014

9 2 1 1 6

15.258 14.674 12.032 10.022 9.568

188.44 191.82 209.32 225.92 230.21

2 2 2 2 2

436.8 437.9 443.5 448.7 450.1

188.45 191.83 209.33 225.94 230.23

2 2 2 2 2

394.8 392.8 382.7 373.1 370.7

2 2 2 2 2

583.2 584.7 592.1 599.1 600.9

0.638 0.649 0.703 0.754 0.767

7 3 8 9 9

8.164 8.150 8.076 8.008 7.991

8 2 3 5 3

940 000 030 000 190

0.001 0.001 0.001 0.001 0.001

017 017 019 022 022

2 2 9 3 8

7.671 7.649 6.197 5.22l9 5.042

251.11 251.38 272.02 289.20 292.95

2 2 2 2 2

456.6 456.7 463.1 468.4 469.6

251.13 251.40 272.06 289.23 292.98

2 2 2 2 2

358.5 358.3 346.2 336.1 333.8

2 2 2 2 2

609.6 609.7 618.3 625.3 626.8

0.831 0.832 0.893 0.943 0.954

2 0 5 9 9

7.909 7.908 7.831 7.768 7.755

6 5 0 6 3

0.038 0.040 0.047 0.050 0.057

580 000 390 000 830

0.001 0.001 0.001 0.001 0.001

025 026 029 030 032

9 5 1 0 5

4.131 3.993 3.407 3.240 2.828

313.90 317.53 334.86 340.44 355.84

2 2 2 2 2

475.9 477.0 482.2 483.9 488.4

313.93 317.58 334.91 340.49 355.90

2 2 2 2 2

221.4 319.2 308.8 305.4 296.0

2 2 2 2 2

635.3 636.8 643.7 645.9 651.9

1.015 1.025 1.075 1.091 1.134

5 9 3 0 3

7.682 7.670 7.612 7.593 7.544

4 0 2 9 5

0.060 0.070 0.070 0.080 0.084

000 000 140 000 550

0.001 0.001 0.001 0.001 0.001

033 036 036 038 039

1 0 0 6 7

2.732 2.365 2.361 2.087 1.981 9

359.79 376.63 376.85 391.58 397.88

2 2 2 2 2

489.6 494.5 494.5 498.8 500.6

359.86 376.70 376.92 391.66 397.96

2 2 2 2 2

293.6 283.3 283.2 274.1 270.2

2 2 2 2 2

653.5 660.0 660.1 665.8 668.1

1.145 1.191 1.192 1.232 1.250

3 9 5 9 0

7.532 7.479 7.479 7.434 7.415

0 7 1 6 9

© 2004 by CRC Press LLC

0.001 0.001 0.001 0.001 0.001

vg

Specific Internal Energy, kJ/kg

8

1587_Book.fm Page 22 Tuesday, September 2, 2003 3:25 PM

4-22

CRC Handbook of Engineering Tables

Saturated Steam, Water, and Ice — SI Units (continued) Liquid—Vapor

vf

vg

96.71 99.63 100.00 110.00 111.37

369.86 372.78 373.15 383.15 384.52

0.090 0.100 0.101 0.143 0.150

000 000 350 270 000

0.001 0.001 0.001 0.001 0.001

041 043 043 051 052

0 2 5 6 8

1.869 1.694 1.672 1.210 1.159

120.00 120.23 130.00 133.55 140.00

393.15 393.38 403.15 406.70 413.15

0.198 0.200 0.270 0.300 0.361

530 000 000 000 300

0.001 0.001 0.001 0.001 0.001

060 060 069 073 079

3 5 7 2 7

143.63 150.00 151.86 160.00 170.00

416.78 423.15 425.01 433.15 443.15

0.400 0.475 0.500 0.617 0.791

000 800 000 800 700

0.001 0.001 0.001 0.001 0.001

083 090 092 102 114

179.91 180.00 190.00 198.32 200.00

453.06 453.15 463.15 471.47 473.15

1.000 1.002 1.254 1.500 1.553

000 100 400 000 800

0.001 0.001 0.001 0.001 0.001

210.00 212.42 220.00 223.99 230.00

483.15 485.57 493.15 497.14 503.15

1.906 2.000 2.318 2.500 2.795

200 000 000 000 000

233.90 240.00 242.60 250.00 250.40

507.05 513.15 515.75 523.15 523.55

3.000 3.344 3.500 3.973 4.000

260.00 263.99 270.00 275.64 280.00

533.15 537.14 543.15 548.79 553.15

285.88 290.00 295.06 300.00 303.40

uf

ug

hf

hfg

hg

sf

sg

0 9 2 3

405.06 417.36 418.94 461.14 466.94

2 2 2 2 2

502.6 506.1 506.5 518.1 519.7

405.15 417.46 419.04 461.30 467.11

2 2 2 2 2

265.7 258.0 257.0 230.2 226.5

2 2 2 2 2

670.9 675.5 676.1 691.5 693.6

1.269 1.302 1.306 1.418 1.433

5 6 9 5 6

7.394 7.359 7.354 7.238 7.223

9 4 9 7 3

0.891 0.885 0.668 0.605 0.508

9 7 5 8 9

503.50 504.49 546.02 561.15 588.74

2 2 2 2 2

529.3 529.5 539.9 543.6 550.0

503.71 504.70 546.31 561.47 589.13

2 2 2 1 2

202.6 201.9 174.2 163.8 144.7

2 2 2 2 2

706.3 706.7 720.5 725.3 733.9

1.527 1.530 1.634 1.671 1.739

6 1 4 8 1

7.129 7.127 7.026 6.991 6.929

6 1 9 9 9

6 5 6 0 3

0.462 0.392 0.374 0.307 0.242

5 8 9 1 8

604.31 631.68 639.68 674.87 718.33

2 2 2 2 2

553.6 559.5 561.2 568.4 576.5

604.74 632.20 640.23 675.55 719.21

2 2 2 2 2

133.8 114.3 108.5 082.6 049.5

2 2 2 2 2

738.6 746.5 748.7 758.1 768.7

1.776 1.841 1.860 1.942 2.041

6 8 7 7 9

6.895 6.837 6.821 6.750 6.666

9 9 3 2 3

127 127 141 153 156

3 4 4 9 5

0.194 0.194 0.156 0.131 0.127

44 05 54 77 36

761.68 762.09 806.19 843.16 850.65

2 2 2 2 2

583.6 583.7 590.0 594.5 595.3

762.81 763.22 807.62 844.89 852.45

2 2 1 1 1

015.3 015.0 978.8 947.3 940.7

2 2 2 2 2

778.1 778.2 786.4 792.2 793.2

2.138 2.139 2.235 2.315 2.330

7 6 9 0 9

6.586 6.585 6.507 6.444 6.432

5 7 9 8 3

0.001 0.001 0.001 0.001 0.001

172 176 190 197 208

6 7 0 3 8

0.104 0.099 0.086 0.079 0.071

41 63 19 98 58

895.53 906.44 940.87 959.11 986.74

2 2 2 2 2

599.5 600.3 602.4 603.1 603.9

897.76 908.79 943.62 962.11 990.12

1 1 1 1 1

900.7 890.7 858.5 841.0 813.8

2 2 2 2 2

798.5 799.5 802.1 803.1 804.0

2.424 2.447 2.517 2.554 2.609

8 4 8 7 9

6.358 6.340 6.286 6.257 6.214

5 9 1 5 6

000 000 000 000 000

0.001 0.001 0.001 0.001 0.001

216 229 234 251 252

5 1 7 2 2

0.066 0.059 0.057 0.050 0.049

68 76 07 13 78

1 1 1 1 1

004.78 033.21 045.43 080.39 082.31

2 2 2 2 2

604.1 604.0 603.7 602.4 602.3

1 1 1 1 1

008.42 037.32 049.75 085.36 087.31

1 1 1 1 1

795.7 766.5 753.7 716.2 714.1

2 2 2 2 2

804.2 803.8 803.4 801.5 801.4

2.645 2.701 2.725 2.792 2.796

7 5 3 7 4

6.186 6.143 6.125 6.073 6.070

9 7 3 0 1

4.688 5.000 5.499 6.000 6.412

000 000 000 000 000

0.001 0.001 0.001 0.001 0.001

275 285 302 318 332

5 9 3 7 1

0.042 0.039 0.035 0.032 0.030

21 44 64 44 17

1 1 1 1 1

128.39 147.81 177.36 205.44 227.46

2 2 2 2 2

599.0 597.1 593.7 589.7 586.1

1 1 1 1 1

134.37 154.23 184.51 213.35 235.99

1 1 1 1 1

662.5 640.1 605.2 571.0 543.6

2 2 2 2 2

796.9 794.3 789.7 784.3 779.6

2.883 2.920 2.975 3.026 3.066

8 2 1 7 8

6.001 5.973 5.930 5.889 5.857

9 4 1 2 1

559.03 563.15 568.21 573.15 576.55

7.000 7.436 8.000 8.581 9.000

000 000 000 000 000

0.001 0.001 0.001 0.001 0.001

351 365 384 403 417

3 6 2 6 8

0.027 0.025 0.023 0.021 0.020

37 57 52 67 48

1 1 1 1 1

257.55 278.92 305.57 332.0 350.51

2 2 2 2 2

580.5 576.0 569.8 563.0 557.8

1 1 1 1 1

267.00 289.07 316.64 344.0 363.26

1 1 1 1 1

505.1 477.1 441.3 404.9 378.9

2 2 2 2 2

772.1 766.2 758.0 749.0 742.1

3.121 3.159 3.206 3.253 3.285

1 4 8 4 8

5.813 5.782 5.743 5.704 5.677

3 1 2 5 2

310.00 311.06 320.00 324.75 330.00

583.15 584.21 593.15 597.90 603.15

9.856 10.000 11.274 12.000 12.845

000 000 000 000 000

0.001 0.001 0.001 0.001 0.001

447 452 498 526 560

4 4 8 7 7

0.018 0.018 0.015 0.014 0.012

350 026 488 263 996

1 1 1 1 1

387.1 393.04 444.6 473.0 505.3

2 2 2 2 2

546.4 544.4 525.5 513.7 498.9

1 1 1 1 1

401.3 407.56 461.5 491.3 525.3

1 1 1 1 1

326.0 317.1 238.6 193.6 140.6

2 2 2 2 2

727.3 724.7 700.1 684.9 665.9

3.349 3.359 3.448 3.496 3.550

3 3 0 2 7

5.623 5.614 5.536 5.492 5.441

0 1 2 4 7

336.75 340.00 347.44 350.00 357.06

609.90 613.15 620.59 623.15 630.21

14.000 14.586 16.000 16.513 18.000

000 000 000 000 000

0.001 0.001 0.001 0.001 0.001

610 637 710 740 839

7 9 7 3 7

0.011 0.001 0.009 0.008 0.007

485 079 7 306 813 489

1 1 1 1 1

548.6 570.3 622.7 641.9 698.9

2 2 2 2 2

476.8 464.6 431.7 418.4 374.3

1 1 1 1 1

571.1 594.2 650.1 670.6 732.0

1 066.5 1 027.9 930.6 893.4 777.1

2 2 2 2 2

637.6 622.0 580.6 563.9 509.1

3.623 3.659 3.746 3.777 3.871

2 4 1 7 5

5.371 5.335 5.245 5.211 5.104

7 7 5 2 4

360.00 365.81 370.00 373.80 374.136

633.15 638.96 643.15 646.95 647.286

18.651 20.000 21.030 22.000 22.090

000 000 000 000 000

0.001 0.002 0.002 0.002 0.003

892 5 036 213 742 155

0.006 0.005 0.004 0.003 0.003

945 834 925 568 155

1 1 1 1 2

725.2 785.6 844.0 961.9 029.6

2 2 2 2 2

351.5 293.0 228.5 087.1 029.6

1 1 1 2 2

760.5 826.3 890.5 022.2 099.3

720.5 583.4 441.6 143.4 0

2 2 2 2 2

481.0 409.7 332.1 165.6 099.3

3.914 4.013 4.110 4.311 4.429

7 9 6 0 8

5.052 4.926 4.797 4.532 4.429

6 9 1 7 8

From Bolz, R.E. and Tuve, G.L., Gases and vapors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 24–25. Originally condensed from Keenan, J.H., Keyes, F.G., Hill, P.G., and Moore, J.G., Steam Tables: Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases, John Wiley & Sons, New York, 1969.

© 2004 by CRC Press LLC

1587_Book.fm Page 23 Monday, September 1, 2003 7:17 PM

4-23

Mechanical Engineering

Viscosity and Thermal Conductivity of Steam and Water—SI Units Symbols and Units m = dynamic viscosity. For N·s/m2 (= kg/m·s) multiply tabulated values by 10–6 v = kinematic viscosity. For m2/s multiply tabulated values by 10–6 k = thermal conductivity in MW/m·K Pressure 0.1 MN/m2

Temperature

0.5 MN/m2

C

K

m

v

k

m

0 50 100 150 200

273.15 323.15 373.15 423.15 473.15

1 750 544 12.11 14.15 16.18

1.75 0.551 20.54 27.39 35.14

569 643 24.8 28.7 33.2

1 750 544 279 181 16.02

250 300 350 400 450

523.15 573.15 623.15 673.15 723.15

18.22 20.25 22.3 24.3 26.4

48.83 53.44 64.02 75.40 88.0

38.2 43.4 49.0 54.9 61.1

18.14 20.23 — 24.4 26.4

500 550 600 650 700

773.15 823.15 873.15 923.15 973.15

28.4 30.4 32.5 34.5 36.5

67.4 73.9 80.6 87.4 94.3

28.4 30.5 32.5 34.5 36.6

101.3 115.4 130.9 146.9 163.9

1.0 MN/m2 k

m

569 644 681 687 33.8

1 750 544 279 181 15.85

1.75 0.550 0.291 0.198 0.327

570 644 681 687 35.1

8.61 10.57 — 15.06 17.5

38.6 43.8 49.4 55.3 61.4

18.06 20.22 — 24.4 26.5

0.420 0.522 — 7.48 0.88

39.3 44.4 49.9 55.7 61.8

20.2 23.1 26.1 29.3 32.8

67.7 74.3 80.9 87.7 94.6

28.5 30.5 32.6 34.6 36.6

0.101 0.115 0.131 0.147 0.164

68.2 74.7 81.4 88.2 95.0

v 1.75 0.551 0.291 0.198 6.81

v

k

Pressure Temperature C K

5.0 MN/m2 m

v

1 750 545 280 182 135

1.75 0.550 0.291 0.198 0.155

10 MN/m2 k

m

573 647 684 690 668

1 750 545 281 183 136

v 1.74 0.549 0.292 0.199 0.156

20 MN/m2 k

m

577 651 688 693 672

1 740 546 283 186 138

0 50 100 150 200

273.15 323.15 373.15 423.15 473.15

250 300 350 400 450

523.15 573.15 623.15 673.15 723.15

107 20.06 — 25.0 26.9

0.134 0.909 — 1.45 1.70

618 52.5 55.4 60.2 65.9

108 90.5 — 25.8 27.6

0.134 0.126 — 0.682 0.821

625 545 68.8 68.6 72.4

500 550 600 650 700

773.15 823.15 873.15 923.15 973.15

28.9 30.9 32.9 34.9 36.9

1.98 2.28 2.59 2.92 3.27

72.0 78.4 85.0 91.7 98.6

29.5 31.5 33.4 35.4 37.4

0.967 1.123 1.282 1.452 1.630

77.6 83.5 89.8 96 103

v

k

1.72 0.548 0.293 0.200 0.158

585 659 695 700 681

111 93 73.5 28.6 29.6

0.136 0.127 0.122 0.285 0.376

639 571 454 107 93

31.1 32.8 34.6 36.5 38.4

0.459 0.543 0.629 0.719 0.812

93 96 101 107 113

Pressure Temperature C K

30 MN/m2 m

v

40 MN/m2 k

m 1 730 548 287 190 143

0 50 100 150 200

273.15 323.15 373.15 423.15 473.15

1.740 547 285 188 140

1.71 0.547 0.293 0.201 0.159

592 666 701 706 689

250 300

523.15 573.15

113 95.5

0.137 0.127

652 592

© 2004 by CRC Press LLC

116 98.1

50 MN/m2 k

m

1.70 0.545 0.294 0.203 0.161

599 672 707 713 697

1 720 549 289 192 145

1.68 0.544 0.295 0.204 0.162

606 678 713 720 704

0.139 0.128

662 609

118 101

0.140 0.130

671 622

v

v

k

1587_Book.fm Page 24 Monday, September 1, 2003 7:17 PM

4-24

CRC Handbook of Engineering Tables

Viscosity and Thermal Conductivity of Steam and Water—SI Units (continued) 350 400 450

623.15 673.15 723.15

78.5 45.8 33.1

0.122 0.128 0.223

496 264 138

82.5 62.8 41.1

0.122 0.120 0.152

529 390 220

85 28.6 29.6

0.123 0.120 0.130

522 436 301

500 550 600 650 700

773.15 823.15 873.15 923.15 973.15

33.4 34.6 36.1 37.7 39.5

0.290 0.352 0.413 0.475 0.540

116 112 114 118 124

36.9 36.9 37.9 39.2 40.8

0.208 0.258 0.307 0.355 0.406

153 134 130 132 135

31.1 32.8 34.6 36.5 38.4

0.164 0.205 0.245 0.286 0.327

206 163 149 147 148

From Bolz, R.E. and Tuve, G.L., Gases and vapors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p 37. Originally adapted from Keenan, J.H., Keyes, F.G., Hill, P.G., and Moore, J.G., Steam Tables: Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases, John Wiley & Sons, New York, 1969.

Properties of Gases Gases and Vapors, Including Fuels and Refrigerants, English and Metric Units The properties of pure gases are given at 25 deg C (77 deg F, 298 K) and atmospheric pressure (except as stated). Common Name(s) Chemical Formula Refrigerant Number

Acetylene (Ethyne) C 2H 2 —

Air [Mixture] 729

Chemical and Physical Properties Molecular weight 26.04 28.966 Specific gravity, air = 1 0.90 1.00 Specific volume, ft3/lb 14.9 13.5 Specific volume, m3/kg 0.93 0.842 Density of liquid (at atm bp), lb/ft3 43.0 54.6 Density of liquid (at atm bp), kg/m3 693. 879. Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 12.1 ¥ 10–6 Viscosity (abs), lbm/ft·sec 6.72 ¥ 10–6 Viscosity (abs), centipoisesa 0.01 0.018 Sound velocity in gas, m/sec 343 346 Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.40 0 240.3 cal/g·degC Specific heat, cp , J/kg·K 1 674. 1 005. Specific heat ratio, cp /cpv 1.25 1.40 Gas constant R, ft-lb/lb·deg F 59.3 53.3 Gas constant R, J/kg·deg C 319 286.8 Thermal conductivity, Btu/hr·ft·deg F 0.014 0.0151 Thermal conductivity, W/m·deg C 0.024 0.026 Boiling point (sat 14.7 psia), deg F –103 –320 Boiling point (sat 760 mm), deg C –75 –195 Latent heat of evap (at bp), Btu/lb 264 88.2 Latent heat of evap (at bp), J/kg 614 000 205 000 Freezing (melting) point, deg F –116 –357.2 (1 atm) Freezing (melting) point, deg C –82.2 –216.2 (1 atm) Latent heat of fusion, Btu/lb 23. 10.0 Latent heat of fusion, J/kg 53 500 23 200 Critical temperature, deg F 97.1 –220.5 Critical temperature, deg C 36.2 –140.3 Critical pressure, psia 907. 550.

© 2004 by CRC Press LLC

Ammonia, anhyd. NH3 717 17.02 0.59 23.0 1.43 42.6 686. 145.4 1.00 6.72 ¥ 10–6 0.010 415 0.52 2 175. 1.3 90.8 488. 0.015 0.026 –28. –33.3 589.3 1 373 000 –107.9

Argon Ar 740 39.948 1.38 9.80 0.622 87.0 1 400.

13.4 ¥ 10–6 0.02 322 0.125 523. 1.67 38.7 208. 0.010 2 0.017 2 –303. –186 70. 163 000 –308.5

–77.7

–189.2

143.0 332 300 271.4 132.5 1 650.

–187.6 –122 707.

1587_Book.fm Page 25 Monday, September 1, 2003 7:17 PM

4-25

Mechanical Engineering

Properties of Gases (continued) Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

Yes 1 450 21 600 50 200

3.8 0.050 0.003 No — — —

11.4 0.068 0.004 24 No — — —

4.87 0.029 9 0.001 86 No — — —

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number Chemical and Physical Properties Molecular weight Specific gravity, air = 1 Specific volume, ft3/lb Specific volume, m3/kg Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3 Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or cal/g·degC Specific heat, cp , J/kg·K Specific heat ratio, cp /cpv Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F Boiling point (sat 760 mm), deg C Latent heat of evap (at bp), Btu/lb Latent heat of evap (at bp), J/kg Freezing (melting) point, deg F (1 atm) Freezing (melting) point, deg C (1 atm) Latent heat of fusion, Btu/lb Latent heat of fusion, J/kg Critical temperature, deg F Critical temperature, deg C Critical pressure, psia Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

6.25

For N·sec/m2 divide by 1 000.

© 2004 by CRC Press LLC

Butadiene C 4H 6 —

n-Butane C4H10 600

54.09 1.87 7.1 0.44

58.12 2.07 6.5 0.405 37.5 604. 35.4 0.024 4 4.8 ¥ 10–6 0.007 216

226 0.341 1 427. 1.12 28.55 154.

0.39

Isobutane (2-Methylpropane) C4H10 600a 58.12 2.07 6.5 0.418 37.2 599. 50.4 0.347

216 0.39

–164

1 675. 1.096 26.56 143. 0.01 0.017 31.2 –0.4 165.6 386 000 –217.

1 630. 1.10 26.56 143. 0.01 0.017 10.8 –11.8 157.5 366 000 –229

–109.

–138.

–145

24.1 –4.5

171. 652.

Yes 2 950 20 900 48 600

19.2 44 700 306 152. 550. 3.8 0.070 0.004 3 Yes 3 300 21 400 49 700

273. 134. 537. 3.7

Yes 3 300 21 400 49 700

l-Butene (Butylene) C 4H 8 — 56.108 1.94 6.7 0.42

222 0.36 1 505. 1.112 27.52 148.

20.6 –6.3 167.9 391 000 –301 6 –185.3 16.4 38 100 –291. 144. 621. 4.28 0.068 0.004 2 Yes 3 150 21 000 48 800

1587_Book.fm Page 26 Monday, September 1, 2003 7:17 PM

4-26

CRC Handbook of Engineering Tables

Properties of Gases (continued) Common Name(s) Chemical Formula Refrigerant Number

cis-2-Butene C 4H 8 —

Chemical and Physical Properties Molecular weight 56.108 Specific gravity, air = 1 1.94 Specific volume, ft3/lb 6.7 Specific volume, m3/kg 0.42 Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3 Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec 223. Thermal and Thermodynamic Properties 0.327 Specific heat, cp , Btu/b·deg F or cal/g·degC Specific heat, cp , J/kg·K 1 368. Specific heat ratio, cp /cpv 1.121 Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F 38.6 Boiling point (sat 760 mm), deg C 3.7 Latent heat of evap (at bp), Btu/lb 178.9 Latent heat of evap (at bp), J/kg 416 000. Freezing (melting) point, deg F –218. (1 atm) Freezing (melting) point, deg C –138.9 (1 atm) Latent heat of fusion, Btu/lb 31.2 Latent heat of fusion, J/kg 72 600. Critical temperature, deg F Critical temperature, deg C 160. Critical pressure, psia 595. Critical pressure, MN/m2 4.10 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Yes Heat of combustion, Btu/ft3 3 150. Heat of combustion, Btu/lb 21 000. Heat of combustion, kJ/kg 48 800. a b

trans-2-Butene C 4H 8 — 56.108 1.94 6.7 0.42

221.

Isobutene C 4H 8 — 56.108 1.94 6.7 0.42

221.

Carbon Dioxide CO2 CO2 744 44.01 1.52 8.8 0.55 — — 931. 6.42 9.4 ¥ 10–6 0.014 270.

0.365

0.37

0.205

1 527. 1.107

1 548. 1.10

876. 1.30 35.1 189. 0.01 0.017 –109.4b –78.5 246. 572 000.

33.6 0.9 174.4 406 000. –158.

19.2 –7.1 169. 393 000.

–105.5 41.6 96 800.

25.3 58 800.

— — 88. 31. 1 072. 7.4

Yes 3 150. 21 000. 48 800.

No — — —

155. 610. 4.20

Yes 3 150. 21 000. 48 800.

For N·sec/m2 divide by 1 000. Sublimes.

Common Name(s) Chemical Formula Refrigerant Number Chemical and Physical Properties Molecular weight Specific gravity, air = 1 Specific volume, ft3/lb Specific volume, m3/kg Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3

© 2004 by CRC Press LLC

Carbon Monoxide CO — 28.011 0.967 14.0 0.874

Chlorine Cl2 — 70.906 2.45 5.52 0.344 97.3 1 559.

Deuterium D2 — 2.014 0.070 194.5 12.12

Ethane C 2H 6 170 30.070 1.04 13.025 0.815 28. 449.

1587_Book.fm Page 27 Monday, September 1, 2003 7:17 PM

4-27

Mechanical Engineering

Properties of Gases (continued) Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec 12.1 ¥ 10–6 Viscosity (abs), centipoisesa 0.018 Sound velocity in gas, m/sec 352. Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.25 cal/g·degC Specific heat, cp , J/kg·K 1 046. Specific heat ratio, cp /cpv 1.40 Gas constant R, ft-lb/lb·deg F 55.2 Gas constant R, J/kg·deg C 297. Thermal conductivity, Btu/hr·ft·deg F 0.014 Thermal conductivity, W/m·deg C 0.024 Boiling point (sat 14.7 psia), deg F –312.7 Boiling point (sat 760 mm), deg C –191.5 Latent heat of evap (at bp), Btu/lb 92.8 Latent heat of evap (at bp), J/kg 216 000. Freezing (melting) point, deg F –337. (1 atm) Freezing (melting) point, deg C –205. (1 atm) Latent heat of fusion, Btu/lb 12.8 Latent heat of fusion, J/kg Critical temperature, deg F –220. Critical temperature, deg C –140. Critical pressure, psia 507. 3.49 Critical pressure, MN/m2 Critical volume, ft3/lb 0.053 0.003 3 Critical volume, m3/kg Flammable (yes or no) Yes Heat of combustion, Btu/ft3 310. Heat of combustion, Btu/lb 4 340. Heat of combustion, kJ/kg 10 100. a

9.4 ¥ 10–6 0.014 215. 0.114 477. 1.35 21.8 117. 0.005 0.008 7 –29.2 –34. 123.7 288 000. –150.

0.756 0.005 2 8.75 ¥ 10–6 0.013 930. 1.73 7 238. 1.40 384. 2 066. 0.081 0.140 —

–101. 41.0 95 400. 291. 144. 1 120. 7.72 0.028 0.001 75 No — — —

Chemical and Physical Properties Molecular weight Specific gravity, air = 1 Specific volume, ft3/lb Specific volume, m3/kg Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3 Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp, Btu/b·deg F or cal/g·degC Specific heat, cp, J/kg·K Specific heat ratio, cp/cp Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C

© 2004 by CRC Press LLC

Ethyl Chloride C2H5Cl 160

Ethylene (Ethene) C 2H 4 1150

64.515 2.23 6.07 0.378 56.5 905.

28.054 0.969 13.9 0.87 35.5 569.

204.

6.72 ¥ 10–6 0.010 331.

0.27

0.37

1 130. 1.13 24.0 129.

1 548. 1.24 55.1 296.

0.41 1 715. 1.20 51.4 276. 0.010 0.017 –127. –88.3 210. 488 000. –278. –172.2

–390.6 –234.8 241. 1.66 0.239 0.014 9

41. 95 300. 90.1 32.2 709. 4.89 0.076 0.004 7 Yes 22 300. 51 800.

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number

64. ¥ 10–6 0.095 316.

Fluorine F2 — 37.996 1.31 10.31 0.706

16.1 ¥ 10–6 0.024 290. 0.198 828. 1.35 40.7 219.

1587_Book.fm Page 28 Monday, September 1, 2003 7:17 PM

4-28

CRC Handbook of Engineering Tables

Properties of Gases (continued) Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F Boiling point (sat 760 mm), deg C Latent heat of evap (at bp), Btu/lb Latent heat of evap (at bp), J/kg Freezing (melting) point, deg F (1 atm) Freezing (melting) point, deg C (1 atm) Latent heat of fusion, Btu/lb Latent heat of fusion, J/kg Critical temperature, deg F Critical temperature, deg C Critical pressure, psia Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

54. 12.2 166. 386 000. –218. –138.9 29.3 68 100. 368.6 187. 764. 5.27 0.049 0.003 06 No — — —

0.010 0.017 –155. –103.8 208. 484 000. –272.

0.016 0.028 –306.4 –188. 74. 172 000. –364.

–169.

–220.

51.5 120 000. 49. 9.5 741. 5.11 0.073 0.004 6 Yes 1 480. 20 600. 47 800.

11. 25 600. –200 –129. 810. 5.58

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number

Fluorocarbons CCl3F 11

CCl2F2 12

Chemical and Physical Properties Molecular weight 137.37 120.91 Specific gravity, air = 1 4.74 4.17 Specific volume, ft3/lb 2.74 3.12 Specific volume, m3/kg 0.171 0.195 Density of liquid (at atm bp), lb/ft3 92.1 93.0 Density of liquid (at atm bp), kg/m3 1 475. 1 490. Vapor pressure at 25 deg C, psia 94.51 Vapor pressure at 25 deg C, MN/m2 0.652 Viscosity (abs), lbm/ft·sec 7.39 ¥ 10–6 8.74 ¥ 10–6 Viscosity (abs), centipoisesa 0.011 0.013 Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.14 0.146 cal/g·degC 586. 611. Specific heat, cp , J/kg·K Specific heat ratio, cp /cpv 1.14 1.14 Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C Thermal conductivity, Btu/hr·ft·deg F 0.005 0.006 Thermal conductivity, W/m·deg C 0.008 7 0.010 4 Boiling point (sat 14.7 psia), deg F 74.9 –21.8 Boiling point (sat 760 mm), deg C 23.8 –29.9 Latent heat of evap (at bp), Btu/lb 77.5 71.1 Latent heat of evap (at bp), J/kg 180 000. 165 000. Freezing (melting) point, deg F –168. –252. (1 atm) Freezing (melting) point, deg C –111. –157.8 (1 atm) Latent heat of fusion, Btu/lb Latent heat of fusion, J/kg

© 2004 by CRC Press LLC

CClF3 13 104.46 3.61 3.58 0.224 95.0 1 522. 516. 3.56

CBrF3 13B1 148.91 5.14 2.50 0.975 124.4 1 993. 234.8 1.619

0.154 644. 1.145

–114.6 –81.4 63.0 147 000. –294.

–72 –57.8 51.1 119 000. –270.

–181.1

–167.8

1587_Book.fm Page 29 Monday, September 1, 2003 7:17 PM

4-29

Mechanical Engineering

Properties of Gases (continued) Critical temperature, deg F Critical temperature, deg C Critical pressure, psia Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

388.4 198. 635. 4.38 0.028 9 0.001 80 No — — —

83.9 28.8 559. 3.85 0.027 7 0.001 73 No — — —

152. 66.7 573. 3.95 0.021 5 0.001 34 No — — —

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number

Fluorocarbons CF4 14

Chemical and Physical Properties Molecular weight 88.00 Specific gravity, air = 1 3.04 Specific volume, ft3/lb 4.34 Specific volume, m3/kg 0.271 Density of liquid (at atm bp), lb/ft3 102.0 Density of liquid (at atm bp), kg/m3 1 634. Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or cal/g·degC Specific heat, cp , J/kg·K Specific heat ratio, cp /cpv Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F –198.2 Boiling point (sat 760 mm), deg C –127.9 Latent heat of evap (at bp), Btu/lb 58.5 Latent heat of evap (at bp), J/kg 136 000. Freezing (melting) point, deg F (1 atm) –299. Freezing (melting) point, deg C –183.8 (1 atm) Latent heat of fusion, Btu/lb 2.53 Latent heat of fusion, J/kg 5 880 Critical temperature, deg F –49.9 Critical temperature, deg C –45.5 Critical pressure, psia 610. Critical pressure, MN/m2 4.21 Critical volume, ft3/lb 0.025 0.001 6 Critical volume, m3/kg Flammable (yes or no) No Heat of combustion, Btu/ft3 — Heat of combustion, Btu/lb — Heat of combustion, kJ/kg — a

233. 111.7 582. 4.01 0.287 0.018 No — — —

For N·sec/m2 divide by 1 000.

© 2004 by CRC Press LLC

CHCl2F 21

CHClF2 22

C2Cl2F4 114

102.92 3.55 3.7 0.231 87.7 1 405. 26.4 0.182 8.06 ¥ 10–6 0.012

86.468 2.99 4.35 0.271 88.2 1 413. 151.4 1.044 8.74 ¥ 10–6 0.013

170.92 5.90 2.6 0.162 94.8 1 519. 30.9 0.213 8.06 ¥ 10–6 0.012

0.139

0.157

0.158

582. 1.18

48.1 9.0 104.1 242 000. –211. –135.

353.3 178.5 750. 5.17 0.030 7 0.001 91 No — — —

657. 1.185

0.007 0.012 –41.3 –40.7 100.4 234 000. –256. –160.

204.8 96.5 715. 4.93 0.030 5 0.001 90 No — — —

661. 1.09

0.006 0.010 38.4 3.55 58.4 136 000. –137. –93.8

294. 475. 3.28 0.027 5 0.001 71 No — — —

1587_Book.fm Page 30 Monday, September 1, 2003 7:17 PM

4-30

CRC Handbook of Engineering Tables

Properties of Gases (continued) Common Name(s) Chemical Formula Refrigerant Number

Fluorocarbons C2ClF5 115

Chemical and Physical Properties Molecular weight 154.47 Specific gravity, air = 1 5.33 Specific volume, ft3/lb 2.44 Specific volume, m3/kg 0.152 Density of liquid (at atm bp), lb/ft3 96.5 Density of liquid (at atm bp), kg/m3 1 546. Vapor pressure at 25 deg C, psia 132.1 Vapor pressure at 25 deg C, MN/m2 0.911 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.161 cal/g·degC Specific heat, cp, J/kg·K 674. Specific heat ratio, cp /cpv 1.091 Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F –38.0 Boiling point (sat 760 mm), deg C –38.9 Latent heat of evap (at bp), Btu/lb 53.4 Latent heat of evap (at bp), J/kg 124 000. Freezing (melting) point, deg F –149. (1 atm) Freezing (melting) point, deg C –100.6 (1 atm) Latent heat of fusion, Btu/lb Latent heat of fusion, J/kg Critical temperature, deg F 176. Critical temperature, deg C Critical pressure, psia 457.6 Critical pressure, MN/m2 3.155 Critical volume, ft3/lb 0.026 1 Critical volume, m3/kg 0.001 63 Flammable (yes or no) No Heat of combustion, Btu/ft3 — Heat of combustion, Btu/lb — Heat of combustion, kJ/kg — a b

C2H3ClF2 142b 100.50 3.47 3.7 0.231 74.6 1 195. 49.1 0.338 5

C 2H 4F 2 152a 66.05 2.28 5.9 0.368 62.8 1 006. 86.8 0.596

Helium He 704 4.002 6 0.138 97.86 6.11 7.80 125.

13.4 ¥ 10–6 0.02 1 015. 1.24

14. –10.0 92.5 215 000.

–13. –25.0 137.1 319 000.

5 188. 1.66 386. 2 077. 0.086 0.149 –452. 4.22 K 10.0 23 300. b

—

387.

No — — —

No — — —

–450.3 5.2 K 33.22 0.231 0.014 4 No — — —

For N·sec/m2 divide by 1 000. Helium cannot be solidified at atmospheric pressure.

Common Name(s) Chemical Formula Refrigerant Number Chemical and Physical Properties Molecular weight Specific gravity, air = 1 Specific volume, ft3/lb Specific volume, m3/kg Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3

© 2004 by CRC Press LLC

Hydrogen H2 702 2.016 0.070 194. 12.1 4.43 71.0

Hydrogen Chloride HCl — 36.461 1.26 10.74 0.670 74.4 1 192.

Hydrogen Sulfide H 2S — 34.076 1.18 11.5 0.093 0 62. 993.

Krypton Kr — 83.80 2.89 4.67 0.291 150.6 2 413.

1587_Book.fm Page 31 Monday, September 1, 2003 7:17 PM

4-31

Mechanical Engineering

Properties of Gases (continued) Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft Viscosity 6.05 ¥ 10–6 10.1 ¥ 10–6 (abs), lbm/ft¥ 10–6 Viscosity (abs), centipoisesa 0.009 0.015 Sound velocity in gas, m/sec 1 315. 310. Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 3.42 0.194 cal/g·degC Specific heat, cp , J/kg·K 14 310. 812. Specific heat ratio, cp /cpv 1.405 1.39 Gas constant R, ft-lb/lb·deg F 767. 42.4 Gas constant R, J/kg·deg C 4 126. 228. Thermal conductivity, Btu/hr·ft·deg F 0.105 0.008 Thermal conductivity, W/m·deg C 0.018 2 0.014 Boiling point (sat 14.7 psia), deg F –423. –121. Boiling point (sat 760 mm), deg C 20.4 K –85. Latent heat of evap (at bp), Btu/lb 192. 190.5 Latent heat of evap (at bp), J/kg 447 000. 443 000. Freezing (melting) point, deg F (1 atm) –434.6 –169.6 Freezing (melting) point, deg C –259.1 –112. (1 atm) Latent heat of fusion, Btu/lb 25.0 23.4 Latent heat of fusion, J/kg 58 000. 54 400. Critical temperature, deg F –399.8 124. Critical temperature, deg C –240.0 51.2 Critical pressure, psia 189. 1 201. 1.30 8.28 Critical pressure, MN/m2 Critical volume, ft3/lb 0.53 0.038 0.033 0.002 4 Critical volume, m3/kg Flammable (yes or no) Yes No Heat of combustion, Btu/ft3 320. — Heat of combustion, Btu/lb 62 050. — Heat of combustion, kJ/kg 144 000. — a

8.74 ¥ 10–6 0.013 302. 0.23 962. 1.33 45.3 244. 0.008 0.014 –76. –60. 234. 544 000. –119.2 –84. 30.2 70 200. 213. 100.4 1 309. 9.02 0.046 0.002 9 Yes 700. 8 000. 18 600.

16.8 ¥ 10–6 0.025 223. 0.059 247. 1.68 18.4 99.0 0.005 4 0.009 3 –244. –153. 46.4 108 000. –272. –169. 4.7 10 900. –63.8 800. 5.52 0.017 7 0.001 1 No — — —

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number Chemical and Physical Properties Molecular weight Specific gravity, air = 1 Specific volume, ft3/lb Specific volume, m3/kg Density of liquid (at atm bp), lb/ft3 Density of liquid (at atm bp), kg/m3 Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec Viscosity (abs), centipoisesa Sound velocity in gas, m/sec Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or cal/g·degC Specific heat, cp , J/kg·K Specific heat ratio, cp /cpv Gas constant R, ft-lb/lb·deg F Gas constant R, J/kg·deg C

© 2004 by CRC Press LLC

Methane CH4 50

Methyl Chloride CH3Cl 40

Neon NE 720

16,044 0.554 24.2 1.51 26.3 421.

50,488 1.74 7.4 0.462 62.7 1 004. 82.2 0.567 7.39 ¥ 10–6 0.011 251.

20.179 0.697 19.41 1.211 75.35 1 207.

7.39 ¥ 10–6 0.011 446. 0.54

0.20

2 260. 1.31 96. 518.

837. 1.28 30.6 165.

21.5 ¥ 10–6 0.032 454. 0.246 1 030. 1.64 76.6 412.

Nitric Oxcide NO — 30.006 1.04 13.05 0.814

12.8 ¥ 10–6 0.019 341. 0.235 983. 1.40 51.5 277.

1587_Book.fm Page 32 Monday, September 1, 2003 7:17 PM

4-32

CRC Handbook of Engineering Tables

Properties of Gases (continued) Thermal conductivity, Btu/hr·ft·deg F Thermal conductivity, W/m·deg C Boiling point (sat 14.7 psia), deg F Boiling point (sat 760 mm), deg C Latent heat of evap (at bp), Btu/lb Latent heat of evap (at bp), J/kg Freezing (melting) point, deg F (1 atm) Freezing (melting) point, deg C (1 atm) Latent heat of fusion, Btu/lb Latent heat of fusion, J/kg Critical temperature, deg F Critical temperature, deg C Critical pressure, psia Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

0.02 0.035 –259. –434.2 219.2 510 000. –296.6 –182.6 14. 32 600. –116. –82.3 673. 4.64 0.099 0.006 2 Yes 985. 2 290.

0.006 0.010 –10.7 –23.7 184.1 428 000. –144. –97.8

0.028 0.048 –410.9 –246. 37. 86 100. –415.6 –248.7

56. 130 000. 289.4 143. 968. 6.67 0.043 0.002 7 Yes

6.8 15 800. –379.8 –228.8 396. 2.73 0.033 0.002 0 No — —

0.015 0.026 –240. –151.5

–258. –161. 32.9 76 500. –136. –93.3 945. 6.52 0.033 2 0.002 07 No — — —

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number

Nitrogen N2 728

Chemical and Physical Properties Molecular weight 28.013 4 Specific gravity, air = 1 0.967 Specific volume, ft3/lb 13.98 Specific volume, m3/kg 0.872 Density of liquid (at atm bp), lb/ft3 50.46 Density of liquid (at atm bp), kg/m3 808.4 Vapor pressure at 25 deg C, psia Vapor pressure at 25 deg C, MN/m2 Viscosity (abs), lbm/ft·sec 12.1 ¥ 10–6 Viscosity (abs), centipoisesa 0.018 Sound velocity in gas, m/sec 353. Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.249 cal/g·degC Specific heat, cp , J/kg·K 1040. 1.40 Specific heat ratio, cp /cpv Gas constant R, ft-lb/lb·deg F 55.2 Gas constant R, J/kg·deg C 297. Thermal conductivity, Btu/hr·ft·deg F 0.015 Thermal conductivity, W/m·deg C 0.026 Boiling point (sat 14.7 psia), deg F –320.4 Boiling point (sat 760 mm), deg C –195.8 Latent heat of evap (at bp), Btu/lb 85.5 Latent heat of evap (at bp), J/kg 199 000. Freezing (melting) point, deg F (1 atm) –346. Freezing (melting) point, deg C –210. (1 atm) Latent heat of fusion, Btu/lb 11.1 Latent heat of fusion, J/kg 25 800. Critical temperature, deg F –232.6 Critical temperature, deg C –147.

© 2004 by CRC Press LLC

Nitrous Oxide N 2O 744A 44.012 1.52 8.90 0.555 76.6 1 227.

10.1 ¥ 10–6 0.015 268. 0.21 879. 1.31 35.1 189. 0.010 0.017 –127.3 –88.5 161.8 376 000. –131.5 –90.8 63.9 149 000. 97.7 36.5

Oxygen O2 732 31.998 8 1.105 12.24 0.764 71.27 1 142.

13.4 ¥ 10–6 0.020 329. 0.220 920. 1.40 48.3 260. 0.015 0.026 –297.3 –182.97 91.7 213 000. 361.1 –218.4 5.9 13 700. –181.5 –118.6

Ozone O3 — 47.998 1.66 8.16 0.509

8.74 ¥ 10–6 0.013

0.196 820. 32.2 173. 0.019 0.033 –170. –112.

–315.5 –193. 97.2 226 000. 16. –9.

1587_Book.fm Page 33 Monday, September 1, 2003 7:17 PM

4-33

Mechanical Engineering

Properties of Gases (continued) Critical pressure, psia Critical pressure, MN/m2 Critical volume, ft3/lb Critical volume, m3/kg Flammable (yes or no) Heat of combustion, Btu/ft3 Heat of combustion, Btu/lb Heat of combustion, kJ/kg a

493. 3.40 0.051 0.003 18 No — — —

1 052. 7.25 0.036 0.002 2 No — — —

726. 5.01 0.040 0.002 5 No — — —

800. 5.52 0.029 8 0.001 86 No — — —

For N·sec/m2 divide by 1 000.

Common Name(s) Chemical Formula Refrigerant Number

Propane C 3H 8 290

Chemical and Physical Properties Molecular weight 44.097 Specific gravity, air = 1 1.52 8.84 Specific volume, ft3/lb Specific volume, m3/kg 0.552 Density of liquid (at atm bp), lb/ft3 36.2 Density of liquid (at atm bp), kg/m3 580. Vapor pressure at 25 deg C, psia 135.7 Vapor pressure at 25 deg C, MN/m2 0.936 Viscosity (abs), lbm/ft·sec 53.8 ¥ 10–6 Viscosity (abs), centipoisesa 0.080 Sound velocity in gas, m/sec 253. Thermal and Thermodynamic Properties Specific heat, cp , Btu/b·deg F or 0.39 cal/g·degC Specific heat, cp , J/kg·K 1 630. Specific heat ratio, cp /cpv 1.2 Gas constant R, ft-lb/lb·deg F 35.0 Gas constant R, J/kg·deg C 188. Thermal conductivity, Btu/hr·ft·deg F 0.010 Thermal conductivity, W/m·deg C 0.017 Boiling point (sat 14.7 psia), deg F –44. Boiling point (sat 760 mm), deg C –42.2 Latent heat of evap (at bp), Btu/lb 184. Latent heat of evap (at bp), J/kg 428 000. Freezing (melting) point, deg F (1 atm) –309.8 Freezing (melting) point, deg C –189.9 (1 atm) Latent heat of fusion, Btu/lb 19.1 Latent heat of fusion, J/kg 44 400. Critical temperature, deg F 205. Critical temperature, deg C 96. Critical pressure, psia 618. Critical pressure, MN/m2 4.26 Critical volume, ft3/lb 0.073 0.004 5 Critical volume, m3/kg Flammable (yes or no) Yes Heat of combustion, Btu/ft3 2 450. Heat of combustion, Btu/lb 21 660. Heat of combustion, kJ/kg 50 340. a

Propylene (Propene) C 3H 6 1 270 42.08 1.45 9.3 0.58 37.5 601. 166.4 1.147 57.1 ¥ 10–6 0.085 261. 0.36 1 506. 1.16 36.7 197. 0.010 0.017 –54. –48.3 188.2 438 000. –301. –185.

197. 91.7 668. 4.61 0.069 0.004 3 Yes 2 310. 21 500. 50 000.

Sulfur Dioxide SO2 764 64.06 2.21 6.11 42.8 585. 56.6 0.390 8.74 ¥ 10–6 0.013 220. 0.11

Xenon Xe — 131.30 4.53 2.98 190.8 3 060.

15.5 ¥ 10–6 0.023 177. 0.115

460. 1.29 24.1 130. 0.006 0.010 14.0 –10. 155.5 362 000. –104. –75.5

481. 1.67 11.8 63.5 0.003 0.005 2 –162.5 –108. 41.4 96 000. –220. –140.

58.0 135 000. 315.5 157.6 1 141. 7.87 0.03 0.001 9

10. 23 300. 61.9 16.6 852. 5.87 0.014 5 0.000 90 Yes — — —

— — —

For N·sec/m2 divide by 1 000. From Bolz, R.E. and Tuve, G.L., Gases and vapors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 38–49.

© 2004 by CRC Press LLC

Typical Composition, Properties, and Uses of Common Materials For MN/m2 multiply strength in thousands of psi by 6.895. Typical Mechanical Properties

No.

Nominal Composition

Material

Form and Condition

Yield Strength (0.2% offset), 1000 lb/sq in.

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

Comments

FERROUS ALLOYS Ferrous alloys comprise the largest volume of metal alloys used in engineering. The actual range of mechanical properties in any particular grade of alloy steel depends on the particular history and heat treatment. The steels listed in this table are intended to give some idea of the range of properties readily obtainable. Many hundreds of steels are available. Cost is frequently an important criterion in the choice of material; in general the greater the percentage of alloying elements present in the alloy, the greater will be the cost. Iron 1 Ingot iron (Included for comparison) Plain Carbon Steels 2 AISI-SAE 1020

Fe

99.9

0.20 0.25

Mn Fe bal.

C Mn

0.25 0.45

Fe bal.

4 AISI-SAE 1035

C

0.35

Mn

5 AISI-SAE 1045

C Mn

0.45 0.75

Fe bal.

C Mn

0.78 0.45

Fe bal.

C Mn

0.95 0.40

Fe bal.

3 AISI 1025

6 AISI-SAE 1078

7 AISI-SAE 1095

© 2004 by CRC Press LLC

0.45

0.75

29

45

26

90

Annealed

19

38

45

67

Hot-rolled Hardened (water-quenched, 1000˚F-tempered) Bar stock Hot-rolled Cold-drawn Hot-rolled Cold-rolled Bar stock Annealed Hot-rolled Cold-drawn Bar stock Hot-rolled; spheroidized Annealed

30 62

55 90

25 25

111 179

32 54 39 67

58 64 72 80

25 15 18 12

116 126 143 163

73 45 77

80 82 91

12 16 12

170 163 179

55 72

100 94

12 10

207 192

Bolts, crankshafts, gears, connecting rods; easily weldable

Medium-strength, engineering steel

CRC Handbook of Engineering Tables

C Si

Hot-rolled

1587_Book.fm Page 34 Monday, September 1, 2003 7:17 PM

4-34

Mechanical Properties of Metals and Alloys

Cold-drawn

58

69

—

137

C 0.17 Cr 0.5 C 0.40 Cr 1.0 Mn 0.9 12% Mn

Mn Si Si Mo

1.2 0.75 0.3 0.2

Stress-relieved

45

75

18

—

Fully-tempered Optimum properties

95 132

108 150

22 18

240 —

Tempered 600˚F Rolled and heat-treated stock

200 44

220 160

10 40

— 170

12 VASCO 300

Ni Co Mo

18.5 9.0 4.8

Ti C

0.6 0.03

Solution treatment 1 500˚F; aged 900·F

110

150

18

—

13 TI (AISI)

W Cr

18.0 4.0

V C

1.0 0.7

Quenched; tempered

R(c)

14 M2 (AISI)

W Cr V Ni Cr

6.5 4.0 2.0 9.0 19.0

Mo C

5.0 0.85

Quenched; tempered

65–66

0.08 max

Annealed; cold-rolled

35–160

85–185

60 8

160–400

16 Stainless steel type 316

Cr Ni Mo

18.0 11.0 2.5

C

0.10 max Fe bal.

Annealed

30–120

90–150

50 8

165

17 Stainless steel type 431

Cr Ni Mn

16.0 2.0 1.0

Si C Fe bal.

1.0 0.20

Annealed Heat-treated

85 150

120 195

25 20

250 400

18 Stainless steel 17–4 PH

Cr Ni Cu

17.0 4.0 4.0

Co C Fe bal.

0.35 0.07

Annealed

110

150

10

363

Alloy Steels 9 ASTM A202/56 10 AISI 4140

11 12% Manganese steel

15 Stainless steel type 304

C

C

Free-cutting, leaded, resulphurized steel; high-speed, automatic machining Low alloy; boilers, pressure vessels High strength; gears, shafts Machine tool parts; wear, abrasionresistant Very high strength, maraging, good machining properties in annealed state High speed tool steel, cutting tools, punches, etc. M-grade, cheaper, tougher General purpose, weldable; nonmagnetic austenitic steel For severe corrosive media, under stress; nonmagnetic austenitic steel Heat-treated stainless steel, with good mechanical strength; magnetic Precipitation hardening; heatresisting type; retains strength up to approx. 600˚F

4-35

© 2004 by CRC Press LLC

0.2 0.1

1587_Book.fm Page 35 Tuesday, September 2, 2003 3:25 PM

0.8

C S

Mechanical Engineering

Mn

8 AISI-SAE 1120

Typical Mechanical Properties

No.

Nominal Composition

Material

Form and Condition

Yield Strength (0.2% offset), 1000 lb/sq in.

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

Comments

CAST IRONS AND CAST STEELS These alloys are used where large and/or intricate-shaped articles are required or where overall dimensional tolerances are not critical. Thus the article can be produced with the fabrication and machining costs held to a minimum. Except for a few heat-treatable cast steels, this class of alloys does not demonstrate high-strength qualities. Cast Irons 19 Cast gray iron C ASTM A48–48, Class 25 Mn 20 White 21 Malleable iron ASTM A47

24 Ni-resist type 2

Cast Steels 25 ASTM A27-62 (60-30)

26 ASTM A148-60 (105-85)

© 2004 by CRC Press LLC

C Mn C Mn

Si

1.8

Cast (as cast)

—

25 min

0.5 max

180

Si

0.7

Cast

—

25

0

450

Si

1.0

Cast (annealed)

33

52

12

130

53 68 108

70 90 135

18 7 5

170 235 310

Sand-cast Chill-cast (tempered)

— —

55 75

— —

550 625

Cast (as cast)

—

27

2

140

30

60

24

—

85

105

17

—

3.4 0.6 2.5 0.55 max C 3.4 Mn 0.40 Ni 1% Si 2.5 C 2.7 Mn 0.5 Cr 2.0 C 3.0 Mn 1.0 Cr 2.5

0.1 max Mg 0.06 Fe bal. Si 0.6 Ni 4.5 Fe bal. Si 2.0 Ni 20.0 Fe bal.

C Si Cr

Mn Ni Mo

0.3 0.8 0.4

P

0.6 0.5 0.2

Cast Cast (as cast) Cast (quenched, tempered)

Engine blocks, flywheels, gears, machine-tool bases

Automotives, axle bearings, track wheels, crankshafts Heavy-duty machines, gears, cams, crankshafts Strength, with heatand corrosionresistance

Low alloy, medium strength, general application High strength; structural application

CRC Handbook of Engineering Tables

22 Ductile or nodular iron (Mg-containing) ASTM A339 ASTM A395 23 Ni-hard type 2

34 0.5

1587_Book.fm Page 36 Monday, September 1, 2003 7:17 PM

4-36

Mechanical Properties of Metals and Alloys (continued)

C

Ni 28 Cast 29-9 alloy (CE-30) ASTM–A296 63T

C Si

29 Cast 28-7 alloy (HD) ASTM–A97-63T

Ni C Si Ni

Mn

1.00 Air-cooled from 1800˚F; tempered at 600˚F max Cr 11.5–14 Air-cooled from 1800˚F; tempered at 1400˚F Fe bal.

150

200

7

390

75

100

30

185

Stainless, corrosionresistant to mildly corrosive alkalis and acids

Min

1.50 max Cr 26–30 Fe bal.

As cast

60

95

15

170

Greater corrosion resistance, especially for oxidizing condition

Mn

As cast

48

85

16

190

Heat-resistant

1.50 max Cr 26–30 Fe bal.

Mechanical Engineering

Si

0.15 max 150 max 1.00 max 0.30 max 2.00 max 8–11 0.50 max 2.00 4–7

SUPER ALLOYS The advent of engineering applications requiring high temperature and high strength, as in jet engines and rocket motors, has lead to the development of a range of alloys collectively called super alloys. These alloys require excellent resistance to oxidation together with strength at high temperatures, typically 1800˚F in existing engines. These alloys are continually being modified to develop better specific properties, and therefore entries in this group of alloys should be considered “fluid”. Both wrought and casting-type alloys are represented. As the high temperature properties of cast materials improve, these alloys become more attractive, since great dimensional precision is now attainable in investment castings. Nickel Base 30 Hastelloy X

31 Hastelloy C

32 Inconel 712C

33 In 100

1.5 max Cr 22.0 W 0.6 C 0.20 max (cast) Cr 16.0

Fe

W

C

4.0

Mo 17.0 Ni (+Co) bal. Mo 4.5 Al 6.0 C 18.0 Mo 3.0 Al 55.0 V 1.0

Fe 18.5 Wrought sheet Mo 9.0 Mill-annealed C 0.15 As investment cast max (wrought) Ni bal. 6.0

0.15 max Ni bal. Cr 13.0 Cb 2.0 Ti 0.6 Cr Ti Co

10.0 4.7 15.0

Sand-cast (annealed) Rolled (annealed) Investment cast

Investment cast

52 — 46.5

113.2 67 —

43 17 —

194 172 —

50 71 50

78 130 80

5 45 10

199 204 215

102

120

6

—

Cast

4-37

© 2004 by CRC Press LLC

Co

1587_Book.fm Page 37 Monday, September 1, 2003 7:17 PM

27 Cast 12 Cr alloy (CA-15)

Typical Mechanical Properties

No.

Material

34 Taz 8

35 Nimonic 90

36 Inconel X

38 Rene 41

39 Udimet 700

40 T.D. Nickel

© 2004 by CRC Press LLC

C 125.0 Mo 4.0 W 4.0 Ta 8.0 Ni (+Co) 57.00 Mn 0.50 S 0.007 Cu 0.05 Al 1.65 Co 16.90 Ni (+Co) 72.85 Mn 0.65 S 0.007 Cu 0.05 Al 0.75 Cb (+Ta) 0.85 C 0.08 Mo 4.3 Co 13.5 C 0.09 Mo 10.0 Al 1.5 C 0.08 Mo 5.0 Al 4.3 Ni 97.5

Form and Condition

Cr Al Zr V C Fe Si Cr Ti

6.0 6.0 1.0 2.5 0.05 0.45 0.20 20.55 2.60

C Fe Si Cr Ti

0.04

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

Comments

Cast

Annealed; wrought

90

155

—

260

Annealed

50

115

50

150 300

6.80 0.30 15.0 2.50

Annealed; age hardened

115

175

25

Cr Ti

19.5 3.0

Cold-rolled

270

275

8

Cr Ti Co Cr Ti Co ThO2

19.0 3.1 11.0 15.0 3.5 18.5 2.4

Wrought

100

145

—

Cold-rolled

280

285

6

85

100

13

Extended and cold-worked

General elevated temperature applications

Rc 51

—

Rc 53

—

High temperature; jet engine parts

CRC Handbook of Engineering Tables

37 Waspaloy

Nominal Composition

Yield Strength (0.2% offset), 1000 lb/sq in.

1587_Book.fm Page 38 Monday, September 1, 2003 7:17 PM

4-38

Mechanical Properties of Metals and Alloys (continued)

0.15 max Ni 10.0 Mn 1.5 C 0.25 Ni 2.5 Cr 28.5

Cr 20.0 W 15.0 Co bal. Mo 5.5 Co. bal.

Wrought sheet; mill annealed

63

140

60

As investment cast

82

103

8

244

313 max

For castings

ALUMINUM ALLOYS Although the strength of aluminum alloys is in general less than that attainable in ferrous alloys or copper-base alloys, their major advantage lies in their high strength-to-weight ratio due to the low density of aluminum. Aluminum alloys have good corrosion resistance for most applications except in alkaline solutions. 6 21 27

16 22 29

40 16 10

28 40 55

0.5

Annealed-O Heat-treated-T4

10 40

26 62

22 22

45 105

Mg Al bal. Al bal.

1.5

Heat-treated-T4

47

68

19

120

Annealed-O Cold-rolled and stabilized H34

13 31

28 38

30 14

47 68

Mg Al bal.

2.5

Cold-rolled and stabilized H38 Annealed-O Heat-treated and artificially aged-T6 Die-cast

37 15 73

42 33 83

8 17 11

77 60 150

24

48

3

—

16 24

32 36

8.5 5

60 75

Al bal.

Sand-cast; heat-treated-T4 Sand-cast; heat-treated and artificially aged-T6 Sand-cast-F

12

25

9

50

Al bal.

Sand-cast; heat-treated-T4

26

48

16

75

Cu Mn

0.12 1.2

Al bal.

44 2017 ASTM B221

Mn Cu

0.5 4.0

Mg Al bal.

45 2024 ASTM B211 46 5052 ASTM B211

Cu Mn Cr Mg

4.5 0.6 0.25 2.5

Cu Cr Zn Si Cu Si Cu

1.6 0.3 5.6 9.0 3.5 0.8 4.5

51 214 ASTM G4A

Mg

3.8

52 220 ASTM G10A

Mg

10.0

47 ASTM B208 48 7075 ASTM B211 49 380 ASTM SC84B 50 195 ASTM C4A

© 2004 by CRC Press LLC

Al bal. Al bal.

Good formability, weldable, medium strength; chemical equipment High strength; structural parts, aircraft, heavy forgings

Medium strength, good fatigue properties; street-light standards High strength, good corrosion resistance General purpose die casting Structural elements, aircraft, and machines Chemical equipment, marine hardware, architectural Strength with shock resistance; aircraft

4-39

Annealed-O Cold-rolled-H14 Cold-rolled-H18

43 3003 ASTM B221

1587_Book.fm Page 39 Tuesday, September 2, 2003 3:25 PM

42 Haynes Stellite alloy 21 AMS 5385 (cast)

C

Mechanical Engineering

Cobalt Base 41 Haynes Stellite alloy 25 (L605)

4-40

Typical Mechanical Properties

No.

Nominal Composition

Material

Form and Condition

Yield Strength (0.2% offset), 1000 lb/sq in.

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

Comments

COPPER ALLOYS Because of their corrosion resistance and the fact that copper alloys have been used for many thousands of years, the number of copper alloys available is second only to the ferrous alloys. In general copper alloys do not have the high-strength qualities of the ferrous alloys, while their density is comparable. The cost per strength-weight ratio is high; however, they have the advantage of ease of joining by soldering, which is not shared by other metals that have reasonable corrosion resistance. 53 Copper

54 55

57

58

59 Naval brass ASTM B21 60 Muntz metal ASTM B111

© 2004 by CRC Press LLC

99.9 plus

Annealed

10

32

45

42

Cold-drawn Cold-rolled

40 40

45 46

15 5

90 100

Bus-bars, switches, architectural, roofing, screens

Cu

95.0

Zn

5.0

Cold-rolled

50

56

5

114

Coinage, ammunition

Cu

70.0

Zn

30.0

Cold-rolled

63

76

8

155

Good cold-working poperties; radiator covers, hardware, electrical

Cu P

90.0 0.25

Sn

10.0

Spring temper

—

122

4

241

Good spring qualities, high-fatigue strength

Cu

65.0

Zn

35.0

Annealed Cold-drawn Cold-rolled (HT)

18 55 60

48 70 74

60 15 10

55 115 180

Good corrosion resistance; plumbing, architectural

Cu Fe Mn Cu Sn

58.5 1.0 0.3 60.0 0.75

Zn Sn

39.2 1.0

Annealed Cold-drawn

30 50

60 80

30 20

95 180

Forgings

Zn

39.25

Annealed Cold-drawn

22 40

56 65

40 35

90 150

Cu

60.0

Zn

40.0

Annealed

20

54

45

80

Condensor tubing; high resistance to salt-water corrosion Condensor tubes; valve stress

CRC Handbook of Engineering Tables

56

ASTM B152 ASTM B124, B133 ASTM B1, B2, B3 Gilding metal ASTM B36 Cartridge 70-30 brass ASTM B14 ASTM B19 ASTM B36 ASTM B134 ASTM B135 Phosphor bronze 10% ASTM B103 ASTM B130 ASTM B159 Yellow brass (high brass) ASTM B36 ASTM B134 ASTM B135 Manganese bronze ASTM B138

Cu

1587_Book.fm Page 40 Monday, September 1, 2003 7:17 PM

Mechanical Properties of Metals and Alloys (continued)

68 Red brass (cast) ASTM B30, No. 4A 69 Silicon bronze ASTM B30, alloy 12A 70 Tin bronze ASTM B30, alloy B

92.0

Al

8.0

Annealed Hard

25 65

70 105

60 7

80 210

32

70

45

104 70 44

110 190 70

5 3 18

Annealed Cold-rolled Cold-drawn wire Cast

25 70 — 18

58 85 105 35

40 4 — 15

B60 (Rockwell) B81 C40 B80 (Rockwell) 70 170 — 55

22 57

44 60

45 15

— —

Be 1.9 Co or Ni 0.25

Cu bal.

Annealed, solution-treated

Cu Pb Cu Ni

62.0 2.5 65.0 18.0

Zn

35.5

Cold-rolled Cold-rolled Cold-drawn

Zn

17.0

Ni Sn Zn Cu Fe

12.5 2.0 20.0 88.35 1.25

Pb 9.0 Cu bal. Ni Mn

10.0 0.4

Annealed Cold-drawn tube

Cu

70.0

Ni

30.0

Wrought

Cu Pb Si Zn Mn Sn

85.0 5.0 4.0 4.0 1.0 8%

Zn Sn Fe Al

5.0 5.0 2.0 1.0

As-cast Castings

Cheaper substitute for tin bronze

Zn

4.0

Castings

Bearings, high-pressure brushings, pump impellers

71 Navy bronze

Bellows, fuse clips, electrical relay parts, valves, pumps Screws, nuts, gears, keys Hardware, optical goods, camera parts Ornamental castings, plumbing; good machining qualities Condensor, salt-water piping Heat-exchanger process equipment, valves

17

35

25

60

Cast TIN AND LEAD-BASE ALLOYS

Major uses for these alloys are as “white”-metal bearing alloys, extruded cable sheathing, and solders. Tin forms the basis of pewter used for culinary applications. 72 Lead-base Babbitt ASTM B23, alloy 19

© 2004 by CRC Press LLC

85.0 10.0 0.5 83.0 16.0 0.6

Sn As

5.0 0.6

Chill east

—

10

5

19

Bearings, light loads and low speeds

Sn As

1.0 1.1

Chill cast

—

10.3

2

20

Bearings, high loads and speeds, diesel engines, steel mills

4-41

73 Arsenical-lead Babbitt ASTM B23, alloy 15

Pb Sb Cu Pb Sb Cu

1587_Book.fm Page 41 Tuesday, September 2, 2003 3:25 PM

64 Nickel silver 18% Alloy A (wrought) ASTM B122, No. 2 65 Nickel silver 13% (cast) 10A ASTM B149, No. 10A 66 Cupronickel 10% ASTM B111 ASTM B171 67 Cupronickel

Cu

Mechanical Engineering

61 Aluminum bronze ASTM B169, alloy A ASTM B124 ASTM B150 62 Beryllium copper 25 ASTM B194 ASTM B197 ASTM B196 63 Free-cutting brass

Typical Mechanical Properties

No.

Nominal Composition

Material

74 Chemical lead

Pb Bi

75 Antimonial lead (hard lead)

Pb

76 Calcium lead

Pb Cu Sb Cu Sb Cu Sn Cu Sn Sn

77 Tin Babbitt alloy ASTM B23–61, grade 1 78 Tin die-casting alloy ASTM B102–52 79 Pewter 80 Solder 50-50 81 Solder

99.9 Cu 0.005 max 94.0 Sb

99.9 0.10 4.5 4.5 13.0 5.0 91.0 2.0 50.0 20.0

Form and Condition

Yield Strength (0.2% offset), 1000 lb/sq in.

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

0.06

Rolled 95%

1.9

2.5

50

5

6.0

Chill east Rolled 95%

— —

6.8 4.1

22 47

(500 kg) 9

0.025

Extruded and aged

—

4.5

25

—

Sn bal.

Chill east

—

9.3

2

17

Sn bal.

Die-cast

—

1

29

Rolled sheet, annealed

—

8.6

40

Cast Cast

4.8 3.6

6.1 5.8

60 16

Ca

Sb

7.0

Pb Pb

50.0 80.0

10

9.5 14 11

Comments

Good corrosion resistance and strength Cable sheathing, creepresistant pipe General bearings and die casting Die-casting alloy

MAGNESIUM ALLOYS Because of their low density these alloys are attractive for use where weight is at a premium. The major drawback to the use of these alloys is their ability to ignite in air (this can be a problem in machining); they are also costly. Magnesium alloys are used in both the wrought and die-cast forms, the latter being the most frequently used form. 82 Magnesium alloy AZ31B

83 Magnesium alloy AZ80A

© 2004 by CRC Press LLC

Zn Al

Zn Al

1.0 3.0

0.5 8.5

Mn

0.20 min Mg. bal.

Mn

0.15 min Mg. bal.

Rolled-plate (strain-hardened, then partially annealed)

24

37

18

—

Rolled-sheet (strain-hardened, then partially annealed) Annealed Extruded Extruded Extruded (age-hardened) Forged (age-hardened)

32

42

15

73

22 28 36 39 34

37 38 49 53 50

21 14 11 6 6

56 — 60 82 72

Structural applications of medium strength

General extruded and forged products

CRC Handbook of Engineering Tables

Ornamental and household items General-purpose solder Coating and joining, filling seams on automobile bodies

1587_Book.fm Page 42 Tuesday, September 2, 2003 3:25 PM

4-42

Mechanical Properties of Metals and Alloys (continued)

86 Magnesium alloy AZ91A and AZl91B

Zn Zr Zn Al

2.0 9.0

5.7 0.55 0.6 9.0

Mn

0.10 min Mg bal.

Sand-cast (as cast) Sand-cast (solution heattreated) Sand-cast (solution heattreated and aged) Sand-cast (age-hardened) Sand-cast and tempered

14 14

24 40

6 12

50 55

19

40

5

83

16 22

30 40

18 3

— 81

Mg bal.

Extruded

43

52

12

82

Mn

Die-cast (as cast)

22

33

3

67

General die-casting applications

27 38 40 60

33 51 60 90

1–3

—

Windows, X-ray tubes

—

Moderator- and reflector-cladding nuclear reactors; heatshield and structuralmember missiles

0.13 min Mg bal.

Pressure-tight sand and permanent mold castings; high UTS and good yield strength

BERYLLIUM 87 Beryllium Hot-pressed Cross-rolled

10–40

NICKEL ALLOYS Nickel and its alloys are expensive and used mainly either for their high-corrosion resistance in many environments or for high-temperature and strength applications. (See Super Alloys, above.) 88 Nickel (cast)

89 K Monel

Cu Mn C C Fe Si Al

0.5 0.8 0.8 0.15 1.00 0.15 2.75

As cast

Annealed Annealed, age-hardened Spring Spring, age-hardened

25

57

22

110

Good corrosionresistance applications

45 100 140 160

100 155 150 185

40 25 5 10

155 270 300 335

High strength and corrosion resistance; aircraft parts, valve stems, pumps

4-43

© 2004 by CRC Press LLC

Ni 95.6 Fe 0.5 Si 1.5 Ni(+ Co) 65.25 Mn 0.60 S 0.005 Cu 29.60 Ti 0.45

1587_Book.fm Page 43 Tuesday, September 2, 2003 3:25 PM

85 Magnesium alloy ZK60A

Zn Al

Mechanical Engineering

84 Magnesium alloy AZ92A

4-44

Typical Mechanical Properties

No.

Nominal Composition

Material

90 A nickel ASTM B160 ASTM B161 ASTM B162 91 Duranickel

92 Cupronickel 55–45 (Constantan)

Ni(+ Co) 99.40 Mn 0.25 S 0.005 Cu 0.05 Ni(+ Co) 93.90 Mn 0.25 S 0.005 Cu 0.05 Ti 0.45 Cu 55.0

C Fe Si

0.06 0.15 0.05

Annealed Hot-rolled Cold-drawn Cold-rolled

C Fe Si Al

0.15 0.15 0.55 4.50

Annealed Annealed, age-hardened Spring Spring, age-hardened

Ni

45.0

20.0

Ni

80.0

Cr

94 “S” Monel

Ni Fe

60.0 2.50 max 4.0

Cu Mn Al

29.0 1.5 max 0.5 max

Tensile Strength 1000 lb/sq in.

Elongation in 2 in., %

Harness, Brinell

Comments

20 25 70 95

70 75 95 105

40 40 25 5

100 110 170 210

Chemical industry for resistance to strong alkalis, plating nickel

45 125 — —

100 170 175 205

40 25 5 10

160 330 320 370

High strength and corrosion resistance; pump rods, shafts, springs

Annealed Cold-drawn Cold-rolled

30 50 65

60 65 85

45 30 20

— — —

Sand-casting

80–115

Electrical-resistance wire; low temperature coefficient, high resistivity Heating elements for furnaces High-strength casting alloy; good bearing properties for valve seats

110–145

2

270–350

TITANIUM ALLOYS The main application for these alloys is in the aerospace industry. Because of the low density and high strength of titanium alloys, they present excellent strength-to-weight ratios. 95 Commercial titanium ASTM B265-58T

96 Titanium alloy ASTM B265-58T-5 Ti-6-Al-4V

© 2004 by CRC Press LLC

Ti

99.4

Annealed at 1100 to 1350˚F (593 to 732˚C)

Water-quenched from 1750˚F (954˚C); aged at 1000˚F (538˚C) for 2 hr

70

80

20

—

160

170

13

—

Moderate strength, excellent fabricability; chemical industry pipes High-temperature strength needed in gas-turbine compressor blades

CRC Handbook of Engineering Tables

93 Nichrome

Si

Form and Condition

Yield Strength (0.2% offset), 1000 lb/sq in.

1587_Book.fm Page 44 Monday, September 1, 2003 7:17 PM

Mechanical Properties of Metals and Alloys (continued)

Fe Mn

0.5 7.0– 8.0

Ti bal.

170

185

13

—

Aircraft forgings and compressor parts

140

150

18

—

Good formability, moderate hightemperature strength; aircraft skin

Battery cans, grommets, lithographer’s sheet Corrugated roofs, articles with maximum stiffness Weatherstrip, spun articles Die casting for automobile parts, padlocks; used also for die material.

ZINC ALLOYS A major use for these alloys is for low-cost die-cast products, such as household fixtures, automotive, parts, and trim. 99 Zinc ASTM B69

Hot-rolled

—

19.5

65

38

1.00 Zn lbal. 0.010

Hot-rolled Cold-rolled

— —

29 36

20 25

61 80

1.00

Hot-rolled Cold-rolled Die-cast

— — —

24 31 47.6

50 40 7

52 60 91

Cd Pb

0.35 0.08

Zn bal.

100 Zilloy–15

Cu Mg

101 Zilloy–40

Cu

102 Zamac–5 ASTM 25

Zn (99.99% Al pure reminder) Mg 0.03– Cu 0.08

Zn bal. 3.5– 4.3 0.75– 1.25

ZIRCONIUM ALLOYS These alloys have good corrosion resistance but are easily oxidized at elevated temperatures in air: The major application is for use in nuclear reactors. 103 Zirconium, commercial 104 Zircaloy 2

O2 Hf Hf Fe Sn

0.07 1.90 0.02 0.15 1.46

C Zr bal. Ni Other Zr bal.

0.15

Annealed

40

65

27

0.05 0.25

Annealed

50

75

22

B80 (Rockwell) B90 (Rockwell)

Nuclear power-reactor cores at elevated temperatures

From Bolz, R.E. and Tuve, G.L., Solids — Metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 103–115.

4-45

© 2004 by CRC Press LLC

1587_Book.fm Page 45 Monday, September 1, 2003 7:17 PM

98 Ti-Mn alloy ASTM B265-58T-7

Water-quenched from 1450˚C); aged at 900˚F (482˚C) for 8 hr Sheet

Mechanical Engineering

97 Titanium alloy Ti-4 Al-4Mn

Liquid Metal At Atmospheric Pressure

Metal

Vapor Pressure At 25˚C (77˚F)

Melting Point, ˚C

Boiling Point, ˚C

Latent Heat of Fusion cal/g

Thermal Conductivity, watts/cm˚C

Specific Heat, cal/g˚C

Specific Heat, cal/g˚C

Coeff. of Linear Expansion (¥ 106) (˚C)–1

660. 630. 1285. 271.4 321. 1860. 1495. 1084. 1063. 2450. 1536. 327.5 650. 1244. –38.86 2620.

2441. 1440. 2475. 1660. 767. 2670. 2925. 2575. 2800. 4390. 2870. 1750. 1090. 2060. 356.55 4651.

95 38.5 324. 12.4 13.2 79 66 49 15 33 65 5.5 88.0 64 2.7 69

3.00* — — — 1.03 1.58 — 4.83* 3.45* — 1.32* 0.396 1.69 — — 1.79

.115 .040 .049 .026 .047 .046 .057 .061 .026 .022 .052 .028 .016 .064 .029 .033

0.215 .050 .436 .030 .055 .110 .10 .092 .031 .031 .108 .031 .243 .114 .033 .060

25 9 12 13 30 6 12 16.6 14.2 6 12 29 25 22 — 5

© 2004 by CRC Press LLC

–3

10 atm Thermal Conductivity, watts/cm˚C 2.37 .185 2.18 .084 .93 .91 .69 3.98 3.15 1.47 .803 .346 1.59 — .0839 1.4

Specific Heat (Liquid) at 2000˚K, calg˚C .26 .062 .78 .036 .063 .224 .164 .118 .0355 .0434 .197 .033 .32 .20 — .089

10–6 atm

10–9 atm

Boiling Point Temperature, ˚K 1,782 1,007 1,793 1,155 655 1,992 2,167 1,862 2,023 3,253 2,093 1,230 857 1,495 393 3,344

1,333 741 1,347 851 486 1,530 1,652 1,391 1,510 2,515 1,594 889 638 1,131 287 2,558

1,063 612 1,085 677 388 1,247 1,345 1,120 1,211 2,062 1,297 698 509 913 227 2,079

CRC Handbook of Engineering Tables

Aluminum Antimony Beryllium Bismuth Cadmium Chromium Cobalt Copper Gold Iridium Iron Lead Magnesium Manganese Mercury Molybdenum

At 100˚K

1587_Book.fm Page 46 Monday, September 1, 2003 7:17 PM

4-46

Thermal Properties of Pure Metals—Metric Units

2800. 4740.

71 68

1.58 0.552

.055 .045

.106 .064

13 7

3025. 1770. 640. 63.3 1965. 217. 1411. 961. 97.83 2980. 1750. 232. 1670. 3400. 1132. 1900. 419.5

4225. 3825. 3230. 760. 3700. 700. 3280. 2212. 884. 5365. 4800. 2600. 3290. 5550. 4240. 3400. 910.

34 24 3 14.5 50 16 430 26.5 27 41 17 14.1 100 46 12 98 27

— 0.79* — — — — — 4.50* — 0.592 — 0.85 0.312 2.35* — — 1.32

— .024 .019 .150 — — .062 .045 .234 .026 .024 .039 .072 .021 .022 .061 .063

.031 .032 .032 .180 .058 .077 .17 .057 .293 .034 .03 .054 .125 .032 .028 .116 .093

5 9 54 83 8 37 3 19 70 6.5 12 20 8.5 4.5 13.4 8 35

.899 .52

.175 .083

2,156 3,523

1,646 2,721

1,343 2,232

.61 .73 .08 .99 1.50 .005 .835 4.27 1.34 .54 .41 .64 .2 1.78 .25 .60 1.15

.039 .043 .041 — .092 — .217 .068 — .040 .047 .058 .188 .040 .048 .207 —

— 2,817 2,200 606 — — 2,340 1,582 701 3,959 3,251 1,857 2,405 4,139 2,861 2,525 752

— 2,155 1,596 430 — — 1,749 1,179 504 3,052 2,407 1,366 1,827 3,228 2,128 1,948 559

— 1,757 1,252 335 — — 1,427 952 394 2,495 1,919 1,080 1,484 2,656 1,699 1,591 449

* Temperatures of maximum thermal conductivity (conductivity values in watts/cm˚C): Aluminum 13˚K, cond. = 71.5; copper 10˚K, cond. = 196; gold 10˚K, cond. = 28.2; iron 20˚K, cond. = 9.97; platinum 8˚K, cond. = 12.9; silver 7˚K, cond. = 193; tungsten 8˚K, cond. = 85.3. From Bolz, R.E. and Tuve, G.L., Solids — Metals, in CRC Handbook of Tables for Applied Engineering Science, CRC Boca Raton, FL, 1973, p. 119.

4-47

© 2004 by CRC Press LLC

1587_Book.fm Page 47 Monday, September 1, 2003 7:17 PM

1453. 2470.

Mechanical Engineering

Nickel Niobium (Columbium) Osmium Platinum Plutonium Potassium Rhodium Selenium Silicon Silver Sodium Tantalum Thorium Tin Titanium Tungsten Uranium Vanadium Zinc

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4-48

CRC Handbook of Engineering Tables

Terms and Units for Radiant Energy and Illumination Note: Any of the following quantities may be restricted to a narrow wavelength interval by addition of the world spectral. Measure of Quantity Rate Intensity Density at surface

Density of beam (at surface)

Terms in Use

Meaning or Definition

Usual Units

Radiant energy Luminous energy Radiant flux Luminous flux Radiant intensity Luminous intensity Radiant emittance Radiant excitance Irradiance Illumination Illuminance (Emittance) Radiance

Total quantity of radiant energy Time rate of flow of radiant energy (power) Radiant flux per unit solid angle (point source) Density of radiant flux incident upon (or emitted from) a surface

Erg, joule, calorie, kilowatt-hour, Btu

Effectiveness (radiating)

Emissivity (Absorptivity)

Brightness

Luminance

Unit intensity normal to the beam per unit of projected area in that direction Ratio of radiant emittance (or absorptance) to that of a perfect blackbody Photometric brightness per unit area

Erg/sec, watt, Bu/hr, lumen Watts per steradian, candela* = lumens/steradian Watts/sq cm, foot-candle = lumens/ sq ft, lux = lumens/sq m, phot = lumens sq cm, Btu/hr ¥ sq ft

Watts sr ¥ sq cm,

Btu hr sr ¥ sq ft

Dimensionless

Candela/sq ft, stilb = cd/sq cm, nit = cd/sq m, foot-lambert = cd/p sq ft, lambert = cd/p sq cm, apostilb = cd/p sq m

* The candela (cd) was formerly called “candlepower.” (One international candle will illuminate a sphere at one foot distance with 4p lumens, or one sq ft of the sphere with one lumen.) From Bolz, R.E. and Tuve, G.L., Electromagnetic radiation, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 205.

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4-49

Mechanical Engineering

Blackbody Radiation

˚K

˚R

Wavelength of Maximum Intensity, Microns, m

10 50 100 200 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2500 3000 4000 6000 8000

18 90 180 360 540 630 720 810 900 990 1080 1260 1440 1620 1800 2160 2520 2880 3240 3600 4500 5400 7200 10,800 14,400

290 58.0 29.0 14.5 9.66 8.28 7.25 6.44 5.80 5.27 4.83 4.14 3.63 3.22 2.90 2.42 2.07 1.81 1.61 1.49 1.156 0.966 0.725 0.483 0.363

Temperature

Maximum Normal Intensity†

Total Maximum Hemispherical Radiation†

W/cm2 m

Btu/hr ft2 m

W/cm2

Btu/hr ft2

1.290 ¥ 10–10 4.030 ¥ 10–7 1.290 ¥ 10–5 4.127 ¥ 10–4 3.134 ¥ 10–3 6.774 ¥ 10–3 1.321 ¥ 10–2 2.380 ¥ 10–2 4.030 ¥ 10–2 6.484 ¥ 10–2 1.003 ¥ 10–1 2.168 ¥ 10–1 4.226 ¥ 10–1 7.616 ¥ 10–1 1.290 3.209 6.936 1.352 ¥ 10 2.437 ¥ 10 4.127 ¥ 10 1.260 ¥ 102 3.134 ¥ 102 1.321 ¥ 103 1.003 ¥ 104 4.226 ¥ 104

4.092 ¥ 10–7 1.278 ¥ 10–3 4.092 ¥ 10–2 1.309 9.941 2.149 ¥ 10 4.190 ¥ 10 7.550 ¥ 10 1.278 ¥ 102 2.057 ¥ 102 3.181 ¥ 102 6.877 ¥ 102 1.341 ¥ 103 2.417 ¥ 103 4.092 ¥ 103 1.018 ¥ 104 2.200 ¥ 104 4.289 ¥ 104 7.730 ¥ 104 1.309 ¥ 105 3.997 ¥ 105 9.941 ¥ 105 4.190 ¥ 106 3.181 ¥ 107 1.340 ¥ 108

5.679 ¥ 10–8 3.549 ¥ 10–5 5.679 ¥ 10–4 9.086 ¥ 10–3 4.600 ¥ 10–2 8.522 ¥ 10–2 1.454 ¥ 10–1 2.328 ¥ 10–1 3.549 ¥ 10–1 5.207 ¥ 10–1 7.360 ¥ 10–1 1.364 2.326 3.726 5.679 1.178 ¥ 10 2.181 ¥ 10 3.722 ¥ 10 5.961 ¥ 10 9.096 ¥ 10 2.218 ¥ 102 4.600 ¥ 102 1.454 ¥ 103 7.360 ¥ 103 2.326 ¥ 104

1.801 ¥ 10–4 1.126 ¥ 10–1 1.801 2.882 ¥ 10 1.459 ¥ 102 2.703 ¥ 102 4.612 ¥ 102 7.385 ¥ 102 1.126 ¥ 103 1.652 ¥ 103 2.335 ¥ 103 4.327 ¥ 103 7.378 ¥ 103 1.182 ¥ 104 1.801 ¥ 104 3.737 ¥ 104 6.918 ¥ 104 1.181 ¥ 105 1.891 ¥ 105 2.882 ¥ 105 7.036 ¥ 105 1.459 ¥ 106 4.612 ¥ 106 2.335 ¥ 107 7.378 ¥ 107

Notes: One half of the blackbody radiation lies on either side of the wavelength computed from l = 4107/T, where l is in microns and T is ˚K. 1 cm = 0.3937 in. = 10,000 microns = 108 Angstrom units. To convert Btu/hr·ft2 to W/m2, multiply by 3.1525. † Zero temperature receiver; no reradiation. From Bolz, R.E. and Tuve, G.L., Electromagnetic radiation, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 207.

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4-50

CRC Handbook of Engineering Tables

Thermodynamic Nonflow Process Equations For a System Containing a Perfect Gas with Constant Specific Heats 1Q2 = 1W2 + (U2 – U1) Constant Pressure

Process p, V, T pV = mRT‡ pu = RT‡

Specific heat c = 1Q2/(T2 – T1)‡ Exponent n for polytropic process Quantity of heat 1Q2 = ÚTdS positive for heat into system from surroundings

p = constant p = p 1 = p2

Constant Volume V = constant V = V1 = V2

Internal energy U2 – U1 dU = mcudT‡

pV = constant

T2 Ê p2 ˆ = T1 ÁË p1 ˜¯

V1 V2 = T1 T2

P1 P2 = T1 T2

p 1V 1 = p 2V 2

T2 Ê V1 ˆ = T1 ÁË V2 ˜¯

Ê kR‡ ˆ cp = Á ˜ Ë k - 1¯

Ê R‡ ˆ cp = Á ˜ Ë k - 1¯

•

•

0

1

mc p (T2 - T1 )

mc v (T2 - T1 )

k W k -1 1 2

U 2 - U1

c p ( p R )(V2 - V1 )

p(V2 V1 )

V ( p2 - p1 ) k -1

ds = =

0

mR(T2 - T1 ) k -1 Q k 1 2

mc v (T2 - T1 )† p(V2 - V1 )‡

mc p (T2 - T1 )† kp(V2 - V1 )‡

(k - 1)

Entropy S2 – S1

p1V 1k = p2V2k = constant

P = constant T

(k - 1)

Enthalpy H2 – H1 d H = mcpdT‡

T = constant T = T1 = T2

V = constant T

H 2 - H1 Quantity of work 1W2 = ÚpdV positive for work done by system on surroundings

Isentropic S = constant

Isothermal

mcp ln(T2/T1) mcp ln(V2/V1)

Ï p1V1 ln(V2 V1 ) Ô Ô Ô p1V1 ln( p1 p2 ) ÔÔ Ì mRT ln(V2 V1 ) Ô Ô mRT ln( p p ) 1 2 Ô ÔQ = W ÔÓ 1 2 1 2

0

(k - 1)

mcu ln(T2/T1) mcu ln(p2/p1)

Ê c †ˆ k=Á p ˜ Ë cv ¯

p2V2 - p1V1 1- k

mc v (T1 - T2 ) U1 - U 2

T2 Ê V1 ˆ = T1 ÁË V2 ˜¯

n-1

(k - n) (1 - n)

n = any value mcn(T2 – T1)

p2V2 - p1V1 1- n

mR(T2 - T1 ) 1- n

n-1 È ù p1V1 Í Ê p2 ˆ n ú 1- Á ˜ ú Í n -1 p Í Ë 1¯ ú Î û

mc v (T2 - T1 )†

mc v (T2 - T1 )†

p2V2 - p1V1 ‡ (k - 1)

p2V2 - p1V1 ‡ (k - 1)

mc p (T2 - T1 )†

mc p (T2 - T1 )†

k( p2V2 - p1V1 )‡

(k - 1)

mR ln(V2/V1) mR ln(p1/p2)

n-1 n

T2 Ê p2 ˆ = T1 ÁË p1 ˜¯

0

0

mc p (T2 - T1 )†

p1V1n = p2V2n = constant

cn = cv

0

k -1 È ù p1V1 Í Ê p2 ˆ k ú 1- Á ˜ ú Í k -1 p Í Ë 1¯ ú Î û

(k - 1)

kV ( p2 - p1 )‡

k -1

Adiabatic

mc v (T2 - T1 )† V ( p2 - p1 )‡

k -1 k

Polytropic pVn = constant

0

k( p2V2 - p1V1 )‡

(k - 1)

mcn ln(T2/T1)

dH Vdp† T T dU pdV † + TG T

† Valid in general, not only for process or processes listed, and not only for perfect gases. ‡ Valid in general for perfect gases, not only for process listed. From Bolz, R.E. and Tuve, G.L., Thermodynamics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 473.

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4-51

Mechanical Engineering

Thermodynamic Cycle Efficiencies Symbols: hc = (TH – TL)/TH = Carnot cycle efficiency, present ho = 1 – r 1–k = Otto cycle efficiency, percent hD = 1 – r 1– k hb = 1 – r

(Sk – 1) ------------------k(S – 1)

(1–k)/k p

= Diesel cycle efficiency, percent

= Brayton (or Joule) cycle efficiency, percent

where TH = absolute temperature of energy reservoir from which energy is drawn TL = absolute temperatue of energy reservoir to which energy is rejected r = compression ratio for Otto and Diesel cycles, maximum volume/minimum volume rp = pressure ratio for Brayton (or Joule) cycle, maximum pressure/minimum pressure S = cut-off ratio for Diesel cycle, volume at end of constant pressure heat addition process/minimum volume k = Cp /Cv = specific heat ratio Otto Cycle Efficiency, o, Percent k=

Compression Ratio, r

cp cv

1.30 1.35 1.40 5/3

5

6

7

8

9

10

11

12

13

14

15

20

50

38.3 43.1 47.5 65.8

41.6 46.6 51.2 69.7

44.2 49.4 54.1 72.7

46.4 51.7 56.5 75.0

48.3 53.7 58.5 76.9

49.9 55.3 60.2 78.5

51.3 56.8 61.7 79.8

52.5 58.1 63.0 80.9

53.7 59.3 64.2 81.9

54.7 60.3 65.2 82.7

55.6 61.2 66.1 83.6

59.3 65.0 69.8 86.4

69.1 74.6 79.1 92.6

Diesel Cycle Efficiency, D , Percent Compression Ratio, r

Cut-Off Ratio, S

5

10

14

15

16

17

18

19

20

25

30

50

1.30 1.30 1.30 1.30

2 3 4 5

30.6 24.7 19.9 15.7

43.6 38.9 34.9 31.5

49.0 44.7 41.2 38.1

50.1 45.9 42.4 39.4

51.0 46.9 43.5 40.5

51.9 47.9 44.5 41.6

52.7 48.8 45.5 42.6

53.5 49.6 46.3 43.5

54.2 50.3 47.2 44.4

57.2 53.6 50.6 48.0

59.5 56.0 53.2 50.8

65.2 62.3 59.9 57.8

1.35 1.35 1.35 1.35

2 3 4 5

34.7 28.2 22.7 18.0

48.7 43.6 39.4 35.6

54.4 49.9 46.1 42.8

55.5 51.1 47.4 44.1

56.5 52.2 48.6 45.4

57.4 53.2 49.6 46.5

58.3 54.1 50.6 47.6

59.1 55.0 51.6 48.6

59.8 55.8 52.4 49.5

62.8 59.1 56.0 53.3

65.1 61.6 58.7 56.2

70.8 67.9 65.5 63.3

1.40 1.40 1.40 1.40

2 3 4 5

38.5 31.4 25.4 20.1

53.4 48.0 43.5 39.4

59.3 54.6 50.6 47.1

60.4 55.8 51.9 48.5

61.4 56.9 53.2 49.8

62.3 58.0 54.3 51.0

63.2 58.9 55.3 52.1

63.9 59.8 56.3 53.2

64.7 60.6 57.2 54.1

67.7 64.0 60.8 58.0

70.0 66.5 63.6 61.0

75.5 72.7 70.3 68.2

k=

cp cv

Brayton (or Joule) Cycle Efficiency, , Percent k=

Pressure Ratio, rp

cp cv

1.30 1.35 1.40 5/3

3

4

5

6

7

8

9

10

12

14

15

20

50

22.4 24.8 27.0 35.6

27.4 30.2 32.7 42.6

31.0 34.1 36.9 47.5

33.9 37.2 40.1 51.2

36.2 39.6 42.7 54.1

38.1 41.7 44.8 56.5

39.8 43.4 46.6 58.5

41.2 45.0 48.2 60.2

43.6 47.5 50.8 63.0

45.5 49.4 52.9 65.1

46.5 50.4 53.9 66.1

49.9 54.0 57.5 69.8

59.5 63.7 67.3 79.1

Carnot Cycle Efficiency, c , Percenta TL

TH, K(R)

K

R

200 (360)

300 (540)

400 (720)

500 (900)

1000 (1800)

1500 (2700)

2000 (3600)

2500 (4500)

3000 (5400)

4000 (7200)

5000 (9000)

100 200 300

180 360 540

50.0 0 —

66.7 33.3 0

75.0 50.0 25.0

80.0 60.0 40.0

90.0 80.0 70.0

93.3 86.7 80.0

95.0 90.0 85.0

96.0 92.0 88.0

96.7 93.3 90.0

97.5 95.0 92.5

98.0 96.0 94.0

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1587_Book.fm Page 52 Monday, September 1, 2003 7:17 PM

4-52

CRC Handbook of Engineering Tables

Thermodynamic Cycle Efficiencies (continued) TL

TH, K(R)

K

R

200 (360)

300 (540)

400 (720)

500 (900)

1000 (1800)

1500 (2700)

2000 (3600)

2500 (4500)

3000 (5400)

4000 (7200)

5000 (9000)

400 500 1000

720 900 1800

— — —

— — —

0 — —

20.0 0 —

60.0 50.0 0

73.3 66.7 33.3

80.0 75.0 50.0

84.0 80.0 40.0

86.7 83.3 66.7

90.0 87.5 75.0

92.0 90.0 80.0

a These values are valid for any reversible cycle with heat addition at T and heat rejection at T . Stirling and Ericcson H L cycles with ideal regeneration meet this requirement, for example.

Otto Cycle. The Otto cycle consists of isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection. Diesel Cycle. The Diesel cycle consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-volume heat rejection. Brayton Cycle. The Brayton, or Joule, cycle consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. Carnot Cycle. The Carnot cycle consists of isothermal compression (with heat rejection), isentropic compression, isothermal expansion (with heat addition), and isentropic expansion. Stirling Cycle. The Stirling cycle consists of isothermal compression (with heat rejection), constant-volume heat addition, isothermal expansion (with heat addition), and constant-volume heat rejection. Ericcson Cycle. The Ericcson cycle consists of isothermal compression (with heat rejection), constant-pressure heat addition, isothermal expansion (with heat addition), and constant-pressure heat rejection. From Bolz, R.E. and Tuve, G.L., Thermodynamics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 477–478.

Heat of Fusion of Some Inorganic Compounds* For heat of fusion in J/kg, multiply values in cal/g by 4184. For heat of fusion in J/mol, multiply values in cal/g·mol (= cal/mol) by 4.184. For melting point in K, add 273.15 to values in ˚C. Values in parentheses are of uncertain reliability.

Compound Actinium227 Aluminum Aluminum bromide Aluminum chloride Aluminum iodide Aluminum oxide Antimony Antimony pentachloride Antimony tribromide Antimony trichloride Antimony trioxide Antimony trisulfide Argon Arsenic Arsenic pentafluoride Arsenic tribromide Arsenic trichloride Arsenic trifluoride Arsenic trioxide Barium Barium bromide

© 2004 by CRC Press LLC

Formula Ac Al Al2Br6 Al2Cl6 Al2I6 Al2O3 Sb SbCl5 SbBr3 SbCl3 Sb4O6 Sb4S6 Ar As AsF5 AsBr3 AsCl3 AsF3 As4O6 Ba BaBr2

Melting Point, ˚C 1050 ± 50 658.5 87.4 192.4 190.9 2045.0 630 4.0 96.8 73.3 655.0 546.0 –190.2 816.8 –80.8 30.0 –16.0 –6.0 312.8 725 846.8

Heat of Fusion Btu/lb (20.) 170. 18.2 114. 17.6 (461.) 70.4 14.4 17.5 23.9 (83.3) 59.4 13.1 (39.6) 29.7 16.0 23.9 34.0 40.0 23.9 39.4

cal/g (11.0) 94.5 10.1 63.6 9.8 (256.0) 39.1 8.0 9.7 13.3 (46.3) 33.0 7.25 (22.0) 16.5 8.9 13.3 18.9 22.2 13.3 21.9

cal/g Mole (3400) 2250 5420 19600 7960 (26000) 4770 2400 3510 3030 (26990) 11200 290 (6620) 2800 2810 2420 2486 8000 1830 6000

1587_Book.fm Page 53 Monday, September 1, 2003 7:17 PM

4-53

Mechanical Engineering

Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Barium chloride Barium fluoride Barium iodide Barium nitrate Barium oxide Barium phosphate Barium sulfate Beryllium Beryllium bromide Beryllium chloride Beryllium oxide Bismuth Bismuth trichloride Bismuth trifluoride Bismuth trioxide Boron Boron tribromide Boron trichloride Boron trifluoride Boron trioxide Bromine Bromine pentafluoride Cadmium Cadmium bromide Cadmium chloride Cadmium fluoride Cadmium iodide Cadmium sulfate Calcium Calcium bromide Calcium carbonate Calcium chloride Calcium fluoride Calcium metasilicate Calcium nitrate Calcium oxide Calcium sulfate Carbon dioxide Carbon monoxide Cerium Cesium Cesium chloride Cesium nitrate Chlorine Chromium Chromium (II) chloride Chromium (III) sequioxide Chromium trioxide Cobalt Cobalt (II) chloride Copper Copper (I) chloride Copper (I) cyanide Copper (I) iodide Copper (I) oxide

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Formula BaCl2 BaF2 BaI2 Ba(NO3)2 BaO Ba3(PO4)2 BaSO4 Be BeBr2 BeCl2 BeO Bi BiCl3 BiF3 Bi2O3 B BBr3 BCl3 BF3 B 2O 3 Br2 BrF5 Cd CdCl2 CdF2 CdI2 CdSO4 Ca CaBr2 CaCO3 CaCl2 CaF2 CaSiO2 Ca(NO3)2 CaO CaSO4 CO2 CO Ce Cs CsCl CsNO3 Cl2 Cr CrCl2 Cr2O3 CrO3 Co CoCl2 Cu CuCl Cu2(CN)2 CuI Cu2O

Melting Point, ˚C 959.8 1286.8 710.8 594.8 1922.8 1727 1350 1278 487.8 404.8 2550.0 271 223.8 726.0 815.8 2300 –48.8 –107.8 –128.0 448.8 –7.2 –61.4 320.8 567.8 567.8 1110 386.8 1000 851 729.8 1282 782 1382 1512 560.8 2707 1297 –57.6 –205 775 28.3 641.8 406.8 –103 ± 5 1890 814 2279 197 1490 727 1083 429 473 587 1230

Heat of Fusion Btu/lb 46.6 30.8 (31.1) (40.7) 168. 55.6 74.9 468. (47.9) (54) 1223. 21.6 14.8 (41.9) 26.3 (882) (5.2) (7.7) 12.6 142. 29.0 12.7 23.2 (33.1) 51.8 (64.6) 18.0 41.2 100. 37.6 (227) 99 94.5 208. 56.2 (393.) 88.6 77.8 12.8 27.2 6.7 38.5 29.9 41.0 112. 119. 49.7 67.9 112. 102. 88.2 47.5 (54.2) (24.5) (168.)

cal/g 25.9 17.1 (17.3) (22.6) 93.2 30.9 41.6 260.0 (26.6) (30) 679.7 12.0 8.2 (23.3) 14.6 (490) (2.9) (4.3) 7.0 78.9 16.1 7.07 12.9 (18.4) 28.8 (35.9) 10.0 22.9 55.7 20.9 (126) 55 52.5 115.4 31.2 (218.1) 49.2 43.2 7.13 15.1 3.7 21.4 16.6 22.8 62.1 65.9 27.6 37.7 62.1 56.9 49.0 26.4 (30.1) (13.6) (93.6)

cal/g Mole 5370 3000 (6800) (5900) 13800 18600 9700 — (4500) (3000) 17000 2505 2600 (6200) 6800 (5300) (700) (500) 480 5500 2580 1355 1460 (5000) 5300 (5400) 3660 4790 2230 4180 (12700) 6100 4100 13400 5120 (12240) 6700 1900. 199.7 2120 500 3600 3250 1531 3600 7700 4200 3770 3640 7390 3110 2620 (5400) (2600) (13400)

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CRC Handbook of Engineering Tables

Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Copper (I) sulfide Copper (II) chloride Copper (II) oxide Cyanogen Cyanogen chloride Deuterium oxide Dysprosium Erbium Europium Europium trichloride Fluorine Gadolinium Gallium Germanium Gold Hafnium Holmium Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen fluoride Hydrogen iodide Hydrogen nitrate Hydrogen oxide (water) Hydrogen peroxide Hydrogen selenate Hydrogen sulfate Hydrogen sulfide Hydrogen sulfide, diHydrogen telluride Indium Iodine Iodine chloride (a) Iodine chloride (b) Iron Iron (II) chloride Iron (II) oxide Iron (II) sulfide Iron (III) chloride Iron carbide Iron oxide Iron pentacarbonyl Lanthanum Lead Lead bromide Lead chloride Lead fluoride Lead iodide Lead molybdate Lead oxide Lead sulfate Lead sulfide Lithium Lithium bromide Lithium chloride

© 2004 by CRC Press LLC

Formula

Melting Point, ˚C

Cu2S CuCl2 CuO C2N2 CNCl D 2O Dy Er Eu EuCl3 F2 Gd Ga Ge Au Hf Ho H2 HBr HCl HF HI HNO3 H 2O H 2O 2 H2SeO4 H2SO4 H 2S H 2S 2 H2Te In I2 ICl ICl Fe FeCl2 FeO FeS Fe2Cl6 Fe3C Fe3O4 Fe(CO)2 La Pb PbBr2 PbCl2 PbF2 Pbl2 PbMoO4 PbO PbSO4 PbS Li LiBr LiCl

1129 430 1446 –27.2 –5.2 3.78 1407 1496 826 622 –219.6 1312 29 959 1063 2214 1461 –259.25 –86.96 –114.3 –83.11 –50.91 –47.2 0 –0.7 57.8 10.4 –85.6 –89.7 –49.0 156.3 112.9 17.1 13.8 1530.0 677 1380 1195 303.8 1226.8 1596 –21.2 920 327.3 487.8 497.8 823 412 1065 890 1087 1114 178.8 552 614

Heat of Fusion Btu/lb 62.3 44.5 63.7 71.3 65.5 136. 45.4 44.1 29.5 (37.6) 11.5 42.8 (34.4) (206.) (27.5) (61.4) 44.6 24.8 12.8 23.4 98.5 9.7 17.1 138. 15.4 42.8 43.2 30.2 49.1 23.2 12.2 25.7 29.5 23.9 115. 111. (193.) 102. 114. 123. 257. 29.7 31.3 10.6 21.1 36.5 13.7 32.2 (127.) 22.7 56.9 31.1 285. 60.1 136.

cal/g 34.6 24.7 35.4 39.6 36.4 75.8 25.2 24.5 16.4 (20.9) 6.4 23.8 19.1 (114.3) 15.3 (34.1) 24.8 13.8 7.1 13.0 54.7 5.4 9.5 79.72 8.58 23.8 24.0 16.8 27.3 12.9 6.8 14.3 16.4 13.3 63.7 61.5 (107.2) 56.9 63.2 68.6 142.5 16.5 17.4 5.9 11.7 20.3 7.6 17.9 70.8 12.6 31.6 17.3 158.5 33.4 75.5

cal/g Mole 5500 4890 2820 2060 2240 1516 4100 4100 2500 (8000) 244.0 3700 1336 (8300) 3030 (6000) 4100 28 575.1 476.0 1094 686.3 601 1436 2920 3450 2360 5683 1805 1670 781 3650 2660 2270 3560 7800 (7700) 5000 20500 12330 33000 3250 2400 1224 4290 5650 1860 5970 (25800) 2820 9600 4150 1100 2900 3200

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Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Lithium fluoride Lithium hydroxide Lithium iodide Lithium metasilicate Lithium molybdate Lithium nitrate Lithium orthosilicate Lithium sulfate Lithium tungstate Lutetium Magnesium Magnesium bromide Magnesium chloride Magnesium fluoride Magnesium oxide Magnesium silicate Magnesium sulfate Manganese Manganese (II) oxide Manganese dichloride Manganese metasilicate Manganese oxide Mercury Mercury bromide Mercury chloride Mercury iodide Mercury sulfate Molybdenum Molybdenum dichloride Molybdenum hexafluoride Molybdenum trioxide Neodymium Neon Nickel Nickel chloride Nickel subsulfide Niobium Niobium pentachloride Niobium pentoxide Nitric oxide Nitrogen Nitrogen tetroxide Nitrous oxide Osmium Osmium tetroxide (white) Osmium tetroxide (yellow) Oxygen Palladium Phosphoric acid Phosphoric acid, hypoPhosphorus acid, hypo Phosphorus acid, orthoPhosphorus oxychloride Phosphorus pentoxide Phosphorus trioxide

© 2004 by CRC Press LLC

Formula LiF LiOH Lil Li2SiO3 Li2MoO4 LiNO3 Li4SiO4 Li2SO4 Li2WO4 Lu Mg MgBr2 MgCl2 MgF2 MgO MgSiO3 MgSO4 Mn MnO MnCl2 MnSiO3 Mn3O4 Hg HgBr2 HgCl2 HgI2 HgSO4 Mo MoCl2 MoF4 MoO3 Nd Ne Ni NiCl2 Ni3S2 Nb NbCl5 Nb2O5 NO N2 N 2O 4 N 2O Os OsO4 OsO4 O2 Pd H3PO4 H 4P 2O 6 H3PO2 H3PO3 POCl3 P4O10 P 4O 6

Melting Point, ˚C 896 462 440 1177 705 250 1249 857 742 1651 650 711 712 1221 2642 1524 1327 1220 1784 650 1274 1590 –39 241 276.8 250 850 2622 726.8 17 795 1020 –248.6 1452 1030 790 2496 211 1511 –163.7 –210 –13.2 –90.9 2700 41.8 55.8 –218.8 1555 42.3 54.8 17.3 73.8 1.0 569.0 23.7

Heat of Fusion Btu/lb (164.) 186. (19.1) 144. 43.4 158. 109. 49.7 (46.1) 47.3 160. 81.0 149. 170. 826. 264. 52.0 113. 330. 105. (113.) (307.) 4.9 19.6 27.5 17.8 8.6 (123.) 64.4 21.4 (31.1) 21.2 6.89 129. 257. 46.4 (124.) 55.4 164. 32.9 11.1 108. 63.9 (66.1) 16.6 27.9 5.9 69.5 46.4 92.2 63.0 67.3 36.5 108. 27.5

cal/g (91.1) 103.3 (10.6) 80.2 24.1 87.8 60.5 27.6 (25.6) 26.3 88.9 45.0 82.9 94.7 459.0 146.4 28.9 62.7 183.3 58.4 (62.6) (170.4) 2.7 10.9 15.3 9.9 (4.8) (68.4) 3.58 11.9 (17.3) 11.8 3.83 71.5 142.5 25.8 (68.9) 30.8 91.0 18.3 6.15 60.2 35.5 (36.7) 9.2 15.5 3.3 38.6 25.8 51.2 35.0 37.4 20.3 60.1 15.3

cal/g Mole (2360) 2480 (1420) 7210 4200 6060 7340 3040 (6700) 4600 2160 8300 8100 5900 18500 14700 3500 3450 13000 7340 (8200) (39000) 557.2 3960 4150 4500 (1440) (6600) 6000 2500 (2500) 1700 77.4 4200 18470 5800 (6500) 8400 24200 549.5 172.3 5540 1563 (7000) 2340 4060 106.3 4120 2520 8300 2310 3070 3110 17080 3360

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Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Phosphorus, yellow Platinum Potassium Potassium borate, metaPotassium bromide Potassium carbonate Potassium chloride Potassium chromate Potassium cyanide Potassium dichromate Potassium fluoride Potassium hydroxide Potassium iodide Potassium nitrate Potassium peroxide Potassium phosphate Potassium pyrophosphate Potassium sulfate Potassium thiocyanate Praseodymium Rhenium Rhenium heptoxide Rhenium hexafluoride Rubidium Rubidium bromide Rubidium chloride Rubidium fluoride Rubidium iodide Rubidium nitrate Samarium Scandium Selenium Selenium oxychloride Silane, hexafluoroSilicon Silicon dioxide (Cristobalite) Silicon dioxide (Quartz) Silicon tetrachloride Silver Silver bromide Silver chloride Silver cyanide Silver iodide Silver nitrate Silver sulfate Silver sulfide Sodium Sodium borate, metaSodium bromide Sodium carbonate Sodium chlorate Sodium chloride Sodium cyanide Sodium fluoride Sodium hydroxide

© 2004 by CRC Press LLC

Formula P4 Pt K KBO2 KBr K2CO3 KCl K2CrO4 KCN K2Cr2O7 KF KOH KI KNO3 K 2O 2 K3PO4 K 4P 2 O 7 K2SO4 KSCN Pr Re Re2O7 ReF6 Rb RbBr RbCl RbF RbI RbNO3 Sm Sc Se SeOCl3 Si2F6 Si SiO2 SiO2 SiCl4 Ag AgBr AgCl AgCN AgI AgNO3 Ag2SO4 Ag2S Na NaBO2 NaBr Na2CO3 NaClO3 NaCl NaCN NaF NaOH

Melting Point, ˚C 44.1 1770 63.4 947 742 897 770 984 623 398 875 360 682 338 490 1340 1092 1074 179 931 3167 ± 60 296 19.0 38.9 677 717 833 638 305 1072 1538 217 9.8 –28.6 1427 2100 1470 –67.7 961 430 455 350 557 209 657 841 97.8 966 747 854 255 800 562 992 322

Heat of Fusion Btu/lb 8.6 43.4 26.3 (124.) 75.6 102. 155. 64.1 (96.7) 53.6 201. (63.5) 44.5 50.6 99.5 75.4 76.3 83.5 41.6 34.2 (76.3) 54.2 29.9 11.0 40.3 65.5 71.1 25.2 16.4 31.1 152. 27.7 11.0 41.2 607. 63.0 102. 19.4 45.0 20.9 39.6 36.9 17.1 29.2 (24.7) 24.3 49.3 242. 107. 119. 89.5 222. (160.) 300. 90.0

cal/g 4.8 24.1 14.6 (69.1) 42.0 56.4 85.9 35.6 (53.7) 29.8 111.9 (35.3) 24.7 28.1 55.3 41.9 42.4 46.4 23.1 19.0 (42.4) 30.1 16.6 6.1 22.4 36.4 39.5 14.0 9.1 17.3 84.4 15.4 6.1 22.9 337.0 35.0 56.7 10.8 25.0 11.6 22.0 20.5 9.5 16.2 (13.7) 13.5 27.4 134.6 59.7 66.0 49.7 123.5 (88.9) 166.7 50.0

cal/g Mole 600 4700 574 (5600) 5000 7800 6410 6920 (3500) 8770 6500 (1980) 4100 2840 6100 8900 14000 8100 2250 2700 (7900) 15340 5000 525 3700 4400 4130 2990 1340 2600 3800 1220 1010 3900 9470 2100 3400 1845 2700 2180 3155 2750 2250 2755 (4280) 3360 630 8600 6140 7000 5290 7220 (4360) 7000 2000

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Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Sodium iodide Sodium molybdate Sodium nitrate Sodium peroxide Sodium phosphate, metaSodium pyrophosphate Sodium silicate, aluminumSodium silicate, diSodium silicate, metaSodium sulfate Sodium sulfide Sodium thiocyanate Sodium tungstate Strontium Strontium bromide Strontium chloride Strontium fluoride Strontium oxide Sulfur (monatomic) Sulfur dioxide Sulfur trioxide (a) Sulfur trioxide (b) Sulfur trioxide (g) Tantalum Tantalum pentachloride Tantalum pentoxide Tellurium Terbium Thallium Thallium bromide, monoThallium carbonate Thallium chloride, monoThallium iodide, monoThallium nitrate Thallium sulfate Thallium sulfide Thorium Thorium chloride Thorium dioxide Thulium Tin Tin bromide, diTin bromide, tetraTin chloride, diTin chloride, tetraTin iodide, tetraTin oxide Titanium Titanium bromide, tetraTitanium chloride, tetraTitanium dioxide Titanium oxide Tungsten Tungsten dioxide Tungsten hexafluoride

© 2004 by CRC Press LLC

Heat of Fusion

Formula

Melting Point, ˚C

Btu/lb

cal/g

cal/g Mole

NaI Na2MoO4 NaNO3 Na2O2 NaPO3 Na4P2O7 NaAlSi3O8 Na2Si2O5 Na2SiO3 Na2SO4 Na2S NaSCN Na2WO4 Sr SrBr2 SrCl2 SrF2 SrO S SO2 SO3 SO3 SO3 Ta TaCl5 Ta2O5 Te Tb Tl TlBr Tl2CO3 TlCl TlI TlNO3 Tl2SO4 Tl2S Th ThCl4 ThO2 Tm Sn SnBr2 SnBr4 SnCl2 SnCl4 SnI4 SnO Ti TiBr4 TiCl4 TiO2 TiO W WO2 WF6

662 687 310 460 988 970 1107 884 1087 884 920 323 702 757 643 872 1400 2430 119 –73.2 16.8 32.3 62.1 2996 ± 50 206.8 1877 453 1356 302.4 460 273 427 440 207 632 449 1845 765 2952 1545 231.7 231.8 29.8 247 –33.3 143.4 1042 1800 38 –23.2 1825 991 3387 1270 –0.5

63.2 31.5 79.6 135. (87.5) (92.7) 90.2 83.5 152. 73.8 (27.7) 98.6 35.3 45.0 34.7 47.7 61.2 290. 16.6 58.0 46.4 65.0 142. (62.3) 74.7 45.2 195. 45.5 44.3 9.0 37.8 17.1 31.9 16.9 15.5 19.6 12.2 (<35.6) 111. 1984. 46.8 25.9 (11.0) 12.2 28.8 15.1 (12.4) (84.2) (188.) (10.1) 21.4 (257.) 394 (82.4) 108. 10.8

35.1 17.5 44.2 75.1 (48.6) (51.5) 50.1 46.4 84.4 41.0 15.4 54.8 19.6 25.0 19.3 26.5 34.0 161.2 9.2 32.2 25.8 36.1 79.0 34.6–41.5 25.1 108.6 25.3 24.6 5.0 21.0 9.5 17.7 9.4 8.6 10.9 6.8 (<19.8) 61.6 1102.0 26.0 14.4 (6.1) 6.8 16.0 8.4 (6.9) (46.8) (104.4) (5.6) 11.9 (142.7) 219 (45.8) 60.1 6.0

5340 3600 3760 5860 (4960) (13700) 13150 8460 10300 5830 (1200) 4450 5800 2190 4780 4100 4260 16700 295 2060 2060 2890 6310 (7500) 9000 48000 3230 3900 1030 5990 4400 4260 3125 2290 5500 3000 (<4600) 22500 291100 4400 1720 (1720) 3000 3050 2190 (4330) (6400) (5000) (2060) 2240 (11400) 14000 (8420) 13940 1800

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Heat of Fusion of Some Inorganic Compounds* (continued)

Compound Tungsten tetrachloride Tungsten trioxide Uranium235 Uranium tetrachloride Vanadium Vanadium dichloride Vanadium oxide Vanadium pentoxide Xenon Ytterbium Yttrium Yttrium oxide Zinc Zinc chloride Zinc oxide Zinc sulfide Zirconium Zirconium dichloride Zirconium oxide

Formula WCl4 WO3 U UCl4 V VCl2 VO V 2O 5 Xe Yb Y Y 2O 3 Zn ZnCl2 ZnO ZnS Zr ZrCl2 ZrO2

Melting Point, ˚C 327 1470 ~1133 590 1917 1027 2077 670 –111.6 823 1504 2227 419.4 283 1975 1745 1857 727 2715

Heat of Fusion Btu/lb 33.1 108. 36 48.8 (126) 118. 403. 154. 10.1 22.9 83.0 199. 43.9 (73.1) 98.8 168. (108) 81.0 304.

cal/g 18.4 60.1 20 27.1 (70) 65.6 224.0 85.5 5.6 12.7 46.1 110.7 24.4 (40.6) 54.9 (93.3) (60) 45.0 168.8

cal/g Mole 6000 13940 3700 10300 (4200) 8000 15000 15560 740 2200 4100 25000 1595 (5540) 4470 (9100) (5500) 7400 20800

From Bolz, R.E. and Tuve, G.L., Thermodynamics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 479–483.

© 2004 by CRC Press LLC

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Conservation Equations of a Viscous, Heat-Conducting Fluid In Curvillnear Orthogonal Coordinates NOMENCLATURE: eij = components of rate of strain tensor E = internal energy per unit mass f = scalar F = body force per unit volume h1h2h3 = scale factors H = static enthalpy per unit mass Ht = total enthalpy, Ht = H + V2/2 k = thermal conductivity p = static pressure q = heat-flux vector qb = heat-flux component normal to the surface t = time

T = temperature u = velocity component in a direction v = velocity component in b direction V = velocity vector w = velocity component in y direction W = heat generation per unit volume a, b, g = orthogonal coordinates k = bulk viscosity l = second viscosity coefficient m = shear viscosity r = density t = viscous stress tensor

I. Introduction Although formulation of the conservation equations of a viscous, heat-conducting fluid in curvilinear orthogonal coordinates is well known through vector and tensor analysis (Refs. 1 and 2), a complete, written-out set of equations, including the energy equation, is not readily available in any given source. The momentum equation was given by Goldstein (Ref. 3) in curvilinear orthogonal coordinates for an incompressible, constant-property fluid, and by Tsien (Ref. 4) for a compressible, variable-property fluid. Only the commonly used special cases of the set of equations in rectangular, cylindrical, and spherical coordinates appear in the literature (e.g., Ref. 5). The purpose of this paper is to briefly present the complete set of equations in stationary, curvilinear orthogonal coordinates. For convenience in expressing the equations in various coordinates, scale factors for eleven coordinate systems are tabulated.

II. Conservation Equations Three forms of the energy equation are considered, one form of which may be best suited for a particular application. These relations involve the total enthalpy Ht, r

∂Ht ∂p - — ◊ q + — ◊ ( t ◊ V) + F ◊ V + W + r(V ◊ —)Ht = ∂t ∂t

the internal energy E, r

∂E + r(V ◊ —)E + p— ◊ V = -— ◊ q + t: (—V) + W ∂t

and the enthalpy H, r

∂H È ∂p ù + r(V ◊ —)H - Í + (V ◊ —) pú = -— ◊ q + t: (—V) + W ∂t Î ∂t û

To complete the set of conservation equations, the continuity and momentum equations are, respectively, ∂r + — ◊ (rV) = 0 ∂t 1 F 1 ∂V + (V ◊ —)V = - —p + + — ◊ t r r r ∂t The quantities that appear in these equations are identified in the nomenclature. By use of the same notation as used by Goldstein (Ref. 3), the orthogonal coordinates are taken as a, b, and g such that the elements of length at a, b, and g in the directions of increasing a, b, and g are h1da, h2db, and h2dg, respectively. The differential arc length ds is, then,

(ds)

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2

= h12 (da ) + h22 (db) + h32 (dg ) 2

2

2

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Conservation Equations of a Viscous, Heat-Conducting Fluid (continued) u, v, and w are components of the velocity vector V in the direction of increasing a, b, and g, the continuity equation is +

1 h1h2h3

È ∂ ù ∂ ¥ Í (h2h3ru) + (h1h3rv ) + ∂∂g (h1h2rw)ú = 0 ∂ ∂ a b Î û the momentum equation written in the a, b, and g directions is ∂u u ∂u v ∂u w ∂u uv ∂h1 uw ∂h1 + + + + + ∂t h1 ∂a h2 ∂b h2 ∂g h1h2 ∂b h1h3 ∂g v 2 ∂h2 w 2 ∂h3 1 1 ∂p Fa 1 =+ + (— ◊ t ) a h1h2 ∂a h1h3 ∂a r h1 ∂a r r ∂v u ∂v v ∂v w ∂v vu ∂h2 vw ∂h2 + + + + + ∂t h1 ∂a h2 ∂b h3 ∂g h1h2 ∂a h2h3 ∂g u 2 ∂h1 w 2 ∂h3 1 1 ∂p Fb 1 =+ + (— ◊ t)b h1h2 ∂b h2h3 ∂b r h2 ∂b r r ∂w u ∂w v ∂w w ∂w wu ∂h3 wv ∂h2 + + + + + ∂t h1 ∂a h2 ∂b h3 ∂g h1h3 ∂a h2h3 ∂b u 2 ∂h1 v 2 ∂h2 1 1 ∂p Fg 1 =+ + (— ◊ t ) g h1h3 ∂b h2h3 ∂g r h3 ∂g r r e components of the divergence of the symmetric stress tensor t in the a, b, and g direction (Ref. 6)1 are:

(— ◊ t ) a = 1 h1h2h3

(

)

(

)

(

)

È ∂ ù ∂ ∂ h1h3 t ab + h1h2 t ga ú Í (h2h3 t aa ) + ∂ a b g ∂ ∂ Î û + t ab

1 ∂h1 1 ∂h1 + t gc h1h2 ∂b h1h3 ∂g

- t bb

1 ∂h2 1 ∂h3 - t gg h1h2 ∂a h1h3 ∂a

(— ◊ t)b = 1 h1h2h3

1

(

)

(

)

È ∂ ù ∂ ∂ h2h3 t ab + hh t + hh t ú Í ∂b 1 3 bb ∂g 1 2 bg û Î ∂a + t ab

1 ∂h2 1 ∂h2 + t bg h1h2 ∂a h2h3 ∂g

- t aa

1 ∂h1 1 ∂h3 - t gg h1h2 ∂b h2h3 ∂b

e, h1, h2, and h3 used by Love are the reciprocals of those used herein.

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Conservation Equations of a Viscous, Heat-Conducting Fluid (continued)

(— ◊ t ) g = 1 h1h2h3

(

)

(

)

(

)

È ∂ ù ∂ ∂ h2h3 t ga + h1h3 t bg + h1h2 t gg ú Í ∂ a b g ∂ ∂ Î û + t ga

1 ∂h3 1 ∂h3 + t bg h1h3 ∂a h2h3 ∂b

- t aa

1 ∂h1 1 ∂h2 - t bb h1h3 ∂g h2h3 ∂g

The components of the viscous stress tensor for a Stokes’ fluid are related to the components of the rate of strain tensor by t aa = l— ◊ V + meaa t bb = l— ◊ V + mebb t gg = l— ◊ V + me gg t ab = t ba = meab t ag = t ga = meag t bg = t gb = mebg where the divergence of the velocity vector is —◊V =

ù 1 È ∂ ∂ (h h v ) + ∂∂g (h1h2w)ú Í (h h u) + ∂b 1 3 h1h2h3 Î ∂a 2 3 û

and the components of the rate of strain tensor are (Ref. 3): v ∂h1 w ∂h1 1 1 ∂u e = + + 2 aa h1 ∂a h1h2 ∂b h3h1 ∂g w ∂h2 u ∂h2 1 1 ∂v e = + + 2 bb h2 ∂b h2h3 ∂g h1h2 ∂a u ∂h3 v ∂h3 1 1 ∂w e = + + 2 gg h3 ∂y h1h3 ∂a h2h3 ∂b eab =

h2 ∂ Ê v ˆ h1 ∂ Ê u ˆ + h1 ∂a ÁË h2 ˜¯ h2 ∂b ÁË h1 ˜¯

eag =

h1 ∂ Ê u ˆ h3 ∂ Ê w ˆ + h3 ∂g ÁË h1 ˜¯ h1 ∂a ÁË h3 ˜¯

ebg =

h3 ∂ Ê w ˆ h2 ∂ Ê v ˆ + h2 ∂b ÁË h3 ˜¯ h3 ∂g ÁË h2 ˜¯

The second viscosity coefficient l is related to the shear viscosity m (first viscosity coefficient) by l = 2/3 m if the bulk viscosity coefficient defined by k = l + 2/3 m is zero. Otherwise, l is given by 2 l=k- m 3

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Conservation Equations of a Viscous, Heat-Conducting Fluid (continued) In the various forms of the energy equations, the operator (V·—) applied to a scalar f, such as Ht, E, p, or H, gives the convection of that quantity by the flow,

(V ◊ —) f = u h1

1

∂f 1 ∂f 1 ∂f +v +w ∂a h2 ∂b h3 ∂g

The divergence of the heat flux vector q is —◊q =

1 h1h2h3

(

)

(

)

È ∂ ù ∂ ∂ hh q + hh q ú Í (h2h3q a ) + ∂b 1 3 b ∂g 1 2 g û Î ∂a

In particular, if the heat flux vector is given by Fourier’s heat-conduction law, q = k — T, then the components are q a = -k

1 ∂T 1 ∂T 1 ∂T , qb = -k , q g = -k h1 ∂a h2 ∂b h3 ∂g

The rate at which work is done by body forces is, simply, F ◊ V = Fau + Fb v + Fg w The rate at which work is done by the viscous stresses is given by — ◊ ( t ◊ V) =

[ (

1 Ï ∂ h h t u + t ba v + t ga w Ì h1h2h3 Ó ∂a 2 3 aa

[ (

)]

)]

+

∂ h h t u + t bb v + t gb w ∂b 1 3 ab

+

¸ ∂ h h t u + t bg v + t gg w ý ∂g 1 2 ag þ

[ (

)]

Lastly, the rate of dissipation of energy takes the form Ê 1 ∂u v ∂h1 w ∂h1 ˆ t: (—V) = t aa Á + + ˜ Ë h1 ∂a h1h2 ∂b h1h3 ∂g ¯ Ê 1 ∂v u ∂h2 w ∂h2 ˆ + t bb Á + + ˜ Ë h2 ∂b h1h2 ∂a h2h3 ∂g ¯ Ê 1 ∂w u ∂h2 v ∂h3 ˆ + t gg Á + + ˜ Ë h3 ∂g h1h3 ∂a h2h3 ∂b ¯ Ê 1 ∂u 1 ∂v v ∂h2 u ∂h1 ˆ + t ab Á + ˜ h h h h h ∂ ∂ ∂ b a a Ë 2 1 1 2 1h2 ∂b ¯ Ê 1 ∂u 1 ∂w w ∂h3 u ∂h1 ˆ + t ag Á + ˜ Ë h3 ∂g h1 ∂a h1h3 ∂a h1h2 ∂g ¯ Ê 1 ∂v 1 ∂w w ∂h2 v ∂h2 ˆ + t bg Á + ˜ Ë h3 ∂g h2 ∂b h2h3 ∂b h2h3 ∂g ¯ This rate of dissipation of energy term usually appears in the literature as F. Table 1 presents descriptive information on a number of orthogonal coordinate systems for which the conservation equations can be readily written by use of the foregoing relations. The last two entries in Table 1, in which the coordinates are taken along and normal to the surface, are useful in analyzing internal and external boundary-layer flows. For many flow problems in these coordinates, the dominant viscous stress is the shear stress that lies in the plane of b = const (tab for a twodimensional flow and tab, tgb for a three-dimensional flow), and the important heat-flux component is normal to the surface, qb.

© 2004 by CRC Press LLC

1. Orthogonal Coordinate System, and 2. Orthogonal coordinates a, b, g

COORDINATE SYSTEMS AND SCALE FACTORS

Rectangular Coordinates

x

y

Scale Factors h1, h2, ha

z

h1

h2

h3

Coordinate Configuration

1 Cylindrical r, q, z

r cos q

r sin q

z

1

z w q r

r

y v

x

u z

Spherical r, f, q

r cos q sin f

r sin q sin f

r cos f

1

f

r sin q

r

x

(

1 2 x - h2 2

Parabolic cylindrical x, h, z

Paraboloidal x, h, f

)

zh

x 2 + h2

z

x 2 + h2

q

u r v z w y

y

1

(

1 2 x - h2 2

xh sin f

)

x 2 + h2

x 2 + h2

xh

z

h = Const x

Elliptic cylindrical x, h, z

a cosh x cos h a sinh x sin h a = const

a sinh x sin h cos f a = const

© 2004 by CRC Press LLC

a sinh x sin h sin f

z

a sinh2 x + sin 2 h

a sinh2 x + sin 2 h

f

a sinh2 x + sin 2 h

a sinh2 x + sin 2 h

a sinh x sin h

u x = Const - Ellipse h = Const - Hyperbola

x

x = Const

a cosh x cos h

x = Const Confocal w h = Const Parabolas v y

u

x = Const

yv

1

x = Const Confocal u h = Const Parabolas x h = Const

h = Const z

h = Const x = Const x

f

u w v

x = Const - Ellipse h = Const - Hyperbola y

4-63

Prolate spheroidal x, h, f

v

x = Const xh cos f

Mechanical Engineering

Table 1.

1587_Book.fm Page 63 Monday, September 1, 2003 7:17 PM

Conservation Equations of a Viscous, Heat-Conducting Fluid (continued)

Table 1.

a cosh x cos h Oblate spheroidal cos f x, h, f a = const

a cosh x cos h sin f

COORDINATE SYSTEMS AND SCALE FACTORS (continued)

a sinh x sin h

a sinh2 x + sin 2 h

a sinh2 x + sin 2 h

a cosh x cos h

z v

x = Const

a sinh h cosh h - cos x

a sinh x cosh h - cos x

f

z

a cosh h - cos x

a cosh h - cos x

a cosh h - cos x

a cosh h - cos x

1

y u v

x = Const

a sinh hcos f cosh h - cos x

a sinh hsin f cosh h - cos x

a sinh x cosh h - cos x

a sinh h cosh h - cos x

a = const

x = Const - Circle y h = Const - Circle h = Const

—

1 + kg

1

1

Local coordinates — along surface (Ref. 3) Symmetric about axis x, y, f

—

—

1 + kg

1

r r Note, r (x,y)

y, v x, u rc = 1/k +

w f End view Axis

r

References 1. “Laminar Flow Theory,” P.A. Lagerstrom, Theory of Laminar Flows, Vol. IV, High-Speed Aerodynamics and Jet Propulsion, F.K. Moore, Ed., Princeton University Press, 1964. 2. “Methods of Theoretical Physics,” P.M. Morse and H. Feshbach, Part I, McGraw-Hill Book Company, 1953. 3. “Modern Developments in Fluid Dynamics,” S. Goldstein, Vol. 1, Oxford University Press, 1938. 4. “The Equations of Gas Dynamics,” H.S. Tsien, Fundamentals of Gas Dynamics, Vol. III, High-Speed Aerodynamics and Jet Propulsion, H.W. Emmons, Ed., Princeton University Press, 1958. 5. “Transport Phenomena,” R.B. Bird, W.E. Stewart, and E.N. Lightfoot, John Wiley & Sons, 1960. 6. “Treatise on the Mathematical Theory of Elasticity,” A.E.H. Love, Dover Publications, 1944, p. 90. From Bolz, R.E. and Tuve, G.L., Fluid and aero mechanics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 496–501. Originally from “JPL Technical Report 32–1332,” L.H. Back, Jet Propulsion Laboratory, California Institute of Technology, 1968.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

—

x = Const - Circle x h = Const - Circle h = Const

z u v w

x = Const

x f

Local coordinates — along surface (Ref. 3) x, y, z

x = Const - Ellipse h = Const - Hyperbola

h = Const

a = const Toroidal x, h, f

w y

x Bipolar x, h, x

u

1587_Section_4.fm Page 64 Wednesday, October 8, 2003 4:47 PM

4-64

Conservation Equations of a Viscous, Heat-Conducting Fluid (continued) (continued)

1587_Book.fm Page 65 Friday, September 26, 2003 12:10 PM

Mechanical Engineering

4-65

Energy Conversions Directions and Methods for Energy Conversion

Energy conversion chart. The circles represent the different forms of energy and the arrows the ways of converting energy from one form to another. From Bolz, R.E. and Tuve, G.L., Fluid and aero mechanics, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 550. Originally from Kettani, M.A., Direct Energy Conversion, Addison-Wesley Publishing Company, 1970, p. 6.

© 2004 by CRC Press LLC

1587_Book.fm Page 66 Monday, September 1, 2003 7:17 PM

4-66

CRC Handbook of Engineering Tables

Helical Steel Springs* Compression or Tension The upper figure is the load in pounds at 100 000 psi (689 MN/m2) stress by the “corrected” stress equation. The lower figure gives spring stiffness in lb/in per single coil, based on a shear modulus of 11.5 ¥ 106 psi (79.3 GN/M2). The stiffness is independent of load. Both figures may be adjusted in direct proportion to selected stress or modulus. For multicoil springs divide the stiffness per coil by the number of active coils. For load in N, multiply the values in lbf by 4.4482. For stiffness in N/m, multiply the values in lbf/in. by 175.13. Helical Springs—Load and Stiffness Wire Diam. in. .010 .012 .014 .016 .018 .020 .022 .024 .028

Outside Diameter of Coil, in. 1/8

3/16

.305 9.47 .522 20.7 .823 40.3 1.21 72.9 1.71 124 2.32 200 3.03 306 3.90 464 5.98 965

.032 .037 .043 .049 .055 .063 .071 .080 .090 .100 .112 .125 .148 .177 .207 .244

© 2004 by CRC Press LLC

.350 5.43 .560 10.5 .824 18.4 1.17 30.7 1.60 48.6 2.12 73.9 2.72 108 4.25 216 6.25 398 9.42 785 14.4 1618

1/4

.422 4.18 .626 7.37 .889 12.1 1.22 18.9 1.60 28.2 2.09 41.4 3.29 80.6 4.84 146 7.41 280 11.4 559 16.4 1019 22.8 1767

5/16

.972 9.06 1.30 13.7 1.68 19.9 2.65 38.0 3.95 68.0 6.01 128 9.33 249 13.7 452 18.9 768 27.9 1461 38.7 2563

3/8

7/16

1.41 11.1 2.24 21.1 3.33 37.5 5.07 69.6 7.91 134 11.6 240 16.2 401 23.8 721 33.4 1295 47.1 2300

1.21 6.67 1.92 12.9 2.85 22.4 4.41 42.2 6.82 80.0 10.1 141 14.1 234 20.9 429 29.4 741 41.3 1285 57.9 2236 77.5 3726

1/2

9/16

1.69 8.37 2.51 14.8 3.88 27.3 6.07 51.6 8.84 90.8 12.4 149 18.6 272 26.1 463 36.9 795 51.7 1368 69.7 2248 95.6 3886 130 6701

1.51 5.79 2.24 10.0 3.44 18.5 5.36 34.9 7.95 60.7 11.2 101 16.6 181 23.6 307 33.4 525 46.9 890 63.3 1449 87.4 2462 119 4205

5/8

2.03 7.27 3.10 13.3 4.89 25.0 7.14 43.2 10.0 70.4 15.1 128 21.3 215 30.2 364 42.9 617 58.0 993 79.7 1678 109 2817 175 6350

11/16

2.83 9.77 4.44 18.3 6.54 32.0 9.23 51.9 13.8 92.6 19.5 156 27.8 262 39.0 442 53.0 707 73.8 1186 101 1977 163 4380

3/4

2.61 7.43 4.10 14.0 6.00 24.1 8.50 39.5 12.7 70.0 18.0 117 25.7 196 36.2 329 49.2 525 68.1 871 93.8 1436 151 3166 250 7485

7/8

3.52 8.60 5.17 14.6 7.32 23.9 10.9 42.3 15.5 70.6 22.2 117 31.2 195 42.6 309 59.3 509 81.9 832 133 1802 222 4150 341 8857

1

4.55 9.66 6.40 15.6 9.60 27.5 13.6 45.3 19.5 75.6 27.6 125 37.6 197 52.2 323 72.5 525 119 1119 198 2526 307 5266 484 11,805

1587_Book.fm Page 67 Monday, September 1, 2003 7:17 PM

4-67

Mechanical Engineering

Helical Steel Springs* Wire Diam. in. .055 .063 .071 .080 .090 .100 .112 .125 .148 .177 .207 .244 .283

Outside Diameter of Coil, in. 1 1/8 5.70 10.7 8.55 18.8 12.2 31.5 17.3 51.4 24.7 85.1 33.5 132 47.0 218 65.0 350 106 741 178 1664 279 3419 444 7462

1 1/4

7.75 13.6 11.1 22.4 15.7 37.0 22.2 60.3 30.5 94.5 42.4 152 58.8 246 96.3 514 163 1145 255 2320 406 4988 614 10,199

.331 .375 .437 .500 .562 .625

1 3/8

1 1/2

9.97 16.4 14.2 27.0 20.2 44.3 27.7 69.0 38.6 112 53.9 180 88.0 375 149 819 235 1658 376 3498 574 7086 882 15,207

9.21 12.6 13.1 20.5 18.6 33.5 25.5 52.4 35.8 84.5 49.4 135 81.2 279 137 609 217 1218 306 2562 534 5154 824 10,785 1166 19,966

1 3/4

2

22.1 32.1 30.7 51.7 42.6 82.0 70.5 168 119 361 188 716 349 1488 467 2919 733 6048 1038 10,903 1587 23,202

19.3 20.9 27.0 33.5 37.6 53.3 62.0 109 105 234 166 457 269 941 415 1820 652 3713 932 6652 1433 13,859 2073 26,645

2 1/4

24.1 23.1 33.4 36.6 55.1 74.3 94.0 159 150 310 241 631 374 1210 589 2449 844 4302 1307 8861 1897 16,817 2623 29,977

2 1/2

2 3/4

3

3 1/4

3 1/2

4

30.2 26.2 49.7 53.1 84.7 113 134 218 218 443 338 849 534 1693 767 2960 1201 6005 1742 11,268 2426 19,533 3239 33,289

45.3 39.1 77.2 83.3 122 160 199 322 309 616 491 1217 704 2124 1102 4243 1617 7880 2251 13,751 3010 22,872

41.7 29.7 71.0 63.2 113 121 183 243 285 460 453 911 652 1575 1019 3132 1500 5736 2096 9957 2825 16,386

65.5 48.4 104 93.6 170 188 263 352 421 694 605 1195 951 2367 1396 4325 1956 7412 2649 12,135

61.2 38.4 97.2 74.1 158 148 247 276 391 543 567 933 888 1835 1310 3330 1832 5686 2491 9240

85.2 48.5 139 95.9 216 180 343 348 497 597 783 1166 1160 2097 1628 3546 2221 5710

From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 605–606. Originally from Ross, H.F., Trans. ASME, 69, 727, 1947.

© 2004 by CRC Press LLC

1587_Book.fm Page 68 Tuesday, September 2, 2003 3:25 PM

4-68

CRC Handbook of Engineering Tables

Ultrasonic Energy and Applications Table A. Applications of Ultrasonics Typical Frequencies, kc/s

Processes HIGH POWER RANGEa Surface cleaning; grease and film removal Emulsifying; homogenizing; production of dispersions Degassing of liquids and molten metals (grain refinement) Stimulating mechanical processes; mixing, diffusion, defoaming, atomizing, drying, plastic sealing, particle agglomeration, flow of powders, adhesion in soldering and welding, grain refinement in casting Cutting and forming; impact grinding of brittle materials; abrasive cutting; die forming with reduced friction Stimulating chemical processes; combustion and other reactions LOW POWER RANGE (ABSORPTION AND ECHO) Inspection and flow detection Pulse-echo counting and inspection Medical examination, diagnosis, and therapy Measurement and control (flow, thickness, density, liquid level, viscosity) Sonic detection and ranging; command signaling; delay lines

15–60 10–40 10–40 10–500

15–100 10–200 500–5000 700–10,000 500–2500 500–20,000 10 000–20 000

a

The desired effects in this range are largely accomplished by cavitation (in a liquid) or by vibrations and high accelerations that affect materials in contact with each other. Cavitation is bubble formation at a nucleus (such as a particle), followed by bubble growth and collapse. High pressures and temperatures occur at the instant of collapse, and the number of bubbles collapsing can be millions per second. Cavitation is suppressed by high static pressure and varies with liquid temperature. As the ultrasonic frequency is increased, up to a practical limit of about 107 cps (hz), the sound intensity must be increased to pass the threshold at which cavitation begins. Intensities very much above the threshold are not advantageous. Cavitation is increased in a liquid of low viscosity, low vapor pressure, and high surface tension. Transmission and matching of acoustics power to the load is often not simple; in fact this step is an art in itself (see references). Table B. Generators or Transducers Typical Limits Type of Generator Air whistles Jet-edge vibrators (gas or liquid) Cavity resonators Sirens (jet interruption) Piezoelectric-quartz Piezoelectric-ceramic (e.g., barium titanate) Magnetostrictive (Ni, Fe, Co, ferrites) Electron tube Rotating alternator a b

a

Mechanical Power, W 75 50 500 1000 4000 5000 1000 25,000

Frequency, kc/s

Efficiency,b %

40 20 12 25 5000 5000 90 30 25

15 15 15 70 90 75 50 50 50

Power intensity per unit area at point of use depends on methods for transmission and focusing. The efficiencies of available equipment for industrial use are often much below these values.

References “High-Intensity Ultrasonics: Industrial Applications,” B. Brown and J.E. Goodman, D. Van Nostrand Co., 1965. “Sources of High-Intensity Ultrasound,” L.D. Rozenberg, Ed., 2 volumes, Plenum Press, 1968. “Ultrasonic Engineering,” J.R. Frederick, John Wiley & Sons, Inc., 1965. “Ultrasonic Machining of Intractable Materials,” A.I. Markov, Ed., Butterworth & Co., 1967. “Ultrasonics: Theory and Application,” G.L. Gooberman, English Universities Press, 1968. From Bolz, R.E. and Tuve, G.L., Dynamics and vibration, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 607.

© 2004 by CRC Press LLC

Log Magnitude Characteristic

D1 x0

K1

20 db/decade w 1 T1 G0 = 0

K2

G0

G0 =

D1 K1

L

D1 K1

G 0T 1

È Ê K ˆ ù T1T2 s 2 + ÍT1 + Á1 + 2 ˜ T2 ú s + 1 Ë K 1 ¯ úû ÍÎ

D1 K1

D2 K2

Transfer Function

T1

T2

1 T1s + 1

D1 K1

L

20 db/decade 1 T1

K1

T1s T1s + 1

G•

0 db x0

T2

G• = 1

D1 xi

T1

G•

0 db

xi

Transfer Function

Mechanical Engineering

LEAD Mechanical Lead Network

1 1 + K2 K1

1 T2

w

G0

T1s + 1 T2 s + 1

G• = 1

D1 xi

x0

D2

Mechanical Lag Network K1 xi

D1

G•

0 db

K1

20 db/decade 40 db/decade w K2

G0 = 0

G0 20 db/decade

x0

G0 = 1

w G• = 0

4-69

1 T1

© 2004 by CRC Press LLC

G• = 1

LAG Log Magnitude Characteristic 0 db

T1T2 s 2

1587_Book.fm Page 69 Monday, September 1, 2003 7:17 PM

Mechanical Components

Mechanical Lag Network K1

Log Magnitude Characteristic

D2

xi

G0

0 db

1 T1

D1

G0

0 db xi

T2 s + 1 T1s + 1

T2 G•

D1 K1

1 È Ê K ˆ ù T1T2 s 2 + ÍT1 + Á1 + 2 ˜ T2 ú s + 1 Ë K 1 ¯ úû ÍÎ

D1 K1

D2 K2

Transfer Function

T1

T2

D1 K1

D2 K2

1 1 + D2/D1

20 db/decade 40 db/decade

x0 K2

T2

w

1 T2 G• =

G0 = 1 K1

T1

20 db/decade G•

x0 D1

Transfer Function

D2

w G0 = 1

G• = 0 LAG-LEAD

D1 xi

D2

Log Magnitude Characteristic K2

0 db

G0

20 db/decade

(T s + 1)(T s + 1)

G1

x0 K1

G•

1 1 T2 T1 G0 = G• = 1 G1 =

1

w

T1 + T2 K T1 + (1 + 2 ) T2 K1

2

È Ê K ˆ ù T1T2 s + ÍT1 + Á1 + 2 ˜ T2 ú s + 1 Ë K 1 ¯ úû ÍÎ 2

From Bolz, R.E. and Tuve, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1088–1089. Originally from Handbook of Automation, Computation, and Control, Vol. 1, Grabbe, E.M., Ramo, S., and Wooldridge, D.E., Eds., John Wiley & Sons, New York, 1958.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Mechanical Lag-Lead Network

1587_Book.fm Page 70 Monday, September 1, 2003 7:17 PM

4-70

Mechanical Components (continued)

Approximate Relationships for High Loop Gain Controllers, e 1 LEAD Plot for T = T1

Pr

Pm - P0 A1 È 1 + T1s ù = Í ú Pc - Pr A2 Î 1 + kT1s û

Restriction Area A2

¬

T1 =

Pm

Pf

Log M

Differential area A1

Pc

A1/kA2 A1/A2

k = change in Pf for a unit change in Pm when is completely closed.

1 2pT

1 2pkT

Log frequency, cpm

= Pressure source

Plot for T = T1 ¬

A3 A1 A2

Pf - Pr Restriction Pm

Pm - P0 A1 È 1 + ( A3 A2 )T1s ù = Í ú Pc - Pr A2 ÎÍ 1 + kT1s úû T1 =

Log M

Pc - Pr

A3/A2

A1/A2 1 2pT

A3/A1 2pT Log frequency, cpm

4-71

© 2004 by CRC Press LLC

1587_Book.fm Page 71 Monday, September 1, 2003 7:17 PM

Mechanical Engineering

Pneumatic Compensating Components

LAG Differential area A1

Pc

Plot for T = T1

A2

T1 = ¬e

'

Pm - P0 A È 1 + 1 T1s ù = 1 Í ú Pc - Pr A2k Î 1 + kT1s û

Pm

Log M

Pr

A1/ A2 A1/A2

= a system constant related to the loop gain.

Pf To atmosphere

1 2pT

¬

Log frequency, cpm

= Pressure source LAG-LEAD

¬2 Restriction Pf1 1

A1

¬1

Pm

T1s È U2 s ù Í 1 + bT U + 1 + 1 + bT U ú 1 2 1 2 ú , = (1 + bT1U 2 ) ◊ Í Í ú U 2 s + T1s + 1 Í ú Î û where bT1U2 1, T1 = 11, U2 = 1/22, b = 1 + 2/1, I = interaction factor.

1/

1/

∋

Pr

∋

Pm - P0 Pc - Pr

Log M

Pf2

Pc

U 2π

1 2πT

Log frequency, cpm

From Bolz, R.E. and Tuve, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1090–1091. Originally from Handbook of Automation, Computation, and Control, Vol. 1, Grabbe, E.M., Ramo, S., and Wooldridge, D.E., Eds., John Wiley & Sons, New York, 1958, pp. 23-46 and 23-47.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

Plot for β = 2, T1U2 = 1/2 Then U = 0.5U2 T = 0.5T1 I = 0.5 UT = 0.125 k=

2

A1

∋

Differential area A1

1587_Book.fm Page 72 Friday, September 26, 2003 12:10 PM

4-72

Pneumatic Compensating Components (continued)

1587_Book.fm Page 73 Friday, September 26, 2003 12:10 PM

4-73

Mechanical Engineering

Dynamic Elements and Networks Element or System 1.

G(s)

Integrating circuit

4 8 I 2.

+

8 I

4

8 I

1 RCS + 1

V2 ( s )

=

RCS RCS + 1

V2 ( s )

=

s + 1 RCS s + (R1 + R2 ) R1R2C

V2 ( s )

=

V1 ( s )

Differentiating circuit

+ 8 I 4 4.

=

Differentiating circuit

+

3.

V2 ( s ) V1 ( s )

8 I

4

8 I

V1 ( s )

Lead-lag filter circuit

+ 4

8 I

8 I

+

4

V1 ( s )

=

(1 + st )(1 + st ) a

b

t a t b s 2 + ( t a + t b + t ab )s + 1

(1 + st )(1 + st ) (1 + st )(1 + st ) a

b

1

2

ta = R1C1, tb = R2C2 tab = R1C1 t1t2 = tatb , t1 + t2 = ta + tb + tab 5.

dc-motor, field controlled

Rf V f s

6.

If

Ia J, f

Lf

q( s )

=

q( s )

=

V f (s)

q, w

Km

(

s( Js + f ) L f s + R f

)

dc-motor, armature controlled

Ra

La

V as

If J, f

Vb Ia

© 2004 by CRC Press LLC

q, w

Va ( s )

[

Km

s (Ra + La s )( J s + f ) + K b K m

]

1587_Book.fm Page 74 Friday, September 26, 2003 12:10 PM

4-74

CRC Handbook of Engineering Tables

Dynamic Elements and Networks (continued) Element or System 7.

G(s)

ac-motor, two-phase control field q( s )

V c(s)

J, f

M

8.

Vc

Km s( ts + 1)

t = J ( f - m)

m = slope of linearized torque- speed

Reference field

curve (normally negative)

id

Ld

Vd ( s ) Vc ( s )

V @s

=

(K R R ) (st + 1)(st + 1) c

c

q

q

t c = Lc Rc , t q = Lq Rq

Lc Rc

Lq

For the unloaded case, id 0, t c t q ,

iq

Rq

0.05 sec < t c < 0.5 sec

Hydraulic actuator

Y (s)

X (s)

=

K s( Ms + B )

K=

Ê Akz A2 ˆ , B=Áf + kp k p ˜¯ Ë

kz =

∂g ∂x

10.

=

Amplidyne

ic

9.

Vc ( s )

, kp = x0

∂g ∂P

g = g (x , P ) A = area of piston

Gear Train

N1 Gm , M m

N2

Gear ratio = n =

GL, M L

N1 N2

N 2q L = N1qm , q L = nqm w L = nw M

11.

, p0

Potentiometer

G

8 I

4

© 2004 by CRC Press LLC

8 8 I

4 4

8 I

V2 ( s ) V1 ( s )

=

R2 R2 = R R1 + R2

R2 q = R qmax

1587_Book.fm Page 75 Friday, September 26, 2003 12:10 PM

4-75

Mechanical Engineering

Dynamic Elements and Networks (continued) Element or System 12.

G(s)

Potentiometer error detector bridge

(

G1

8battery

V2 ( s ) = ks qerror ( s )

8 2(I)

Error voltage

13.

Vbattery

k2 =

qmax

Tachometer

G(I), M(I) 14.

)

V2 ( s ) = ks q1 ( s ) - q2 ( s )

G2

V2 ( s ) = K t w( s )

8 2(I)

= K t sq( s )

dc-amplifier V2 ( s )

+

V1 ( s )

+

8 I

=

ka st + 1

R0 = output resistance

8 I

C0 = output capacitance t = R0C0 , t 1 and is often negligible for servomechanism amplifier

15.

Accelerometer x 0 (t ) = y(t ) - x in (t ) ,

Frame Mass

M

K

X 0 (s)

xin(t)

X in ( s )

=

For low-frequency oscillations, where

f

y ( t)

w < wn , X 0 ( jw )

X in ( jw ) 16.

-s2 s + ( f M )s + K M 2

w2 K M

Thermal Heating System ¡( s )

Á

q( s )

Á

1 , where Ct s + (QS + 1 R )

¡ = ¡0 - ¡e = temperature difference due to thermal process

Á

Ct = thermal capacitance

Á

=

Q = fluid flow rate = constant S = specific heat of water Rt = thermal resistance of insulation q( s ) = rate of heat flow of heating element

From Bolz, R.E. and Tuve, G.L., Automatic control, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 1092–1094. Originally from Dorf, R.C., Modern Control Systems, Addison-Wesley, Reading, MA, 1967.

© 2004 by CRC Press LLC

1587_Book.fm Page 76 Monday, September 1, 2003 7:17 PM

4-76

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Temperature) t (˚C) 0 0.01 1 2 3 4 5

Volume, m3/kg

Pressure MPa *0.000 0.000 0.000 0.000 0.000 0.000 0.000

611 611 657 706 758 813 872

nL 2 7 1 0 1 5 6

0.001 0.001 0.001 0.001 0.001 0.001 0.001

000 000 000 000 000 000 000

Dn

Enthalpy, kJ/kg

nv

hL

Entropy, kJ/(kg˚K)

Dh

hv

sL

Ds

sv

t (˚C)

2 2 1 1 1 1 1

206.14 206.00 192.44 179.76 168.01 157.12 147.02

206.14 206.00 192.44 179.76 168.01 157.12 147.02

–0.042 0.001 4.177 8.392 12.604 16.813 21.019

2500.9 2500.9 2498.6 2496.2 2493.8 2491.4 2489.1

2500.9 2500.9 2502.7 2504.6 2506.4 2508.2 2510.1

–0.0002 0.0000 0.0153 0.0306 0.0459 0.0611 0.0763

9.1559 9.1555 9.1138 9.0721 9.0306 8.9895 8.9486

9.1558 9.1555 9.1291 9.1027 9.0765 9.0506 9.0249

0 0.01 1 2 3 4 5

137.64 128.93 120.83 113.31 106.31

137.64 128.93 120.83 113.31 106.31

25.224 29.426 33.626 37.824 42.021

2486.7 2484.3 2481.9 2479.6 2477.2

2511.9 2513.7 2515.6 2517.4 2519.2

0.0913 0.1064 0.1213 0.1362 0.1511

8.9081 8.8678 8.8278 8.7882 8.7488

8.9994 8.9742 8.9492 8.9244 8.8998

6 7 8 9 10

6 7 8 9 10

0.000 0.001 0.001 0.001 0.001

935 4 0.001 000 1 002 0.001 000 1 073 0.001 000 2 148 0.001 000 3 228 0.001 000 3

11 12 13 14 15

0.001 0.001 0.001 0.001 0.001

313 403 498 599 706

0.001 0.001 0.001 0.001 0.001

000 000 000 000 000

4 5 7 8 9

99.792 93.723 88.059 82.797 77.880

99.792 93.724 88.070 82.798 77.881

46.216 50.410 54.602 58.794 62.984

2474.8 2472.5 2470.1 2467.7 2465.4

2521.1 2522.9 2524.7 2526.5 2528.4

0.1659 0.1806 0.1953 0.2099 0.2245

8.7096 8.6708 8.6322 8.5939 8.5559

8.8755 8.8514 8.8275 8.8038 8.7804

11 12 13 14 15

16 17 18 19 20

0.001 0.001 0.002 0.002 0.002

819 938 065 198 339

0.001 0.001 0.001 0.001 0.001

001 001 001 001 001

1 3 5 6 8

73.290 69.005 65.002 61.260 57.760

73.291 69.006 65.003 61.261 57.761

67.173 71.361 75.548 79.734 83.920

2463.0 2460.6 2458.3 2455.9 2453.5

2530.2 2532.0 2533.8 2535.7 2537.5

0.2390 0.2534 0.2678 0.2822 0.2965

8.5181 8.4806 8.4434 8.4064 8.3696

8.7571 8.7341 8.7112 8.6886 8.6661

16 17 18 19 20

21 22 23 24 25

0.002 0.002 0.002 0.002 0.003

488 645 811 986 170

0.001 0.001 0.001 0.001 0.001

002 002 002 002 003

1 3 5 8 0

54.486 51.421 48.551 45.862 43.340

54.487 51.422 48.552 45.863 43.341

88.105 92.289 96.473 100.66 104.84

2451.2 2448.8 2446.4 2444.1 2441.7

2539.3 2541.1 2542.9 2544.7 2546.5

0.3108 0.3250 0.3391 0.3532 0.3673

8.3331 8.2969 8.2609 8.2251 8.1895

8.6439 8.6218 8.6000 8.5783 8.5568

21 22 23 24 25

26 27 28 29 30

0.003 0.003 0.003 0.004 0.004

364 568 783 009 247

0.001 0.001 0.001 0.001 0.001

003 003 003 004 004

3 5 8 1 4

40.976 38.757 36.674 34.718 32.881

40.977 38.758 36.675 34.719 32.882

109.92 113.20 117.38 121.56 125.75

2439.3 2437.0 2434.6 2432.2 2429.8

2548.4 2550.2 2552.0 2553.8 2555.6

0.3813 0.3952 0.4091 0.4230 0.4368

8.1542 8.1192 8.0843 8.0497 8.0153

8.5355 8.5144 8.4934 8.4727 8.4521

26 27 28 29 30

31 32 33 34 35

0.004 0.004 0.005 0.005 0.005

497 759 035 325 629

0.001 0.001 0.001 0.001 0.001

004 005 005 005 006

7 0 4 7 0

31.153 29.528 28.000 26.561 25.207

31.154 29.529 28.001 26.562 25.208

129.93 134.11 138.29 142.47 146.64

2427.5 2425.1 2422.7 2420.3 2417.9

2557.4 2559.2 2561.0 2562.8 2564.6

0.4506 0.4643 0.4780 0.4916 0.5052

7.9812 7.9472 7.9135 7.8800 7.8467

8.4317 8.4115 8.3914 8.3715 8.3518

31 32 33 34 35

36 37 38 39 40

0.005 0.006 0.006 0.007 0.007

947 282 632 000 384

0.001 0.001 0.001 0.001 0.001

006 006 007 007 007

4 8 1 5 9

23.931 22.728 21.594 20.525 19.516

23.932 22.729 21.595 20.526 19.517

150.82 155.00 159.18 163.36 167.54

2415.6 2413.2 2410.8 2408.4 2406.0

2566.4 2568.2 2570.0 2571.8 2573.5

0.5187 0.5322 0.5457 0.5591 0.5724

7.8136 7.7807 7.7480 7.7155 7.6832

8.3323 8.3129 8.2936 8.2746 8.2557

36 37 38 39 40

41 42 43 44 45

0.007 0.008 0.008 0.009 0.009

787 209 650 112 594

0.001 0.001 0.001 0.001 0.001

008 008 009 009 009

3 7 1 5 9

18.564 17.664 16.815 16.012 15.252

18.565 17.665 16.816 16.013 15.253

171.72 175.90 180.08 184.26 188.44

2403.6 2401.2 2398.8 2396.4 2394.0

2575.3 2577.1 2578.9 2580.7 2582.5

0.5858 0.5990 0.6123 0.6255 0.6386

7.6512 7.6193 7.5876 7.5561 7.5248

8.2369 8.2183 8.1999 8.1816 8.1634

41 42 43 44 45

46 47 48 49 50

0.010 0.010 0.011 0.011 0.012

099 626 176 751 351

0.001 0.001 0.001 0.001 0.001

010 010 011 011 012

3 8 2 7 1

14.534 13.855 13.212 12.603 12.027

14.535 13.856 13.213 12.604 12.028

192.62 196.80 200.98 205.16 209.34

2391.6 2389.2 2386.8 2384.4 2382.0

2584.2 2586.0 2587.8 2589.5 2591.3

0.6517 0.6648 0.6778 0.6908 0.7038

7.4937 7.4628 7.4320 7.4015 7.3711

8.1454 8.1276 8.1099 8.0923 8.0749

46 47 48 49 50

51 52 53 54 55

0.012 0.013 0.014 0.015 0.015

977 631 312 022 761

0.001 0.001 0.001 0.001 0.001

012 031 013 014 014

6 1 6 0 5

11.481 10.963 10.472 10.006 9.5639

11.482 10.964 10.473 10.007 9.5649

213.52 217.70 221.88 226.06 230.24

2379.6 2377.1 2374.7 2372.3 2369.9

2593.1 2594.8 2596.6 2598.4 2600.1

0.7167 0.7296 0.7424 0.7552 0.7680

7.3409 7.3109 7.2811 7.2514 7.2219

8.0576 8.0405 8.0235 8.0066 7.9899

51 52 53 54 55

© 2004 by CRC Press LLC

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4-77

Mechanical Engineering

Properties of Saturated Water and Steam (Temperature) (continued) t (˚C)

Volume, m3/kg

Pressure MPa

nL

Dn

Enthalpy, kJ/kg

nv

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

t (˚C)

56 57 58 59 60

0.016 0.017 0.018 0.019 0.019

532 335 171 041 946

0.001 0.001 0.001 0.001 0.001

015 015 016 016 017

0 5 1 6 1

9.1444 8.7461 8.3678 8.0083 7.6666

9.1454 8.7471 8.3688 8.0093 7.6677

234.42 238.61 242.79 246.97 251.15

2367.4 2365.0 2362.6 2360.1 2357.7

2601.9 2603.6 2605.4 2607.1 2608.8

0.7807 0.7934 0.8060 0.8186 0.8312

7.1926 7.1634 7.1344 7.1056 7.0770

7.9733 7.9568 7.9405 7.9243 7.9082

56 57 58 59 60

61 62 63 64 65

0.020 0.021 0.022 0.023 0.025

887 866 884 942 041

0.001 0.001 0.001 0.001 0.001

017 018 018 019 019

6 2 7 3 9

7.3418 7.0328 6.7389 6.4591 6.1928

7.3428 7.0338 6.7399 6.4601 6.1938

255.34 259.52 263.71 267.89 272.08

2355.2 2352.8 2350.3 2347.9 2345.4

2610.6 2612.3 2614.1 2615.8 2617.5

0.8438 0.8563 0.8687 0.8811 0.8935

7.0485 7.0201 6.9919 6.9639 6.9361

7.8922 7.8764 7.8607 7.8451 7.8296

61 62 63 64 65

66 67 68 69 70

0.026 0.027 0.028 0.029 0.031

183 368 599 876 201

0.001 0.001 0.001 0.001 0.001

020 021 021 022 022

4 0 6 2 8

5.9392 5.6976 5.4674 5.2479 5.0387

5.9402 5.6986 5.4684 5.2490 5.0397

276.27 280.45 284.64 288.83 293.02

2343.0 2340.5 2338.0 2335.6 2333.1

2619.2 2621.0 2622.7 2624.4 2626.1

0.9059 0.9182 0.9305 0.9428 0.9550

6.9083 6.8808 6.8534 6.8261 6.7990

7.8142 7.7990 7.7839 7.7689 7.7540

66 67 68 69 70

71 72 73 74 75

0.032 0.034 0.035 0.037 0.038

575 000 478 009 595

0.001 0.001 0.001 0.001 0.001

023 024 024 025 025

4 0 6 2 8

4.8392 4.6488 4.4671 4.2937 4.1281

4.8402 4.6498 4.4681 4.2947 4.1291

297.21 301.40 305.59 309.78 313.97

2330.6 2328.1 2325.6 2323.1 2320.6

2627.8 2629.5 2631.2 2632.9 2634.6

0.9672 0.9793 0.9915 1.0035 1.0156

6.7720 6.7452 6.7185 6.6920 6.6656

7.7392 7.7245 7.7100 7.6955 7.6812

71 72 73 74 75

76 77 78 79 80

0.040 0.041 0.043 0.045 0.047

239 941 703 527 415

0.001 0.001 0.001 0.001 0.001

026 027 027 028 029

5 1 7 4 0

3.9699 3.8188 3.6743 3.5363 3.4042

3.9709 3.8198 3.6754 3.5373 3.4053

318.17 322.36 326.56 330.75 334.95

2318.1 2315.6 2313.1 2310.6 2308.1

2636.3 2638.0 2639.7 2641.3 2643.0

1.0276 1.0396 1.0516 1.0635 1.0754

6.6393 6.6132 6.5872 6.5613 6.5356

7.6669 7.6528 7.6388 7.6248 7.6110

76 77 78 79 80

81 82 83 84 85

0.049 0.051 0.053 0.055 0.057

368 387 476 636 867

0.001 0.001 0.001 0.001 0.001

029 030 031 031 032

7 4 0 7 4

3.2780 3.1572 3.0415 2.9309 2.8249

3.2790 3.1582 3.0426 2.9319 2.8259

339.15 343.34 347.54 351.74 355.95

2305.5 2303.0 2300.5 2297.9 2295.4

2644.7 2646.4 2648.0 2649.7 2651.3

1.0873 1.0991 1.1109 1.1227 1.1344

6.5100 6.4846 6.4592 6.4340 6.4090

7.5973 7.5837 7.5701 7.5567 7.5434

81 82 83 84 85

86 87 88 89 90

0.060 0.062 0.065 0.067 0.070

174 556 017 559 182

0.001 0.001 0.001 0.001 0.001

033 033 034 035 035

1 8 5 2 9

2.7234 2.6262 2.5330 2.4437 2.3581

2.7244 2.6272 2.5341 2.4448 2.3591

360.15 364.35 368.56 372.76 376.97

2292.8 2290.3 2287.7 2285.1 2282.6

2653.0 2654.6 2656.3 2657.9 2659.5

1.1461 1.1578 1.1694 1.1811 1.1927

6.3840 6.3592 6.3345 6.3099 6.2854

7.5301 7.5170 7.7039 7.4909 7.4781

86 87 88 89 90

91 92 93 94 95

0.072 0.075 0.078 0.081 0.084

890 685 568 542 609

0.001 0.001 0.001 0.001 0.001

036 037 038 038 039

7 4 1 9 6

2.2760 2.1973 2.1217 2.0492 1.9796

2.2771 2.1983 2.1228 2.0502 1.9806

381.18 385.38 389.59 393.81 398.02

2280.0 2277.4 2274.8 2272.2 2269.6

2661.2 2662.8 2664.4 2666.0 2667.6

1.2042 1.2158 1.2273 1,2387 1.2502

6.2611 6.2368 6.2127 6.1887 6.1648

7.4653 7.4526 7.4400 7.4275 7.4150

91 92 93 94 95

96 97 98 99 100

0.087 0.091 0.094 0.097 0.101

771 031 390 852 42

0.001 0.001 0.001 0.001 0.001

040 041 041 042 043

4 1 9 7 5

1.9128 1.8486 1.7870 1.7277 1.6708

1.9138 1.8497 1.7880 1.7288 1.6719

402.23 406.45 410.66 414.88 419.10

2267.0 2264.4 2261.7 2259.1 2256.5

2669.2 2670.8 2672.4 2674.0 2675.6

1.2616 1.2730 1.2844 1.2957 1.3070

6.1411 6.1174 6.0938 6.0704 6.0471

7.4027 7.3904 7.3782 7.3661 7.3541

96 97 98 99 100

101 102 103 104 105

0.105 0.108 0.112 0.116 0.120

09 87 77 78 90

0.001 0.001 0.001 0.001 0.001

044 045 045 046 047

2 0 8 6 4

1.6161 1.5635 1.5129 1.4642 1.4174

1.6171 1.5645 1.5140 1.4653 1.4185

423.32 427.54 431.76 435.99 440.21

2253.8 2251.2 2248.5 2245.9 2243.2

2677.1 2678.7 2680.3 2681.8 2683.4

1.3183 1.3296 1.3408 1.3520 1.3632

6.0238 6.0007 5.9777 5.9548 5.9320

7.3421 7.3303 7.3185 7.3068 7.2951

101 102 103 104 105

106 107 108 109 110

0.125 0.129 0.134 0.138 0.143

15 51 01 63 38

0.001 0.001 0.001 0.001 0.001

048 049 049 050 051

3 1 9 7 6

1.3724 1.3290 1.2873 1.2471 1.2083

1.3734 1.3301 1.2883 1.2481 1.2094

444.44 448.67 452.90 457.13 461.36

2240.5 2237.8 2235.1 2232.4 2229.7

2684.9 2686.5 2588.0 2689.5 2691.1

1.3743 1.3854 1.3965 1.4076 1.4187

5.9092 5.8866 5.8641 5.8417 5.8194

7.2836 7.2721 7.2607 7.2493 7.2380

106 107 108 109 110

© 2004 by CRC Press LLC

1587_Book.fm Page 78 Monday, September 1, 2003 7:17 PM

4-78

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Temperature) (continued) t (˚C)

Volume, m3/kg

Pressure MPa

nL

Enthalpy, kJ/kg

nv

Dn

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

t (˚C)

111 112 113 114 115

0.148 0.153 0.158 0.163 0.169

26 28 43 73 18

0.001 0.001 0.001 0.001 0.001

052 053 054 055 055

4 3 1 0 9

1.1710 1.1351 1.1005 1.0671 1.0349

1.1721 1.1362 1.1015 1.0681 1.0359

465.60 469.83 474.07 478.31 482.55

2227.0 2224.3 2221.5 2218.8 2216.0

2692.6 2694.1 5695.6 2697.1 2698.6

1.4297 1.4407 1.4517 1.4626 1.4735

5.7972 5.7750 5.7530 5.7310 5.7092

7.2268 7.2157 7.2047 7.1937 7.1827

111 112 113 114 115

116 117 118 119 120

0.174 0.180 0.186 0.192 0.198

77 51 40 45 67

0.001 0.001 0.001 0.001 0.001

056 057 058 059 060

8 6 5 4 3

1.0038 0.973 90 0.945 01 0.917 14 0.890 24

1.0049 0.974 95 0.946 07 0.918 20 0.891 30

486.80 491.04 495.29 499.53 503.78

2213.3 2210.5 2207.7 2204.9 2202.1

2700.1 2701.5 2703.0 2704.5 2705.9

1.4844 1.4953 1.5062 1.5170 1.5278

5.6874 5.6658 5.6442 5.6227 5.6013

7.1719 7.1611 7.1504 7.1397 7.1291

116 117 118 119 120

121 122 123 124 125

0.205 0.211 0.218 0.225 0.232

04 58 29 17 22

0.001 0.001 0.001 0.001 0.001

061 062 063 064 064

2 2 1 0 9

0.864 0.839 0.815 0.791 0.769

28 21 01 63 05

0.865 0.840 0.816 0.792 0.770

34 28 07 69 11

508.04 512.29 516.55 520.80 525.06

2199.3 2196.5 2193.7 2190.9 2188.0

2707.4 2708.8 2710.3 2711.7 2713.1

1.5386 1.5494 1.5601 1.5708 1.5815

5.5800 5.5587 5.5376 5.5165 5.4955

7.1186 7.1081 7.0977 7.0873 7.0770

121 122 123 124 125

126 127 128 129 130

0.239 0.246 0.254 0.262 0.270

46 88 48 27 26

0.001 0.001 0.001 0.001 0.001

065 066 067 068 069

9 8 8 7 7

0.747 0.726 0.705 0.686 0.667

23 14 76 06 01

0.748 0.727 0.706 0.687 0.668

29 21 83 13 08

529.32 533.59 537.85 542.12 546.39

2185.2 2182.3 2179.5 2176.6 2173.7

2714.5 2715.9 2717.3 2718.7 2720.1

1.5922 1.6028 1.6134 1.6240 1.6346

5.4746 5.4538 5.4330 5.4124 5.3918

7.0668 7.0566 7.0465 7.0364 7.0264

126 127 128 129 130

131 132 133 134 135

0.278 0.286 0.295 0.304 0.313

44 82 41 20 20

0.001 0.001 0.001 0.001 0.001

070 071 072 073 074

7 7 7 6 7

0.648 0.630 0.613 0.596 0.580

59 78 54 87 73

0.649 0.631 0.614 0.597 0.581

66 85 61 94 80

550.66 554.93 559.21 563.49 567.77

2170.8 2167.9 2165.0 2162.0 2159.1

2721.5 2722.8 2724.2 2725.5 2726.9

1.6452 1.6557 1.6662 1.6767 1.6872

5.3713 5.3508 5.5305 5.3102 5.2900

7.0165 7.0066 6.9967 6.9869 6.9772

131 132 133 134 135

136 137 138 139 140

0.322 0.331 0.341 0.351 0.361

42 85 51 39 50

0.001 0.001 0.001 0.001 0.001

075 076 077 078 079

7 7 7 7 8

0.565 0.549 0.535 0.521 0.507

11 99 35 17 44

0.566 0.551 0.536 0.522 0.508

18 06 42 25 52

572.05 576.33 580.62 584.91 589.20

2156.2 2153.2 2150.2 2147.2 2144.2

2728.2 2729.5 2730.8 2732.1 2733.4

1.6977 1.7081 1.7185 1.7289 1.7393

5.2698 5.2498 5.2298 5.2098 5.1900

6.9675 6.9579 6.9483 6.9388 6.9293

136 137 138 139 140

141 142 143 144 145

0.371 0.382 0.393 0.404 0.415

85 43 25 32 63

0.001 0.001 0.001 0.001 0.001

080 081 082 084 085

8 9 9 0 0

0.494 0.481 0.468 0.456 0.444

14 25 77 66 93

0.495 0.482 0.469 0.457 0.446

22 33 85 75 02

593.49 597.79 602.09 606.39 610.69

2141.2 2138.2 2135.2 2132.2 2129.1

2734.7 2736.0 2737.3 2738.5 2739.8

1.7496 1,7600 1.7703 1,7806 1,7909

5.1702 5.1505 5.1308 5.1112 5.0917

6.9198 6.9105 6.9011 6.8918 6.8826

141 142 143 144 145

146 147 148 149 150

0.427 0.439 0.451 0.463 0.476

21 03 12 48 10

0.001 0.001 0.001 0.001 0.001

086 087 088 089 090

1 2 3 4 5

0.433 0.422 0.411 0.401 0.391

56 54 84 47 41

0.434 0.423 0.412 0.402 0.392

65 62 93 56 50

615.00 619.31 623.62 627.93 632.25

2126.0 2123.0 2119.9 2116.8 2113.7

2741.0 2742.3 2743.5 2744.7 2745.9

1.8011 1.8114 1.8216 1.8318 1.8420

5.0723 5.0529 5.0335 5.0143 4.9951

6.8734 6.8642 6.8551 6.8461 6.8370

146 147 148 149 150

152 154 156 158 160

0.502 0.529 0.557 0.587 0.618

18 38 76 33 14

0.001 0.001 0.001 0.001 0.001

092 095 097 099 102

7 0 3 6 0

0.372 0.354 0.337 0.320 0.305

18 07 00 90 72

0.373 0.355 0.338 0.322 0.306

27 16 09 00 82

640.89 649.55 658.21 666.89 675.57

2107.4 2101.1 2094.7 2088.3 2081.9

2748.3 2750.6 2752.9 2755.2 2757.4

1.8623 1.8825 1.9027 1.9228 1.9428

4.9569 4.9189 4.8811 4.8436 4.8063

6.8191 6.8014 6.7838 6.7664 6.7491

152 154 156 158 160

162 164 166 168 170

0.650 0.683 0.718 0.754 0.792

22 62 36 50 05

0.001 0.001 0.001 0.001 0.001

104 106 109 111 114

4 8 3 7 3

0.291 0.277 0.265 0.252 0.241

38 84 05 95 50

0.292 0.278 0.266 0.254 0.242

49 95 16 06 62

684.28 692.99 701.71 710.45 719.21

2075.3 2068.8 2062.1 2055.4 2048.7

2759.6 2761.7 2763.8 2765.9 2767.9

1.9627 1.9826 2.0025 2.0222 2.0419

4.7693 4.7324 4.6957 4.6593 4.6230

6.7320 6.7150 6.6982 6.6815 6.6649

162 164 166 168 170

172 174 176 178 180

0.831 08 0.871 61 0.913 68 0.957 34 1.0026

0.001 0.001 0.001 0.001 0.001

116 119 122 124 127

8 4 0 7 4

0.230 0.220 0.210 0.201 0.192

67 41 69 47 73

0.231 0.221 0.211 0.202 0.193

78 53 81 60 86

727.97 736.75 745.55 754.36 763.19

2041.9 2035.0 2028.1 2021.1 2014.0

2769.9 2771.8 2773.6 2775.4 2777.2

2.0616 2.0811 2.1007 2.1201 2.1395

4.5870 4.5511 4.5154 4.4799 4.4445

6.6485 6.6322 6.6161 6.6000 6.5841

172 174 176 178 180

© 2004 by CRC Press LLC

1587_Book.fm Page 79 Monday, September 1, 2003 7:17 PM

4-79

Mechanical Engineering

Properties of Saturated Water and Steam (Temperature) (continued) t (˚C)

Volume, m3/kg

Pressure MPa

nL

Enthalpy, kJ/kg

nv

Dn

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

t (˚C)

182 184 186 188 190

1.0496 1.0983 1.1487 1.2009 1.2550

0.001 0.001 0.001 0.001 0.001

130 132 135 138 141

1 9 7 6 4

0.184 0.176 0.169 0.161 0.155

44 57 09 99 24

0.185 0.177 0.170 0.163 0.156

57 70 23 13 38

772.03 780.89 789.76 798.66 807.57

2006.9 1999.7 1992.5 1985.1 1977.7

2778.9 2780.6 2782.2 2783.8 2785.3

2.1589 2.1782 2.1974 2.2166 2.2358

4.4094 4.3743 4.3395 4.3048 4.2702

6.5682 6.5525 6.5369 6.5214 6.5060

182 184 186 188 190

192 194 196 198 200

1.3110 1.3689 1.4288 1.4907 1.5547

0.001 0.001 0.001 0.001 0.001

144 147 150 153 156

4 3 4 4 5

0.148 0.142 0.136 0.131 0.126

81 70 88 34 07

0.149 0.143 0.138 0.132 0.127

96 85 03 50 22

816.49 825.44 834.40 843.39 852.39

1970.3 1962.7 1955.1 1947.4 1939.7

2786.8 2788.2 2789.5 2790.8 2792.1

2.2549 2.2739 2.2929 2.3119 2.3308

4.2358 4.2015 4.1674 4.1334 4.0995

6.4907 6.4755 6.4603 6.4453 6.4303

192 194 196 198 200

202 204 206 208 210

1.6208 1.6891 1.7596 1.8323 1.9074

0.001 0.001 0.001 0.001 0.001

160 163 166 169 173

0.121 0.116 0.111 0.107 0.103

04 24 66 30 13

0.122 0.117 0.112 0.108 0.104

20 40 83 47 30

861.42 870.46 879.53 888.62 897.73

1931.8 1923.9 1915.9 1907.8 1899.6

2793.2 2794.4 2795.4 2796.4 2797.4

2.3497 2.3685 2.3873 2.4060 2.4248

4.0657 4.0321 3.9985 3.9651 3.9318

6.4154 6.4006 6.3858 6.3711 6.3565

202 204 206 208 210

212 214 216 218 220

1.9848 2.0647 2.1470 2.2319 2.3193

0.001 0.001 0.001 0.001 0.001

176 180 183 187 190

0.009 0.095 0.091 0.088 0.084

15 345 710 235 911

0.100 0.096 0.092 0.089 0.086

32 525 893 421 101

906.86 916.02 925.20 934.41 943.64

1891.4 1883.0 1874.6 1866.0 1857.4

2798.2 2799.0 2799.8 2800.4 2801.1

2.4434 2.4621 2.4807 2.4883 2.5178

3.8985 3.8654 3.8323 3.7993 3.7664

6.3420 6.3275 6.3130 6.2986 6.2842

212 214 216 218 220

222 224 226 228 230

2.4093 2.5020 2.5975 2.6957 2.7968

0.001 0.001 0.001 0.001 0.001

194 198 201 205 209

0.081 0.078 0.075 0.072 0.070

730 685 770 977 301

0.082 0.079 0.076 0.074 0.071

924 883 971 182 510

952.90 962.19 971.50 980.84 990.21

1848.7 1839.9 1830.9 1821.9 1812.8

2801.6 2802.1 2802.4 2802.8 2803.0

2.5363 2.5548 2.5733 2.5917 2.6102

3.7336 3.7008 3.6681 3.6355 3.6029

6.2699 6.2557 6.2414 6.2272 6.2131

222 224 226 228 230

232 234 236 238 240

2.9008 3.0077 3.1176 3.2306 3.3467

0.001 0.001 0.001 0.001 0.001

213 217 221 225 229

0.067 0.065 0.062 0.060 0.058

736 277 917 654 481

0.068 0.066 0.064 0.061 0.059

949 494 138 879 710

999.61 1009.0 1018.5 1028.0 1037.5

1803.6 1794.2 1784.8 1775.2 1765.5

2803.2 2803.3 2803.3 2803.2 2803.1

2.6285 2.6469 2.6653 2.6836 2.7019

3.5704 3.5379 3.5054 3.4730 3.4406

6.1989 6.1848 6.1707 6.1566 6.1425

232 234 236 238 240

242 244 246 248 250

3.4659 3.5884 3.7142 3.8434 3.9759

0.001 0.001 0.001 0.001 0.001

234 238 243 247 252

0.056 0.054 0.052 0.050 0.048

394 390 465 614 835

0.057 0.055 0.053 0.051 0.050

628 628 707 861 087

1047.1 1056.7 1066.3 1076.0 1085.7

1757.7 1745.8 1735.8 1725.6 1715.3

2802.8 2802.5 2802.1 2801.6 2801.0

2.7203 2.7385 2.7568 2.7751 2.7934

3.4082 3.3759 3.3435 3.3112 3.2788

6.1285 6.1144 6.1003 6.0863 6.0722

242 244 246 248 250

252 254 256 258 260

4.1120 4.2515 4.3947 4.5415 4.6921

0.001 0.001 0.001 0.001 0.001

256 261 266 271 276

0.047 0.045 0.043 0.042 0.040

124 477 893 368 899

0.048 0.046 0.045 0.043 0.042

380 739 159 639 175

1095.4 1105.2 1115.0 1124.9 1134.8

1704.9 1694.3 1683.6 1672.8 1661.8

2800.3 2799.6 2798.7 2797.7 2796.6

2.8117 2.8299 2.8482 2.8664 2.8847

3.2465 3.2141 3.1818 3.1494 3.1170

6.0582 6.0441 6.0300 6.0158 6.0017

252 254 256 258 260

262 264 266 368 270

4.8464 5.0046 5.1667 5.3327 5.5028

0.001 0.001 0.001 0.001 0.001

281 287 292 297 303

0.039 0.038 0.036 0.035 0.034

485 122 808 541 319

0.040 0.039 0.038 0.036 0.035

766 408 100 839 622

1144.8 1154.8 1164.8 1174.9 1185.1

1650.7 1639.4 1628.0 1616.4 1604.6

2795.5 2794.2 2792.8 2791.3 2789.7

2.9030 2.9213 2.9396 2.9579 2.9762

3.0845 3.0520 3.0195 2.9869 2.9542

5.9875 5.9733 5.9590 5.9448 5.9304

262 264 266 268 270

272 274 276 278 280

5.671 5.8555 6.0381 6.2251 6.4165

0.001 0.001 0.001 0.001 0.001

309 315 321 327 333

0.033 0.032 0.030 0.029 0.028

141 003 905 845 821

0.034 0.033 0.032 0.031 0.030

450 318 226 172 154

1195.3 1205.6 1215.9 1226.2 1236.7

1592.7 1580.6 1568.3 1555.8 1543.2

2788.0 2786.1 2784.1 2782.0 2779.8

2.9945 3.0129 3.0312 3.0496 3.0681

2.9215 2.8887 2.8558 3.8228 2.7898

5.9160 5.9016 5.8871 5.8725 5.8578

272 274 276 278 280

282 284 286 288 290

6.6123 6.8126 7.0176 7.2272 7.4416

0.001 0.001 0.001 0.001 0.001

339 346 352 359 366

0.027 0.026 0.025 0.025 0.024

832 875 950 056 191

0.029 0.028 0.027 0.026 0.025

171 221 303 415 557

1247.2 1257.7 1268.3 1279.0 1289.8

1530.3 1517.3 1504.0 1490.5 1476.8

2777.5 2775.0 2772.3 2769.6 2766.6

3.0865 3.1050 3.1236 3.1421 3.1608

2.7566 2.7232 2.6898 2.6562 2.6225

5.8431 5.8283 5.8134 5.7984 5.7832

282 284 286 288 290

© 2004 by CRC Press LLC

1587_Book.fm Page 80 Monday, September 1, 2003 7:17 PM

4-80

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Temperature) (continued) t (˚C)

Volume, m3/kg

Pressure MPa

nL

Enthalpy, kJ/kg

nv

Dn

hL

Entropy, kJ/(kg˚K)

Dh

hv

sL

Ds

sv

t (˚C)

292 294 296 298 300

7.6609 7.8850 8.1142 8.3484 8.5877

0.001 0.001 0.001 0.001 0.001

373 381 388 396 404

0.023 0.022 0.021 0.020 0.020

353 542 757 996 259

0.024 0.023 0.023 0.022 0.021

727 923 145 392 663

1300.6 1311.5 1322.5 1333.6 1344.8

1462.9 1448.8 1434.4 1419.7 1404.8

2763.6 2760.3 2756.9 2753.3 2749.6

3.1794 3.1982 3.2170 3.2358 3.2547

2.5886 2.5545 2.5202 2.4857 2.4510

5.7680 5.7526 5.7372 5.7215 5.7058

292 294 296 298 300

302 304 306 308 310

8.8323 9.0822 9.3375 9.5983 9.8647

0.001 0.001 0.001 0.001 0.001

412 421 430 439 448

0.019 0.018 0.018 0.017 0.016

544 851 178 525 891

0.020 0.020 0.019 0.018 0.018

956 272 608 964 339

1356.0 1367.4 1378.8 1390.4 1402.0

1389.6 1374.1 1358.4 1342.3 1325.9

2745.6 2741.5 2737.2 2732.7 2727.9

3.2737 3.2928 3.3120 3.3312 3.3506

2.4161 2.3809 2.3455 2.3098 2.2737

5.6898 5.6737 5.6575 5.6410 5.6243

302 304 306 308 310

312 314 316 318 320

10.137 10.415 10.698 10.988 11.284

0.001 0.001 0.001 0.001 0.001

457 467 478 488 499

0.016 0.015 0.015 0.014 0.013

275 676 094 528 977

0.017 0.017 0.016 0.016 0.015

732 144 572 016 476

1413.8 1425.6 1437.6 1449.8 1462.1

1309.2 1292.1 1274.7 1256.8 1238.6

2723.0 2717.8 2712.3 2706.6 2700.7

3.3700 3.3896 3.4093 3.4291 3.4491

2.2374 2.2007 2.1636 2.1261 2.0882

5.6074 5.5903 5.5729 5.5553 5.5373

312 314 316 318 320

322 324 326 328 330

11.586 11.894 12.209 12.530 12.858

0.001 0.001 0.001 0.001 0.001

510 522 534 547 561

0.013 0.012 0.012 0.011 0.011

440 917 407 909 423

0.014 0.014 0.013 0.013 0.012

951 439 941 457 984

1474.5 1487.0 1499.8 1512.7 1525.7

1220.0 1200.8 1181.3 1161.2 1140.5

2694.4 2687.9 2681.0 2673.8 2666.2

3.4692 3.4895 3.5100 3.5307 3.5516

2.0498 2.0110 1.9715 1.9316 1.8909

5.5191 5.5005 5.4816 5.4622 5.4425

322 324 326 328 330

332 334 336 338 340

13.192 13.533 13.882 14.237 14.600

0.001 0.001 0.001 0.001 0.001

575 589 604 621 638

0.010 0.010 0.010 0.009 0.009

949 484 029 584 146

0.012 0.012 0.011 0.011 0.010

523 073 634 204 784

1539.0 1552.5 1566.2 1580.2 1594.4

1119.3 1097.4 1074.9 1051.7 1027.6

2658.3 2649.9 2641.1 2631.9 2622.1

3.5727 3.5940 3.6157 3.6376 3.6599

1.8496 1.8075 1.7646 1.7208 1.6760

5.4223 5.4016 5.3803 5.3584 5.3359

332 334 336 338 340

342 344 346 348 350

14.970 15.348 15.734 16.127 16.529

0.001 0.001 0.001 0.001 0.001

655 675 695 717 740

0.008 0.008 0.007 0.007 0.007

717 294 878 467 061

0.010 0.009 0.009 0.009 0.008

372 969 573 184 801

1609.0 1623.9 1639.1 1654.8 1670.9

1002.7 976.87 950.00 921.99 892.73

2611.7 2600.7 2589.1 2576.7 2563.6

3.6826 3.7058 3.7294 3.7535 3.7783

1.6300 1.5829 1.5344 1.4843 1.4326

5.3127 5.2886 5.2637 5.2378 5.2109

342 344 346 348 350

352 354 356 358 360

16.939 17.358 17.785 18.221 18.666

0.001 0.001 0.001 0.001 0.001

765 793 823 857 895

0.006 0.006 0.005 0.005 0.005

659 258 858 456 050

0.008 0.008 0.007 0.007 0.006

424 051 681 313 945

1687.5 1704.8 1722.8 1741.6 1761.5

862.02 829.63 795.33 758.77 719.50

2549.6 2534.4 2518.1 2500.4 2481.0

3.8039 3.8302 3.8577 3.8863 3.9164

1.3789 1.3229 1.2641 1.2022 1.1364

5.1828 5.1531 5.1218 5.0885 5.0527

352 354 356 358 360

361 362 363 364 365

18.893 19.121 19.352 19.586 19.822

0.001 0.001 0.001 0.001 0.002

915 937 961 987 016

0.004 0.004 0.004 0.004 0.003

845 637 425 210 989

0.006 0.006 0.006 0.006 0.006

760 574 387 197 004

1771.9 1782.6 1793.8 1805.4 1817.6

698.65 676.87 654.01 629.93 604.41

2470.5 2459.5 2447.8 2435.3 2422.0

3.9321 3.9483 3.9651 3.9827 4.0011

1.1017 1.0657 1.0281 0.9887 0.9471

5.0338 5.0140 4.9932 4.9714 4.9482

361 362 363 364 365

366 367 368 369 370

20.061 20.302 20.546 20.793 21.043

0.002 0.002 0.002 0.002 0.002

047 082 122 167 222

0.003 0.003 0.003 0.003 0.002

761 524 276 012 724

0.005 0.005 0.005 0.005 0.004

808 606 398 179 946

1830.4 1844.1 1858.8 1874.8 1892.6

577.19 547.89 515.99 480.72 440.86

2407.6 2392.0 2374.8 2355.5 2333.5

4.0204 4.0410 4.0631 4.0872 4.1142

0.9031 0.8559 0.8048 0.7486 0.6855

4.9235 4.8968 4.8679 4.8358 4.7996

366 367 368 369 370

371 372 373 373.5

21.296 21.553 21.813 21.945

0.002 0.002 0.002 0.002

290 382 526 658

0.002 0.002 0.001 0.001

401 017 495 087

0.004 0.004 0.004 0.003

691 398 021 745

1913.3 1938.5 1974.1 2003.0

394.20 336.15 253.42 186.19

2307.5 2274.7 2227.6 2189.1

4.1453 4.1836 4.2377 4.2818

0.6120 0.5210 0.3922 0.2879

4.7573 4.7046 4.6299 4.5697

371 372 373. 373.5

Tc

22.064

0.003 106

0.003 106

2087.5

0.

2087.5

4.4120

0.

4.4120

Tc

0.

* Values in italics indicate points where thermodynamic equilibrium state is a solid; computed values are for the metastable liquid. Tc 373.946˚C From ASME International Steam Tables for Industrial Use, pp. 55–59.

© 2004 by CRC Press LLC

1587_Book.fm Page 81 Monday, September 1, 2003 7:17 PM

4-81

Mechanical Engineering

Properties of Saturated Water and Steam (Pressure) Volume, m3/kg p MPa

nL

t (˚C)

Dn

Enthalpy, kJ/kg

nv

hL

Dh

sL

Ds

sv

0.010

0.001 000 2 206.00

206.00

0.0007 0.0008 0.0009 0.0010

1.881 3.761 5.444 6.970

0.001 0.001 0.001 0.001

000 000 000 000

1 1 1 1

181.22 159.65 142.76 129.18

7.890 15.809 22.888 29.298

2496.5 2492.0 2488.0 2484.4

2504.3 2507.8 2510.9 2513.7

0.0288 0.0575 0.0830 0.1059

9.0770 8.9992 8.9305 8.8690

9.1058 9.0567 9.0135 8.9749

0.0007 0.0008 0.0009 0.0010

0.0012 0.0014 0.0016 0.0018 0.0020

9.654 11.969 14.010 15.838 17.495

0.001 0.001 0.001 0.001 0.001

000 000 000 001 001

3 108.67 5 93.902 8 82.745 1 74.013 4 66.989

108.67 93.903 82.746 74.014 66.990

40.569 50.282 58.836 66.494 73.435

2478.0 2472.5 2467.7 2463.4 2459.5

2518.6 2522.8 2526.6 2529.9 2532.9

0.1460 0.1802 0.2101 0.2366 0.2606

8.7624 8.6720 8.5935 8.5242 8.4621

8.9083 8.8521 8.8036 8.7609 8.7227

0.0012 0.0014 0.0016 0.0018 0.0020

0.0022 0.0024 0.0026 0.0028 0.0030

19.013 20.415 21.718 22.936 24.080

0.001 0.001 0.001 0.001 0.001

001 001 002 002 002

6 9 2 5 8

61.212 56.376 52.266 48.730 45.654

61.213 56.377 52.267 48.731 45.655

79.790 85.656 91.108 96.204 100.99

2455.9 3452.6 2449.5 2446.6 2443.9

2535.7 2538.2 2540.6 2542.8 2544.9

0.2824 0.3024 0.3210 0.3382 0.3543

8.4059 8.3545 8.3071 8.2632 8.2222

8.6883 8.6569 8.6280 8.6014 8.5766

0.0022 0.0024 0.0026 0.0028 0.0030

0.0032 0.0034 0.0036 0.0038 0.0040

25.159 26.182 27.153 28.078 28.962

0.001 0.001 0.001 0.001 0.001

003 003 003 003 004

0 3 6 8 1

42.953 40.562 38.431 36.518 34.791

42.954 40.563 38.432 36.519 34.792

105.51 109.78 113.84 117.71 121.40

2441.3 2438.9 2436.6 2434.4 2432.3

2546.8 2548.7 2550.4 2552.1 2553.7

0.3695 0.3838 0.3973 0.4102 0.4224

8.1839 8.1479 8.1138 8.0816 8.0510

8.5534 8.5316 8.5112 8.4918 8.4735

0.0032 0.0034 0.0036 0.0038 0.0040

0.0042 0.0044 0.0046 0.0048 0.0050

29.808 30.619 31.400 32.151 32.875

0.001 0.001 0.001 0.001 0.001

004 004 004 005 005

4 6 8 1 3

33.225 31.798 30.492 29.292 28.185

33.226 31.799 30.493 29.293 28.186

124.94 128.33 131.60 134.74 137.77

2430.3 2428.4 2426.5 2424.7 2423.0

2555.2 2556.7 2558.1 2559.5 2560.8

0.4341 0.4453 0.4560 0.4663 0.4763

8.0219 7.9941 7.9676 7.9421 7.9177

8.4561 8.4395 8.4236 8.4084 8.3939

0.0042 0.0044 0.0046 0.0048 0.0050

0.0055 0.0060 0.0065 0.0070 0.0075

34.583 36.160 37.628 39.001 40.292

0.001 0.001 0.001 0.001 0.001

005 006 007 007 008

9 4 0 5 0

25.762 23.733 22.009 20.524 19.233

25.763 23.734 22.010 20.525 19.234

144.90 151.49 157.63 163.37 168.76

2418.9 2415.2 2411.7 2408.4 2405.3

2563.8 2566.7 2569.3 2571.8 2574.1

0.4995 0.5209 0.5407 0.5591 0.5763

7.8605 7.8083 7.7601 7.7155 7.6739

8.3600 8.3291 8.3008 8.2746 8.2502

0.0055 0.0060 0.0065 0.0070 0.0075

0.0080 0.0085 0.0090 0.0095 0.010

41.510 42.665 43.762 44.808 45.808

0.001 0.001 0.001 0.001 0.001

008 008 009 009 010

5 9 4 8 3

18.098 17.094 16.199 15.395 14.670

18.099 17.095 16.200 15.396 14.671

173.85 178.68 183.26 187.63 191.81

2402.4 2399.6 2397.0 2394.5 2392.1

2576.2 2578.3 2580.3 2582.1 2583.9

0.5925 0.6078 0.6223 0.6361 0.6492

7.6349 7.5982 7.5636 7.5308 7.4997

8.2274 8.2060 8.1859 8.1669 8.1489

0.0080 0.0085 0.0090 0.0095 0.010

0.011 0.012 0.013 0.014 0.015

47.684 49.420 51.035 52.548 53.970

0.001 0.001 0.001 0.001 0.001

011 011 012 013 014

1 9 6 3 0

13.411 12.358 11.462 10.690 10.019

13.412 12.359 11.463 10.691 10.020

199.66 206.91 213.66 219.99 225.94

2387.6 2383.4 2379.5 2375.8 2372.4

2587.2 2590.3 2593.1 2595.8 2598.3

0.6737 0.6963 0.7172 0.7366 0.7548

7.4417 7.3887 7.3399 7.2945 7.2523

8.1155 8.0850 8.0570 8.0312 8.0071

0.011 0.012 0.013 0.014 0.015

0.016 0.017 0.018 0.019 0.020

55.314 56.588 57.799 58.954 60.059

0.001 0.001 0.001 0.001 0.001

014 015 016 016 017

7 3 0 6 1

9.4299 8.9079 8.4423 8.0244 7.6471

9.4309 8.9089 8.4433 8.0254 7.6482

231.55 236.88 241.95 246.78 251.40

2369.1 2366.0 2363.1 2360.2 2357.5

2600.7 2602.9 2605.0 2607.0 2608.9

0.7720 0.7882 0.8035 0.8181 0.8320

7.2127 7.1754 7.1403 7.1069 7.0753

7.9847 7.9636 7.9437 7.9250 7.9072

0.016 0.017 0.018 0.019 0.020

0.022 0.024 0.026 0.028 0.030

62.133 64.054 65.843 67.518 69.095

0.001 0.001 0.001 0.001 0.001

018 019 020 021 022

3 3 3 3 2

6.9927 6.4445 5.9783 5.5769 5.2275

6.9938 6.4455 5.9793 5.5779 5.2286

260.08 268.12 275.61 282.62 289.23

2352.5 2347.8 2343.4 2339.2 2335.3

2612.6 2615.9 2619.0 2621.8 2624.6

0.8579 0.8818 0.9040 0.9246 0.9439

7.0164 6.9624 6.9127 6.8666 6.8235

7.8743 7.8442 7.8167 7.7912 7.7675

0.022 0.024 0.026 0.028 0.030

© 2004 by CRC Press LLC

2500.9 0.0000 9.1555 9.1555

p MPa

*pt

181.22 159.65 142.76 129.18

0.001 2500.9

Entropy, kJ/(kg˚K) hv

*pt

1587_Book.fm Page 82 Monday, September 1, 2003 7:17 PM

4-82

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Pressure) (continued) Volume, m3/kg

Enthalpy, kJ/kg

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

p MPa

4.9216 4.6498 4.4073 4.1897 3.9931

295.47 301.40 307.04 312.42 317.57

2331.6 2328.1 2324.8 2321.6 2318.5

2627.1 2629.5 2631.8 2634.0 2636.1

0.9621 0.9793 0.9956 1.0111 1.0259

6.7832 6.7452 6.7093 6.6754 6.6431

7.7453 7.7245 7.7050 7.6865 7.6690

0.032 0.034 0.036 0.038 0.040

3.8137 3.6511 3.5022 3.3653 3.2391

3.8147 3.6521 3.5032 3.3664 3.2401

322.50 327.25 331.82 336.22 340.48

2315.5 2312.7 2309.9 2307.3 2304.7

2638.0 2639.9 2641.8 2643.5 2645.2

1.0400 1.0535 1.0665 1.0790 1.0910

6.6123 6.5829 6.5548 6.5279 6.5020

7.6523 7.6365 7.6213 7.6068 7.5930

0.042 0.044 0.046 0.048 0.050

5 1 5 9 2

2.9626 2.7308 2.5337 2.3639 2.2160

2.9636 2.7318 2.5347 2.3649 2.2171

350.52 359.84 368.53 376.68 384.37

2298.7 2293.0 2287.7 2282.7 2278.0

2649.2 2652.9 2656.2 2659.4 2662.4

1.1192 1.1452 1.1694 1.1919 1.2130

6.4414 6.3859 6.3346 6.2871 6.2427

7.5606 7.5311 7.5040 7.4790 7.4557

0.055 0.060 0.065 0.070 0.075

038 039 040 042 043

5 7 9 0 1

2.0862 1.9711 1.8684 1.7762 1.6930

2.0872 1.9721 1.8695 1.7773 1.6940

391.64 398.55 405.13 411.42 417.44

2273.5 2269.3 2265.2 2261.3 2257.5

2665.2 2667.8 2670.3 2672.7 2674.9

1.2328 1.2516 1.2694 1.2864 1.3026

6.2011 6.1618 6.1248 6.0897 6.0562

7.4339 7.4135 7.3942 7.3760 7.3588

0.080 0.085 0.090 0.095 0.10

0.001 0.001 0.001 0.001 0.001

045 047 049 051 052

3 3 2 0 7

1.5485 1.4274 1.3244 1.2356 1.1583

1.5496 1.4284 1.3254 1.2366 1.1594

428.77 439.30 449.13 458.37 467.08

2250.4 2243.8 2237.5 2231.6 2226.0

2679.2 2683.1 2686.6 2690.0 2693.1

1.3328 1.3608 1.3867 1.4109 1.4335

5.9940 5.9369 5.8842 5.8352 5.7894

7.3268 7.2976 7.2708 7.2460 7.2229

0.11 0.12 0.13 0.14 0.15

113.298 115.149 116.912 118.597 120.212

0.001 0.001 0.001 0.001 0.001

054 056 057 059 060

4 0 6 1 5

1.0904 1.0302 0.976 48 0.928 24 0.884 67

1.0914 1.0312 0.977 53 0.929 30 0.885 74

475.34 483.18 490.67 497.82 504.68

2220.7 2215.6 2210.7 2206.1 2201.6

2696.0 2698.8 2701.4 2703.9 2706.2

1.4549 1.4752 1.4944 1.5127 1.5301

5.7464 5.7059 5.6677 5.6313 5.5968

7.2014 7.1811 7.1620 7.1440 7.1269

0.16 0.17 0.18 0.19 0.20

0.21 0.22 0.23 0.24 0.25

121.761 123.251 124.688 126.074 127.414

0.001 0.001 0.001 0.001 0.001

061 063 064 065 067

9 3 6 9 2

0.845 0.809 0.776 0.745 0.717

13 06 02 65 63

0.846 0.810 0.777 0.746 0.718

19 12 09 72 70

511.27 517.62 523.73 529.64 535.35

2197.2 2193.0 2188.9 2185.0 2181.2

2708.5 2710.6 2712.7 2714.6 2716.5

1.5468 1.5628 1.5782 1.5930 1.6072

5.5638 5.5323 5.5021 5.4731 5.4452

7.1106 7.0951 7.0802 7.0660 7.0524

0.21 0.22 0.23 0.24 0.25

0.26 0.27 0.28 0.29 0.30

128.711 129.968 131.188 132.373 133.525

0.001 0.001 0.001 0.001 0.001

068 069 070 072 073

5 7 9 0 2

0.691 0.667 0.645 0.624 0.604

69 62 20 28 71

0.692 0.668 0.646 0.625 0.605

76 69 27 36 79

540.88 546.25 551.46 556.53 561.46

2177.4 2173.8 2170.3 2166.8 2163.4

2718.3 2720.0 2721.7 2723.3 2724.9

1.6210 1.6343 1.6472 1.6597 1.6718

5.4183 5.3924 5.3674 5.3432 5.3198

7.0393 7.0267 7.0146 7.0029 6.9916

0.26 0.27 0.28 0.29 0.30

0.31 0.32 0.33 0.34 0.35

136.647 135.740 136.806 137.845 138.861

0.001 0.001 0.001 0.001 0.001

074 075 076 077 078

3 4 5 5 6

0.586 0.569 0.552 0.537 0.523

36 12 89 58 12

0.587 0.570 0.553 0.538 0.524

44 20 97 66 20

566.26 570.93 575.50 579.96 584.31

2160.1 2156.9 2153.8 2150.7 2147.7

2726.4 2727.9 2729.3 2730.6 2732.0

1.6835 1.6950 1.7061 1.7169 1.7275

5.2971 5.2751 5.2537 5.2329 5.2126

6.9806 6.9700 6.9597 6.9498 6.9401

0.31 0.32 0.33 0.34 0.35

0.36 0.37 0.38 0.39 0.40

139.853 140.823 141.773 142.702 143.613

0.001 0.001 0.001 0.001 0.001

079 080 081 082 083

6 6 6 6 6

0.509 0.496 0.484 0.472 0.461

43 46 15 44 31

0.510 0.497 0.485 0.473 0.462

51 54 23 53 39

588.57 592.74 596.81 600.81 604.72

2144.7 2141.8 2138.9 2136.1 2133.3

2733.3 2734.5 2735.7 2736.9 2738.1

1.7378 1.7478 1.7576 1.7672 1.7766

5.1929 5.1737 5.1550 5.1367 5.1188

6.9307 6.9215 6.9126 6.9039 6.8954

0.36 0.37 0.38 0.39 0.40

nL

t (˚C)

0.032 0.034 0.036 0.038 0.040

70.586 72.000 73.345 74.629 75.857

0.001 0.001 0.001 0.001 0.001

023 024 024 025 026

1 0 8 6 4

4.9206 4.6488 4.4063 4.1886 3.9921

0.042 0.044 0.046 0.048 0.050

77.034 78.165 79.254 80.303 81.317

0.001 0.001 0.001 0.001 0.001

027 027 028 029 029

1 8 6 2 9

0.055 0.060 0.065 0.070 0.075

83.709 85.926 87.993 89.932 91.758

0.001 0.001 0.001 0.001 0.001

031 033 034 035 037

0.080 0.085 0.090 0.095 0.10

93.485 95.125 96.687 98.178 99.606

0.001 0.001 0.001 0.001 0.001

0.11 0.12 0.13 0.14 0.15

102.292 104.784 107.109 109.292 111.350

0.16 0.17 0.18 0.19 0.20

© 2004 by CRC Press LLC

nv

Dn

p MPa

1587_Book.fm Page 83 Monday, September 1, 2003 7:17 PM

4-83

Mechanical Engineering

Properties of Saturated Water and Steam (Pressure) (continued) Volume, m3/kg

Enthalpy, kJ/kg

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

p MPa

66 75 43 50 80

612.33 619.66 626.73 633.57 640.19

2127.9 2122.7 2117.6 2112.7 2107.9

2740.3 2742.4 2744.4 2746.3 2748.1

1.7948 1.8122 1.8289 1.8450 1.8606

5.0843 5.0513 5.0197 4.9892 4.9600

6.8791 6.8635 6.8486 6.8343 6.8206

0.42 0.44 0.46 0.48 0.50

0.361 0.348 0.336 0.325 0.315

20 57 82 84 58

646.60 652.83 658.88 664.77 670.50

2103.2 2098.7 2094.2 2089.9 2085.6

2749.9 2751.5 2753.1 2754.7 2756.1

1.8756 1.8901 1.9042 1.9179 1.9311

4.9318 4.9045 4.8782 4.8528 4.8281

6.8074 6.7947 6.7824 6.7706 6.7592

0.52 0.54 0.56 0.58 0.60

85 80 28 25 66

0.305 0.296 0.288 0.280 0.272

95 90 39 35 76

676.09 681.54 686.86 692.06 697.14

2081.5 2077.4 2073.4 2069.5 2065.6

2757.6 2758.9 2760.2 2761.5 2762.7

1.9440 1.9565 1.9686 1.9805 1.9921

4.8041 4.7809 4.7583 4.7363 4.7149

6.7481 6.7374 6.7269 6.7168 6.7070

0.62 0.64 0.66 0.68 0.70

0.264 0.257 0.251 0.245 0.239

47 66 20 06 21

0.265 0.268 0.252 0.246 0.240

58 77 31 17 33

702.12 706.99 711.76 716.43 721.02

2061.8 2058.1 2054.4 2050.8 2047.3

2763.9 2765.1 2766.2 2767.3 2768.3

2.0034 2.0144 2.0252 2.0357 2.0460

4.6940 4.6737 4.6539 4.6345 4.6156

6.6974 6.6881 6.6790 6.6702 6.6615

0.72 0.74 0.76 0.78 0.80

1 4 7 9 2

0.233 0.228 0.223 0.218 0.213

64 33 25 40 75

0.234 0.229 0.224 0.219 0.214

76 44 37 52 87

725.52 729.93 734.27 738.53 742.72

2043.8 2040.4 2037.0 2033.6 2030.3

2769.3 2770.3 2771.2 2772.1 2773.0

2.0561 2.0659 2.0756 2.0851 2.0944

4.5970 4.5789 4.5612 4.5438 4.5268

6.6531 6.6449 6.6368 6.6289 6.6212

0.82 0.84 0.86 0.88 0.90

122 123 124 126 127

4 6 9 0 2

0.209 0.205 0.200 0.197 0.193

30 03 94 00 22

0.210 0.206 0.202 0.198 0.194

42 16 06 13 35

746.85 750.90 754.89 758.82 762.58

2027.1 2023.8 2020.7 2017.5 2014.4

2773.9 2774.7 2775.6 2776.3 2777.1

2.1035 2.1125 2.1213 2.1299 2.1384

4.5102 4.4938 4.4778 4.4620 4.4465

6.6137 6.6063 6.5991 6.5919 6.5850

0.92 0.94 0.96 0.98 1.00

0.001 0.001 0.001 0.001 0.001

130 133 135 138 141

1 0 8 5 2

0.184 0.176 0.168 0.161 0.155

37 30 91 11 84

0.185 0.177 0.170 0.163 0.156

50 44 05 25 98

772.10 781.20 789.99 798.50 806.75

2006.8 1999.5 1992.3 1985.3 1978.4

2779.0 2780.7 2782.3 2783.8 2785.2

2.1591 2.1789 2.1979 2.2163 2.2340

4.4091 4.3731 4.3386 4.3054 4.2734

6.5681 6.5520 6.5365 6.5217 6.5074

1.05 1.10 1.15 1.20 1.25

191.613 193.355 195.047 196.693 198.295

0.001 0.001 0.001 0.001 0.001

143 146 148 151 153

8 4 9 4 9

0.150 0.144 0.139 0.134 0.130

03 64 62 93 55

0.151 0.145 0.140 0.136 0.131

17 79 77 08 70

814.76 822.55 830.13 837.52 844.72

1971.7 1965.2 1958.8 1952.5 1946.3

2786.5 2787.7 2788.9 2790.0 2791.0

2.2512 2.2678 2.2839 2.2995 2.3147

4.2425 4.2126 4.1836 4.1556 4.1284

6.4936 6.4804 6.4675 6.4551 6.4431

1.30 1.35 1.40 1.45 1.50

1.55 1.60 1.65 1.70 1.75

199.856 201.378 202.864 204.315 205.733

0.001 0.001 0.001 0.001 0.001

156 158 161 163 165

3 7 0 4 7

0.126 0.122 0.118 0.115 0.112

44 57 94 50 26

0.127 0.123 0.120 0.116 0.113

59 73 10 67 43

851.74 858.61 865.32 871.89 878.32

1940.2 1934.3 1928.4 1922.6 1917.0

2792.0 2792.9 2793.7 2794.5 2795.3

2.3294 2.3438 2.3578 2.3715 2.3848

4.1019 4.0762 4.0512 4.0268 4.0030

6.4314 6.4200 6.4090 6.3983 6.3878

1.55 1.60 1.65 1.70 1.75

1.80 1.85 1.90 1.95 2.0

207.120 208.477 209.806 211.108 212.385

0.001 0.001 0.001 0.001 0.001

167 170 172 174 176

9 2 4 6 8

0.109 0.106 0.103 0.100 0.098

19 29 53 90 404

0.110 0.107 0.104 0.102 0.099

36 46 70 08 581

884.61 890.79 896.84 902.79 908.62

1911.4 1905.9 1900.4 1895.1 1889.8

2796.0 2796.6 2797.3 2797.8 2798.4

2.3978 2.4105 2.4229 2.4351 2.4470

3.9798 3.9571 3.9350 3.9133 3.8921

6.3776 6.3676 6.3579 6.3484 6.3392

1.80 1.85 1.90 1.95 2.0

nL

nv

Dn

p MPa

t (˚C)

0.42 0.44 0.46 0.48 0.50

145.380 147.081 148.721 150.305 151.836

0.001 0.001 0.001 0.001 0.001

085 087 089 090 092

5 3 1 8 6

0.440 0.421 0.404 0.388 0.373

57 66 34 41 71

0.441 0.422 0.405 0.389 0.374

0.52 0.54 0.56 0.58 0.60

153.320 154.758 156.155 157.512 158.832

0.001 0.001 0.001 0.001 0.001

094 095 097 099 100

2 9 5 1 6

0.360 0.347 0.335 0.324 0.314

11 48 72 74 47

0.62 0.64 0.66 0.68 0.70

160.118 161.371 162.594 163.787 164.953

0.001 0.001 0.001 0.001 0.001

102 103 105 106 108

1 6 1 5 0

0.304 0.295 0.287 0.279 0.271

0.72 0.74 0.76 0.78 0.80

166.092 167.207 168.298 169.366 170.414

0.001 0.001 0.001 0.001 0.001

109 110 112 113 114

4 8 1 5 8

0.82 0.84 0.86 0.88 0.90

171.440 172.447 173.435 174.405 175.358

0.001 0.001 0.001 0.001 0.001

116 117 118 119 121

0.92 0.94 0.96 0.98 1.00

176.294 177.214 178.119 179.010 179.886

0.001 0.001 0.001 0.001 0.001

1.05 1.10 1.15 1.20 1.25

182.017 184.070 186.050 187.965 189.817

1.30 1.35 1.40 1.45 1.50

© 2004 by CRC Press LLC

1587_Book.fm Page 84 Monday, September 1, 2003 7:17 PM

4-84

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Pressure) (continued) Volume, m3/kg p MPa

nL

t (˚C)

Enthalpy, kJ/kg

nv

Dn

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

p MPa

2.1 2.2 2.3 2.4 2.5

214.865 217.256 219.564 221.795 223.956

0.001 0.001 0.001 0.001 0.001

181 185 189 193 197

0 2 4 4 4

0.093 0.089 0.085 0.082 0.078

753 510 623 049 750

0.094 0.090 0.086 0.083 0.079

934 695 812 242 947

919.99 930.98 941.63 951.95 961.98

1879.4 1869.2 1859.3 1849.6 1840.1

2799.4 2800.2 2800.9 2801.5 2802.0

2.4701 2.4924 2.5138 2.5244 2.5544

3.8511 3.8116 3.7736 3.7370 3.7015

6.3212 6.3040 6.2874 6.2714 6.2560

2.1 2.2 2.3 2.4 2.5

2.6 2.7 2.8 2.9 3.0

226.052 228.086 230.063 231.986 233.858

0.001 0.001 0.001 0.001 0.001

201 205 209 212 216

4 3 1 9 7

0.075 0.072 0.070 0.067 0.065

696 860 219 754 447

0.076 0.074 0.071 0.068 0.066

897 065 428 967 664

971.74 981.24 990.50 999.54 1008.4

1830.7 1821.5 1812.5 1803.6 1794.9

2802.5 2802.8 2803.0 2803.2 2803.3

2.5738 2.5925 2.6107 2.6284 2.6456

3.6673 3.6341 3.6019 3.5706 3.5402

6.2411 6.2266 6.2126 6.1990 6.1878

2.6 2.7 2.8 2.9 3.0

3.1 3.2 3.3 3.4 3.5

235.684 237.464 239.203 240.901 242.562

0.001 0.001 0.001 0.001 0.001

220 224 227 231 235

4 1 8 4 0

0.063 0.061 0.059 0.057 0.055

284 251 336 530 823

0.064 0.062 0.060 0.058 0.057

504 475 564 761 058

1017.0 1025.5 1033.7 1041.8 1049.8

1786.3 1777.8 1769.4 1761.1 1753.0

2803.3 2803.2 2803.1 2803.0 2802.7

2.6624 2.6787 2.6946 2.7102 2.7254

3.5105 3.4817 3.4535 3.4260 3.3991

6.1729 6.1604 6.1481 6.1362 6.1245

3.1 3.2 3.3 3.4 3.5

3.6 3.7 3.8 3.9 4.0

244.186 245.776 247.334 248.861 250.358

0.001 0.001 0.001 0.001 0.001

238 242 245 249 252

5 1 6 1 6

0.054 0.052 0.051 0.049 0.048

208 676 222 840 524

0.055 0.053 0.052 0.051 0.049

446 918 468 089 777

1057.6 1065.2 1072.8 1080.2 1087.4

1744.9 1736.9 1729.0 1721.2 1713.5

2802.5 2802.1 2801.8 2801.4 2800.9

2.7403 2.7548 2.7690 2.7830 2.7967

3.3728 3.3471 3.3219 3.2973 3.2731

6.1131 6.1019 6.0910 6.0802 6.0697

3.6 3.7 3.8 3.9 4.0

4.1 4.2 4.3 4.4 4.5

251.826 253.267 254.683 256.073 257.439

0.001 0.001 0.001 0.001 0.001

256 259 262 206 269

0 5 9 3 7

0.047 0.046 0.044 0.043 0.042

270 073 930 836 790

0.048 0.047 0.046 0.045 0.044

526 333 193 103 059

1094.6 1101.6 1108.6 1115.4 1122.1

1705.8 1698.2 1690.7 1683.2 1675.9

2800.4 2799.9 2799.3 2798.7 2798.0

2.8101 2.8232 2.8362 2.8488 2.8613

3.2493 3.2260 3.2031 3.1806 3.1585

6.0594 6.0492 6.0393 6.0294 6.0198

4.1 4.2 4.3 4.4 4.5

4.6 4.7 4.8 4.9 5.0

258.783 260.104 261.404 262.683 263.943

0.001 0.001 0.001 0.001 0.001

273 276 280 283 286

0.041 0.040 0.039 0.039 0.038

787 825 901 013 160

0.043 0.042 0.041 0.040 0.039

060 101 181 296 446

1128.8 1135.3 1141.8 1148.2 1154.5

1668.5 1661.2 1654.0 1646.8 1639.7

2797.3 2796.6 2795.8 2795.0 2794.2

2.8736 2.8857 2.8975 2.9092 2.9207

3.1367 3.1153 3.0942 3.0734 3.0530

6.0103 6.0010 5.9917 5.9827 5.9737

4.6 4.7 4.8 4.9 5.0

5.1 5.2 5.3 5.4 5.5

265.183 266.405 267.610 268.797 269.967

0.001 0.001 0.001 0.001 0.001

290 293 296 300 303

0.037 0.036 0.035 0.035 0.034

338 547 785 049 339

0.038 0.037 0.037 0.036 0.035

628 840 081 349 642

1160.7 1166.9 1173.0 1179.0 1184.9

1632.7 1625.6 1618.6 1611.7 1604.8

2793.4 2792.5 2791.6 2790.7 2789.7

2.9321 2.9433 2.9543 2.9652 2.9759

3.0328 3.0129 2.9933 2.9739 3.9548

5.9649 5.9562 5.9475 5.9390 5.9307

5.1 5.2 5.3 5.4 5.5

5.6 5.7 5.8 5.9 6.0

271.121 272.260 273.383 274.492 275.586

0.001 0.001 0.001 0.001 0.001

306 309 313 316 319

0.033 0.032 0.032 0.031 0.031

654 991 350 730 129

0.034 0.034 0.033 0.033 0.032

960 300 663 046 449

1190.8 1196.6 1202.4 1208.1 1213.7

1597.9 1591.1 1584.3 1577.6 1570.8

2788.7 2787.7 2786.7 2785.6 2784.6

2.9865 2.9969 3.0072 3.0174 3.0274

2.9359 2.9173 2.8988 2.8806 2.8626

5.9224 5.9141 5.9060 5.8980 5.8901

5.6 5.7 5.8 5.9 6.0

6.1 6.2 6.3 6.4 6.5

276.667 277.734 278.788 279.830 280.859

0.001 0.001 0.001 0.001 0.001

323 326 329 332 336

0.030 0.029 0.029 0.028 0.028

548 984 437 907 392

0.031 0.031 0.030 0.030 0.029

870 310 766 239 728

1219.3 1224.9 1230.3 1235.8 1241.2

1564.1 1557.5 1550.8 1544.2 1537.7

2783.5 2782.3 2781.2 2780.0 2778.8

3.0374 3.0472 3.0569 3.0665 3.0760

2.8448 2.8272 2.8098 2.7926 2.7755

5.8822 5.8744 5.8667 5.8591 5.8515

6.1 6.2 6.3 6.4 6.5

6.6 6.7 6.8 6.9 7.0

281.876 282.881 283.875 284.858 285.830

0.001 0.001 0.001 0.001 0.001

339 342 345 349 352

0.027 0.027 0.026 0.026 0.026

892 406 934 475 028

0.029 0.028 0.028 0.027 0.027

231 748 279 823 380

1246.5 1251.8 1257.1 1262.3 1267.4

1531.1 1524.6 1518.1 1511.6 1505.1

2777.6 2776.4 2775.1 2773.9 2772.6

3.0854 3.0947 3.1039 3.1130 3.1220

2.7586 2.7419 2.7253 2.7089 2.6926

5.8440 5.8366 5.8292 5.8219 5.8146

6.6 6.7 6.8 6.9 7.0

© 2004 by CRC Press LLC

1587_Book.fm Page 85 Monday, September 1, 2003 7:17 PM

4-85

Mechanical Engineering

Properties of Saturated Water and Steam (Pressure) (continued) Volume, m3/kg p MPa

nL

t (˚C)

Enthalpy, kJ/kg

nv

Dn

Entropy, kJ/(kg˚K)

hL

Dh

hv

sL

Ds

sv

p MPa

7.1 7.2 7.3 7.4 7.5

286.791 287.743 288.684 289.615 290.537

0.001 0.001 0.001 0.001 0.001

355 358 362 365 368

0.025 0.025 0.024 0.024 0.023

593 169 757 355 963

0.026 0.026 0.026 0.025 0.025

948 528 119 720 331

1272.6 1277.7 1282.7 1287.7 1292.7

1498.7 1492.3 1485.9 1479.5 1473.1

2771.3 2769.9 2768.6 2767.2 2765.8

3.1309 3.1398 3.1485 3.1572 3.1658

2.6765 2.6605 2.6447 2.6290 2.6134

5.8074 5.8003 5.7932 5.7862 5.7792

7.1 7.2 7.3 7.4 7.5

7.6 7.7 7.8 7.9 8.0

291.449 292.352 293.247 294.132 295.009

0.001 0.001 0.001 0.001 0.001

371 375 378 381 385

0.023 0.023 0.022 0.022 0.022

581 208 845 490 143

0.024 0.024 0.024 0.023 0.023

952 583 223 871 528

1297.6 1302.5 1307.4 1312.3 1317.1

1466.8 1460.4 1454.1 1447.8 1441.5

2764.4 2763.0 2761.5 2760.1 2758.6

3.1743 3.1827 3.1911 3.1994 3.2077

2.5979 2.5826 2.5673 2.5522 2.5372

5.7722 5.7653 5.7584 5.7516 5.7448

7.6 7.7 7.8 7.9 8.0

8.1 8.2 8.3 8.4 8.5

295.878 296.738 297.591 298.435 299.272

0.001 0.001 0.001 0.001 0.001

388 391 395 398 401

0.021 0.021 0.021 0.020 0.020

804 473 150 834 525

0.023 0.022 0.022 0.022 0.021

192 865 545 232 926

1321.9 1326.6 1331.3 1336.0 1340.7

1435.3 1429.0 1422.7 1416.5 1410.3

2757.1 2755.6 2754.1 2752.5 2751.0

3.2158 3.2239 3.2320 3.2399 3.2478

2.5223 2.5075 2.4928 2.4782 2.4637

5.7381 5.7314 5.7247 5.7181 5.7115

8.1 8.2 8.3 8.4 8.5

8.6 8.7 8.8 8.9 9.0

300.102 300.924 301.738 302.546 303.347

0.001 0.001 0.001 0.001 0.001

405 408 411 415 418

0.020 0.019 0.019 0.019 0.019

222 926 636 353 075

0.021 0.021 0.021 0.020 0.020

627 334 048 767 493

1345.3 1350.0 1354.5 1359.1 1363.7

1404.0 1397.8 1391.6 1385.4 1379.2

2749.4 2747.8 2746.2 2744.5 2742.9

3.2557 3.2635 3.2712 3.2789 3.2866

2.4493 2.4349 2.4207 2.4065 2.3924

5.7050 5.6984 5.6919 5.6855 5.6790

8.6 8.7 8.8 8.9 9.0

9.1 9.2 9.3 9.4 9.5

304.141 304.928 305.709 306.483 307.251

0.001 0.001 0.001 0.001 0.001

422 425 428 432 435

0.018 0.018 0.018 0.018 0.017

803 536 275 019 767

0.020 0.019 0.019 0.019 0.019

224 961 703 450 203

1368.2 1372.7 1371.1 1381.6 1386.0

1373.0 1366.9 1360.7 1354.5 1348.4

2741.2 2739.5 2737.8 2736.1 2734.4

3.2942 3.3017 3.3092 3.3166 3.3240

2.3784 2.3645 2.3507 2.3369 2.3232

5.6726 5.6662 5.6598 5.6535 5.6472

9.1 9.2 9.3 9.4 9.5

9.6 9.7 9.8 9.9 10.0

308.013 308.768 309.518 310.262 310.999

0.001 0.001 0.001 0.001 0.001

439 442 446 449 453

0.017 0.017 0.017 0.016 0.016

521 279 042 809 581

0.018 0.018 0.018 0.018 0.018

960 721 488 259 034

1390.4 1394.8 1399.2 1403.5 1407.9

1342.2 1336.1 1329.9 1323.8 1317.6

2732.6 2730.9 2729.1 2727.3 2725.5

3.3313 3.3386 3.3459 3.3531 3.3603

2.3095 2.2960 2.2824 2.2690 2.2556

5.6409 5.6346 5.6283 5.6221 5.6159

9.6 9.7 9.8 9.9 10.0

10.2 10.4 10.6 10.8 11.0

312.458 313.895 315.311 316.706 318.081

0.001 0.001 0.001 0.001 0.001

460 467 474 481 489

0.016 0.015 0.015 0.014 0.014

136 707 293 893 505

0.017 0.017 0.016 0.016 0.015

596 174 767 374 994

1416.5 1425.0 1433.5 1441.9 1450.3

1305.3 1293.0 1280.7 1268.4 1256.1

2721.8 2718.0 2714.2 2710.3 2706.4

3.3745 3.3886 3.4025 3.4163 3.4300

2.2290 2.2026 2.1764 2.1504 2.1246

5.6035 5.5912 5.5789 5.5667 5.5545

10.2 10.4 10.6 10.8 11.0

11.2 11.4 11.6 11.8 12.0

319.437 320.774 322.093 323.394 324.678

0.001 0.001 0.001 0.001 0.001

496 503 511 519 526

0.014 0.013 0.013 0.013 0.012

130 767 415 074 743

0.015 0.015 0.014 0.014 0.014

626 271 926 593 269

1458.6 1466.8 1475.0 1483.2 1491.3

1243.8 1231.4 1219.1 1206.7 1194.3

2702.4 2698.3 2694.1 2689.9 2685.6

3.4435 3.4569 3.4702 3.4834 3.4965

2.0989 2.0734 2.0480 2.0228 1.9977

5.5424 5.5303 5.5182 5.5062 5.4941

11.2 11.4 11.6 11.8 12.0

12.2 12.4 12.6 12.8 13.0

325.946 327.197 328.432 329.652 330.857

0.001 0.001 0.001 0.001 0.001

534 542 550 558 506

0.012 0.012 0.011 0.011 0.011

421 108 803 507 219

0.013 0.013 0.013 0.013 0.012

955 650 354 065 785

1499.4 1507.5 1515.5 1523.4 1531.4

1181.8 1169.3 1156.7 1144.1 1131.5

2681.2 2676.7 2672.2 2667.6 2662.9

3.5095 3.5224 3.5352 3.5479 3.5606

1.9726 1.9477 1.9228 1,8980 1.8733

5.4821 5.4700 5.4580 5.4459 5.4339

12.2 12.4 12.6 12.8 13.0

13.2 13.4 13.6 13.8 14.0

332.047 333.223 334.385 335.534 336.669

0.001 0.001 0.001 0.001 0.001

575 583 592 601 610

0.010 0.010 0.010 0.010 0.009

937 663 396 134 879

0.012 0.012 0.011 0.011 0.011

512 247 988 735 489

1539.3 1547.2 1555.1 1563.0 1570.9

1118.8 1106.0 1093.1 1080.2 1067.2

2658.1 2653.2 2648.3 2643.2 2638.1

3.5732 3.5857 3.5982 3.6106 3.6230

1.8486 1.8240 1.7993 1.7747 1.7500

5.4218 5.4097 5.3975 5.3853 5.3730

13.2 13.4 13.6 13.8 14.0

© 2004 by CRC Press LLC

1587_Book.fm Page 86 Tuesday, September 2, 2003 3:25 PM

4-86

CRC Handbook of Engineering Tables

Properties of Saturated Water and Steam (Pressure) (continued) Volume, m3/kg p MPa

nL

t (˚C)

Enthalpy, kJ/kg

nv

Dn

Entropy, kJ/(kg˚K)

p MPa

hL

Dh

hv

sL

Ds

sv

1054.1 1040.9 1027.6 1014.2 1000.7

2632.9 2627.5 2622.1 2616.5 2610.9

3.6353 3.6477 3.6599 3.6722 3.6844

1.7254 1.7007 1.6760 1.6512 1.6264

5.3607 5.3484 5.3359 5.3234 5.3108

14.2 14.4 14.6 14.8 15.0

14.2 14.4 14.6 14.8 15.0

337.792 338.902 339.999 341.084 342.158

0.001 0.001 0.001 0.001 0.001

619 628 638 647 657

0.009 0.009 0.009 0.008 0.008

630 385 147 912 683

0.011 0.011 0.010 0.010 0.010

248 014 784 560 340

1578.7 1586.6 1594.4 1602.3 1610.2

15.2 15.4 15.6 15.8 16.0

343.220 344.270 345.310 346.339 347.357

0.001 0.001 0.001 0.001 0.001

667 677 688 699 710

0.008 0.008 0.008 0.007 0.007

458 237 021 808 599

0.010 0.009 0.009 0.009 0.009

125 915 709 506 308

1618.0 1625.9 1633.8 1641.7 1649.7

987.07 973.30 959.39 945.34 931.13

2605.1 2599.2 2593.2 2587.1 2580.8

3.6967 3.7089 3.7212 3.7334 3.7457

1.6014 1.5764 1.5513 1.5260 1.5006

5.2981 5.2853 5.2724 5.2594 5.2463

15.2 15.4 15.6 15.8 16.0

16.2 16.4 16.6 16.8 17.0

348.364 349.361 350.349 351.326 352.293

0.001 0.001 0.001 0.001 0.001

721 732 744 757 769

0.007 0.007 0.006 0.006 0.006

393 190 991 794 600

0.009 0.008 0.008 0.008 0.008

114 923 736 551 369

1657.6 1665.7 1673.8 1681.9 1690.0

916.76 902.22 887.50 872.55 857.38

2574.4 2567.9 2561.2 2554.4 2547.4

3.7580 3.7703 3.7827 3.7952 3.8077

1.4750 1.4493 1.4234 1.3973 1.3708

5.2330 5.2196 5.2061 5.1924 5.1785

16.2 16.4 16.6 16.8 17.0

17.2 17.4 17.6 17.8 18.0

353.252 354.200 355.140 356.070 356.992

0.001 0.001 0.001 0.001 0.001

782 796 810 824 839

0.006 0.006 0.006 0.005 0.005

408 218 030 844 659

0.008 0.008 0.007 0.007 0.007

190 014 840 668 499

1698.3 1706.6 1715.0 1723.4 1732.0

841.96 826.29 810.34 794.09 777.51

2540.2 2532.9 2525.3 2517.5 2509.5

3.8203 3.8329 3.8457 3.8586 3.8717

1.3441 1.3171 1.2898 1.2620 12339

5.1644 5.1501 5.1355 5.1206 5.1055

17.2 17.2 17.6 17.8 18.0

18.2 18.4 18.6 18.8 19.0

357.905 358.809 359.704 360.592 361.471

0.001 0.001 0.001 0.001 0.001

855 872 889 907 925

0.005 0.005 0.005 0.004 0.004

476 293 111 929 747

0.007 0.007 0.006 0.006 0.006

331 164 999 836 673

1740.7 1749.5 1785.5 1767.6 1776.9

760.57 743.24 752.49 707.27 688.52

2501.3 2492.8 2484.0 2474.9 2465.4

3.8849 3.8982 3.9118 3.9256 3.9396

1.2052 1.1761 1.1464 1.1160 1.0849

5.0901 5.0743 5.0582 5.0416 5.0246

18.2 18.4 18.6 18.8 19.0

19.2 19.4 19.6 19.8 20.0

362.342 363.205 364.060 364.907 365.746

0.001 0.001 0.001 0.002 0.002

945 966 989 013 039

0.004 0.004 0.004 0.004 0.003

565 381 197 010 820

0.006 0.006 0.006 0.006 0.005

510 348 186 022 858

1786.4 1796.1 1806.1 1816.4 1827.1

669.18 649.19 628.46 606.87 584.29

2455.6 2445.3 2434.6 2423.3 2411.4

3.9540 3.9687 3.9838 3.9993 4.0154

1.0530 1.0202 0.9863 0.9511 0.9145

5.0070 4.9888 4.9700 4.9299 4.9299

19.2 19.4 19.6 19.8 20.0

20.2 20.4 20.6 20.8 21.0

366.577 367.401 368.218 369.026 369.827

0.002 0.002 0.002 0.002 0.002

067 097 131 169 212

0.003 0.003 0.003 0.003 0.002

626 426 220 004 776

0.005 0.005 0.005 0.005 0.004

692 523 351 173 988

1838.2 1849.8 1862.1 1875.2 1889.4

560.55 535.43 508.63 479.74 448.15

2398.8 2385.3 2370.8 2355.0 2337.5

4.0321 4.0496 4.0681 4.0879 4.1093

0.8762 0.8359 0.7930 0.7471 0.6970

4.9083 4.8855 4.8612 4.8349 4.8062

20.2 20.4 20.6 20.8 21.0

21.2 21.4 21.6 21.8 22.0

370.621 371.406 372.182 372.950 373.707

0.002 0.002 0.002 0.002 0.002

262 324 403 517 750

0.002 0.002 0.001 0.001 0.000

529 255 936 527 826

0.004 0.004 0.004 0.004 0.003

791 579 338 044 577

1905.0 1922.8 1944.0 1971.9 2021.9

412.91 372.44 323.61 258.69 142.27

2317.9 2295.2 2267.6 2230.6 2164.2

4.1328 4.1597 4.1918 4.2343 4.3109

0.6414 0.5778 0.5015 0.4004 0.2199

4.7742 4.7375 4.6933 4.6347 4.5308

21.2 21.4 21.6 21.8 22.0

pc

373.946

0.003 106

4.4120

pc

0

0.003 106 2087.5

*Pt = 611.657 Pa pc = 22.064 MPa From ASME International Steam Tables for Industrial Use, pp. 60–64.

© 2004 by CRC Press LLC

0

2087.5 4.4120 0

1587_Book.fm Page 87 Tuesday, September 2, 2003 3:25 PM

4-87

Mechanical Engineering

Thermal Conductivity of Water and Steam (mW·m–1·K–1) Pressure (MPa) t (˚C)

0.01

0.02

0.05

0.1

0.2

0.5

1

2

5

10

20

50

75

100

Sat Liq. Sat. Vap.

635.7 19.9

650.8 21.1

667.8 23.0

677.6 24.8

683.6 27.0

683.6 31.0

674.7 35.4

654.4 41.6

600.5 55.6

524.5 79.0

403.7 226.5

0 10 20

562.0 581.9 599.5

562.0 581.9 599.5

562.0 581.9 599.5

562.0 582.0 599.5

562.1 582.0 599.6

562.3 582.2 599.7

562.6 582.5 600.0

563.2 583.0 600.6

564.9 584.7 602.2

567.8 587.5 604.8

573.6 593.0 610.1

590.6 608.8 625.4

603.5 621.4 637.5

616.0 633.4 649.1

25

607.5

607.5

607.5

607.5

607.6

607.7

608.0

608.5

610.1

612.7

617.9

633.0

645.0

656.4

30 40 50

615.0 628.6 20.3

615.0 628.6 640.5

615.0 628.6 640.5

615.0 628.6 640.5

615.1 628.7 640.6

615.2 628.8 640.7

615.5 629.1 641.0

616.0 629.6 641.5

617.6 631.1 643.0

620.2 633.7 645.6

625.3 638.8 650.6

640.2 633.5 665.2

652.1 665.1 676.8

663.4 676.3 687.8

60 70 80 90 100

21.0 21.8 22.6 23.4 24.3

650.8 21.9 22.7 23.5 24.3

650.8 659.6 667.0 23.6 24.4

650.8 659.6 667.0 673.0 24.8

650.9 659.7 667.0 673.1 677.8

651.0 659.8 667.2 673.2 678.0

651.3 660.1 667.5 673.5 678.3

651.8 660.6 668.0 674.1 678.8

653.3 662.2 669.6 675.7 680.5

655.9 664.8 672.2 678.3 683.2

661.0 669.8 677.4 683.6 688.6

675.5 684.5 692.2 698.7 704.0

687.1 696.1 703.9 710.5 716.0

698.1 707.2 715.1 721.8 727.5

110 120 130 140 150

25.1 26.0 26.8 27.7 28.6

25.1 26.0 26.8 27.7 28.6

25.2 26.1 26.9 27.8 28.7

25.5 26.3 27.1 27.9 28.8

681.3 683.6 27.6 28.4 29.2

681.5 683.8 684.9 685.0 683.9

681.8 684.1 685.2 685.3 684.2

682.3 684.7 685.9 685.9 684.9

684.1 686.4 687.7 687.8 686.9

686.9 689.4 690.7 691.0 690.2

692.4 695.1 696.6 697.1 696.5

708.2 711.3 713.3 714.3 714.4

720.5 723.8 726.2 727.7 728.2

732.1 735.7 738.4 740.2 741.0

160 170 180 190 200

29.5 30.4 31.4 32.3 33.2

29.5 30.4 31.4 32.3 33.3

29.6 30.5 31.4 32.3 33.3

29.7 30.6 31.5 32.4 33.4

30.0 30.8 31.7 32.6 33.5

31.4 32.0 32.7 33.4 34.2

682.1 678.9 35.4 35.6 36.1

682.8 679.6 675.4 670.1 663.8

684.9 681.8 677.7 672.6 666.4

688.3 685.4 681.5 676.6 670.7

695.0 692.4 688.9 684.4 678.9

713.6 711.8 709.1 705.6 701.3

727.8 726.5 724.5 721.6 717.9

741.0 740.2 738.6 736.2 733.2

220 240 260 280 300

35.2 37.2 39.2 41.3 43.4

35.2 37.2 39.2 41.3 43.4

35.2 37.2 39.2 41.3 43.4

35.3 37.3 39.3 41.4 43.5

35.4 37.4 39.4 41.5 43.6

36.0 37.8 39.8 41.8 43.9

37.3 38.8 40.6 42.5 44.5

41.5 41.8 42.8 44.2 46.0

650.9 630.9 606.0 53.7 53.0

655.8 636.7 613.0 584.0 548.1

665.2 647.5 625.8 599.7 568.3

690.2 675.8 658.4 637.8 614.0

708.4 696.0 681.0 663.3 643.0

724.9 714.0 700.8 685.2 667.4

320 340 360 380 400

45.6 47.8 50.0 52.3 54.6

45.6 47.8 50.0 52.3 54.7

45.6 47.8 50.1 52.3 54.7

45.7 47.9 50.1 52.4 54.7

45.7 47.9 50.2 52.5 54.8

46.0 48.2 50.4 52.7 55.0

46.6 48.7 50.9 53.1 55.4

47.8 49.8 51.9 54.1 56.3

53.5 54.5 56.0 57.6 59.5

74.7 69.8 67.7 66.7 67.2

530.4 483.1 419.8 129.4 103.4

586.8 556.0 521.1 481.7 438.3

620.3 595.1 567.4 537.2 504.7

647.6 625.9 602.3 576.9 550.0

420 440 460 480 500

57.0 59.4 61.9 64.3 66.8

57.0 59.4 61.9 64.3 66.8

57.0 59.4 61.9 64.4 66.9

57.1 59.5 61.9 64.4 66.9

57.2 59.5 62.0 64.5 67.0

57.4 59.8 62.2 64.7 67.2

57.8 60.1 62.6 65.0 67.5

58.6 60.9 63.3 65.8 68.2

61.6 63.7 65.9 68.2 70.6

68.3 69.7 71.4 73.3 75.3

94.6 90.8 89.1 88.7 89.1

391.5 342.0 289.0 240.3 205.5

470.4 434.7 398.9 363.9 330.9

521.9 492.7 463.1 433.5 404.8

520 540 560 580 600

69.4 72.0 74.6 77.2 79.8

69.4 72.0 74.6 77.2 79.9

69.4 72.0 74.6 77.2 79.9

69.4 72.0 74.6 77.2 79.9

69.5 72.1 74.7 77.3 80.0

69.7 72.3 74.9 77.5 80.1

70.0 72.6 75.2 77.8 80.4

70.7 73.3 75.8 78.4 81.0

73.0 75.4 77.9 80.5 83.0

77.5 79.7 82.0 84.3 86.8

90.0 91.2 92.7 94.4 96.2

182.8 168.2 158.5 152.0 147.7

300.6 273.8 251.4 233.4 219.2

377.7 352.7 329.9 309.6 291.7

620 640 660 680 700

82.5 85.2 88.0 90.7 93.5

82.5 85.3 88.0 90.7 93.5

82.6 85.3 88.0 90.8 93.5

82.6 85.3 88.0 90.8 93.6

82.6 85.4 88.1 90.8 93.6

82.8 85.5 88.2 91.0 93.8

83.1 85.8 88.5 91.3 94.0

83.7 86.4 89.1 91.8 94.6

85.6 88.2 90.9 93.6 96.3

89.2 91.7 94.3 96.9 99.5

98.2 100.3 102.5 104.7 107.0

144.8 142.9 141.9 141.4 141.4

208.2 199.8 193.3 188.3 184.5

276.2 263.0 252.0 242.7 235.0

© 2004 by CRC Press LLC

1587_Book.fm Page 88 Monday, September 1, 2003 7:17 PM

4-88

CRC Handbook of Engineering Tables

Thermal Conductivity of Water and Steam (mW·m–1·K–1) (continued) Pressure (MPa) t (˚C)

0.01

0.02

0.05

0.1

0.2

0.5

1

2

5

10

20

50

75

100

720 740 760 780 800

96.3 99.1 102.0 104.8 107.7

96.3 99.1 102.0 104.8 107.7

96.3 99.2 102.0 104.8 107.7

96.4 99.2 102.0 104.9 107.7

96.4 99.2 102.1 104.9 107.8

96.6 99.4 102.2 105.1 107.9

96.8 99.6 102.5 105.3 108.2

97.4 100.2 103.0 105.8 108.6

99.0 101.8 104.6 107.4 110.2

102.1 104.8 107.5 110.2 113.0

109.4 111.8 114.3 116.8 119.3

141.8 142.5 143.5 144.6 145.9

181.7 179.6 178.2 177.2 176.7

228.7 223.5 219.3 215.9 213.2

From ASME International Steam Tables for Industrial Use, p. 149.

© 2004 by CRC Press LLC

1587_Book.fm Page 1 Monday, September 1, 2003 7:17 PM

5 General Engineering and Mathematics Constants — Types of Numbers ...............................................................................................................5-3 Decimal Multiples and Prefixes .................................................................................................................5-4 Powers of 10 in Hexadecimal Scale ...........................................................................................................5-4 Factorials ....................................................................................................................................................5-5 Prime Numbers ..........................................................................................................................................5-6 Reliability ....................................................................................................................................................5-7 Conversion: Metric to English ...................................................................................................................5-7 Conversion: English to Metric ...................................................................................................................5-7 Interpretations of Powers of 10 .................................................................................................................5-8 Typical Values for Coefficients of Static Friction .....................................................................................5-8 Properties of Plane Areas ...........................................................................................................................5-9 Moments of Inertia of Homogeneous Solids .........................................................................................5-10 Dynamic Viscosity of Liquids ..................................................................................................................5-14 Resistor Color Code .................................................................................................................................5-14 The Problem of Total Cost Visbility........................................................................................................5-15 Trigonometry ...........................................................................................................................................5-15 Series .........................................................................................................................................................5-19 Differential Calculus ................................................................................................................................5-26 Integral Calculus ......................................................................................................................................5-30 Special Functions .....................................................................................................................................5-35 Moore's Laws ............................................................................................................................................5-44 Approximate Current Densities in Electrons per Second per Square Nanometer Calculated from Experimental Data for Selected Molecular Electronic and Macroscopic Metal Devices .................5-44 Comparison of Memory Technologies for the Year 2011 ......................................................................5-45 Size and Scale of Naturally Occurring Structures as Compared with Human-Made Structures ........5-45 Trends in Miniaturization of Integrated Circuits in the Last 25 Years ..................................................5-46 Civilizations, Technology Periods (Ages), and Historical Revolutions as a Function of Time ............5-47 Abbreviations ...........................................................................................................................................5-48 Boiling Point Law, General ......................................................................................................................5-49 Hall Effect .................................................................................................................................................5-50 Ideal Mixtures, Law of .............................................................................................................................5-50 Large Numbers, Law of ............................................................................................................................5-50

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5-2

CRC Handbook of Engineering Tables

Maxwell Electromagnetic Field Equations ..............................................................................................5-51 Moore Law................................................................................................................................................5-51 Newton Laws of Motion ..........................................................................................................................5-51 Normal Law ..............................................................................................................................................5-52 Photoelectric Effect, Laws of ...................................................................................................................5-52 Shannon Law or Formula Theorem ........................................................................................................5-52 Skin Effect ................................................................................................................................................5-53 Snell Law...................................................................................................................................................5-53 Thermodynamics, Laws of .......................................................................................................................5-54 Young Modulus, E ....................................................................................................................................5-55 Types of Manufacturing — Characteristics and Examples ....................................................................5-56 Coefficient of Friction — Identical Metals .............................................................................................5-57 Coefficient of Friction — Identical Alloy Pairs ......................................................................................5-58 Coefficient of Friction — Dissimilar Metals ..........................................................................................5-59 Coefficient of Friction — Single Crystals ...............................................................................................5-60 Coefficients of Friction — Non-Metals ..................................................................................................5-61 Coefficient of Friction — Lubricating Powders .....................................................................................5-62 Coefficients of Static and Sliding Friction ..............................................................................................5-62 The Greek and Russian Alphabets ..........................................................................................................5-64 Units and Their Conversion ....................................................................................................................5-65 International System (SI) Metric Units...................................................................................................5-67 Conversions to SI Units ...........................................................................................................................5-70 Fundamental Physical Constants.............................................................................................................5-79 Numerical Constants ...............................................................................................................................5-81 Mathematical Constants ..........................................................................................................................5-83 Derivatives ................................................................................................................................................5-84 Facts from Algebra ...................................................................................................................................5-87 Integrals — Elementary Forms ...............................................................................................................5-88 Series .........................................................................................................................................................5-90 Tables of Statistical Probability ...............................................................................................................5-98 Ordinates and Areas for Normal or Gaussian Probability Distribution .............................................5-100 Student's t-Distribution .........................................................................................................................5-103 Chi-Square Distribution ........................................................................................................................5-104 F-Distribution ........................................................................................................................................5-105 Binomial Distribution — Cumulative Probabilities: P ........................................................................5-108 Poisson Distribution — Cumulative Probabilities: P ...........................................................................5-110 Critical Values for the Sign Test ............................................................................................................5-113 Factors for Computing Control Limits .................................................................................................5-114 Number Systems and Change of Base ..................................................................................................5-117 Binary, Octal, and Decimal Numbers ...................................................................................................5-119 Octal-Decimal Integer Conversion........................................................................................................5-121 Boolean Theorems .................................................................................................................................5-125 Applications and Functions of Two Variables ......................................................................................5-126

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5-3

General Engineering and Mathematics

Constants Types of Numbers Natural numbers The set of natural numbers, {0, 1, 2, …}, is customarily denoted by . Many authors do not consider 0 to be a natural number. Integers The set of integers, {0, ±1, ±2, …}, is customarily denoted by . The positive integers are {1, 2, 3, …}. Rational numbers The set of rational numbers, denoted by . Two fractions

p --q

{ p--q p, q Œ , q π 0 },

is customarily

rs

and are equal if and only if ps = qr.

Addition of fractions is defined by of fractions is defined by p--q ◊ r-s = pr ---qs- .

ps + qr p r --q + - = ---------------qs - . s

Multiplication

Real numbers The set of real numbers is customarily denoted by . Real numbers are defined to be converging sequences of rational numbers or as decimals that might or might not repeat. Real numbers are often divided into two subsets. One subset, the algebraic numbers, are real numbers which solve a polynomial equa1- is an tion in one variable with integer coefficients. For example: -----2

algebraic number because it solves the polynomial equation 2x2 – 1 = 0; and all rational numbers are algebraic. Real numbers that are not algebraic numbers are called transcendental numbers. Examples of transcendental numbers include p and e. Complex numbers The set of complex numbers is customarily denoted by . They are numbers of the form a + bi, where i 2 = –1, and a and b are real numbers. Operation

Computation

Result

addition multiplication

(a + bi) + (c + di) (a + bi) (c + di)

(a + c) + i(b + d) (ac – bd) + (ad + bc)i

reciprocal complex conjugate

1 a + bi z = a + bi

a b i a2 + b2 a2 + b2 z = a - bi

Properties include: z + w = z + w and zw = zw . From Bolinger, K., Glasser, M.L., Gross, R., and Sloane, N.J.A., Analysis, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 3.

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5-4

CRC Handbook of Engineering Tables

Decimal Multiples and Prefixes The prefix names and symbols below re taken from Conference Générale des Poids et Mesures, 1991. The common names are for the U.S. Factor

Prefix

Symbol

(10100)

10 10100 1024 1021 1018 1015 1012 109 106 103 102 101 10–1 10–2 10–3 10–6 10–9 10–12 10–15 10–18 10–21 10–24

yotta zetta exa peta tera giga mega kilo hecto deka deci centi milli micro nano pico femto atto zepto yocto

Y Z E P T G M k H da d c m m (Greek mu) n p f a z y

Common Name googolplex googol heptillion hexillion quintillion quadrillion trillion billion million thousand hundred ten tenth hundreth thousandth millionth billionth trillionth quadrillionth quintillionth hexillionth heptillionth

From Bolinger, K., Glasser, M.L., Gross, R., and Sloane, N.J.A., Analysis, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 6.

Powers of 10 In Hexadecimal Scale n

10n

10–n

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

116 A16 6416 3E816 271016 186A016 F424016 98968016 5F5E10016 3B9ACA0016 2540BE40016 174876E80016 E8D43A5100016 9184E72A00016 5AF3107A400016 38D7EA4C6800016 2386F26FC1000016

116 0.19999999999999999999…16 0.028F5C28F5C28F5C28F5…16 0.004189374BC6A7EF9DB2…16 0.00068DB8BAC710CB295E…16 0.000A7C5AC471B478412…16 0.000010C6F7A0B5ED8D36…16 0.000001AD7F29ABCAF485…16 0.0000002AF31DC4611873…16 0.000000044B82FA09B5A5…16 0.000000006DF37F675EF6…16 0.000000000AFEBFF0BCB2…16 0.000000000119799812DE…16 0.00000000001C25C26849…16 0.000000000002D09370D4…16 0.000000000000480EBE7B…16 0.0000000000000734ACA5…16

From Bolinger, K., Glasser, M.L., Gross, R., and Sloane, N.J.A., Analysis, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 13.

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5-5

General Engineering and Mathematics

Factorials For non-negative integers n, the factorial of n, denoted n!, is the product of all positive integers less than or equal to n; n! = n·(n – 1)·(n – 2)L2·1. If n is a negative integer (n = –1, –2,…) then n! = ±•. Note that, since the empty product is 1, it follows that 0! = 1. The generalization of the factorial function to non-integer arguments is the gamma function. When n is an integer, G(n) = (n – 1)!. The double factorial of n, denoted n!!, is the product of every other integer: n!! = n·(n – 2)·(n – 4)L, where the last element in the product is either 2 or 1, depending on whether n is even or odd. The shifted factorial (also called the rising factorial and Pochhammer’s symbol) is – denoted by (a)n (sometimes an) and is defined as a + 1) ◊ (a + 2)L(a + n - 1) = (a)n = a1◊ (4444 4244444 3 n terms

(a + n - 1)! = G(a + n) G (a ) (a - 1)!

Approximations to n! for large n include Stirling’s formula Ê nˆ n! ª 2pe Á ˜ Ëe¯

n+

1 2

and Burnsides’s formula 1ˆ Ê n+ Á 2˜ n! ª 2p Á e ˜ Á ˜ Ë ¯ n

n! 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 50

© 2004 by CRC Press LLC

1 1 2 6 24 120 720 5040 40320 3.6288 ¥ 105 3.6288 ¥ 106 3.9917 ¥ 107 4.7900 ¥ 108 6.2270 ¥ 109 8.7178 ¥ 1010 1.3077 ¥ 1012 2.0923 ¥ 1013 3.5569 ¥ 1014 6.4024 ¥ 1015 1.2165 ¥ 1017 2.4329 ¥ 1018 5.1091 ¥ 1019 1.1240 ¥ 1021 2.5852 ¥ 1022 6.2045 ¥ 1023 1.5511 ¥ 1025 2.6525 ¥ 1032 8.1592 ¥ 1047 3.0414 ¥ 1064

log10 n! 0.00000 0.00000 0.30103 0.77815 1.38021 2.07918 2.85733 3.70243 4.60552 5.55976 6.55976 7.60116 8.68034 9.79428 10.94041 12.11650 13.32062 14.55107 15.80634 17.08509 18.38612 19.70834 21.05077 22.41249 23.79271 25.19065 32.42366 47.91165 64.48307

n+

1 2

n!! 1 1 2 3 8 15 48 105 384 945 3840 10395 46080 1.3514 ¥ 105 6.4512 ¥ 105 2.0270 ¥ 106 1.0322 ¥ 107 3.4459 ¥ 107 1.8579 ¥ 108 6.5473 ¥ 108 3.7159 ¥ 109 1.3749 ¥ 1010 8.1750 ¥ 1010 3.1623 ¥ 1011 1.9620 ¥ 1012 7.9059 ¥ 1012 4.2850 ¥ 1016 2.5511 ¥ 1024 5.2047 ¥ 1032

log10 n!! 0.00000 0.00000 0.30103 0.47712 0.90309 1.17609 1.68124 2.02119 2.58433 2.97543 3.58433 4.01682 4.66351 5.13077 5.80964 6.30686 7.01376 7.53731 8.26903 8.81606 9.57006 10.13828 10.91249 11.50001 12.29270 12.89795 16.63195 24.40672 32.71640

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CRC Handbook of Engineering Tables

Factorials (continued) 8.3210 ¥ 1081 1.1979 ¥ 10100 7.1569 ¥ 10118 1.4857 ¥ 10138 9.3326 ¥ 10157 1.5882 ¥ 10178 6.6895 ¥ 10198 6.4669 ¥ 10219 1.3462 ¥ 10241 5.7134 ¥ 10262 1.2201 ¥ 101134 4.0239 ¥ 102567

60 70 80 90 100 110 120 130 140 150 500 1000

81.92017 100.07841 118.85473 138.17194 157.97000 178.20092 198.82539 219.81069 241.12911 262.75689 1134.0864 2567.6046

2.8481 ¥ 1041 3.5504 ¥ 1050 8.9711 ¥ 1059 4.2088 ¥ 1069 3.4243 ¥ 1079 4.5744 ¥ 1089 9.5934 ¥ 1099 3.0428 ¥ 10110 1.4141 ¥ 10121 9.3726 ¥ 10131 5.8490 ¥ 10567 3.9940 ¥ 101284

41.45456 50.55028 59.95284 69.62416 79.53457 89.66033 99.98197 110.48328 121.15050 131.97186 567.76709 1284.6014

From Bolinger, K., Glasser, M.L., Gross, R., and Sloane, N.J.A., Analysis, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, pp. 17–18.

Prime Numbers 1. A prime number is a positive integer greater than 1 with no positive, integral divisors other than 1 and itself. There are infinitely many prime numbers, 2, 3, 5, 7,…. The sum 1 1 1 1 = + + +L = •. of the reciprocals of the prime numbers diverges: n pn 3 5 7 2. Twin primes are prime numbers that differ by two: (3, 5), (5, 7), (11, 13), (17, 19),…. It is not known whether there are infinitely many twin primes. The sum of the reciprocals of the twin primes converges; the value

Â

Ê1 1 ˆ Ê 1 1ˆ Ê 1 1ˆ Ê 1 1 ˆ B = Á + ˜ + Á + ˜ + Á + ˜ +L+ Á + ˜ +L Ë 3 5 ¯ Ë 5 7 ¯ Ë 11 13 ¯ Ë p p + 2¯ known as Brun’s constant is approximately B ª 1.90216054. 3. For every integer n ≥ 2, the numbers {n! + 2, n! + 3,…, n! + n} are a sequence of n – 1 consecutive composite (i.e., not prime) numbers. 4. Dirichlet’s theorem on primes in arithmetic progressions: Let a and b be relatively prime positive integers. Then the arithmetic progression an + b (for n = 1, 2,…) contains infinitely many primes. 5. Goldbach conjecture: every even number is the sum of two prime numbers. 6. The function p(x) represents the number of primes less than x. The prime number theorem states that p(x) ~ x/log x as x Æ •. The exact number of primes less than a given number is: x p(x)

100 25

1000 168

x p(x)

1010 455,052,511

10,000 1,229

105 9,592

1015 29,844,570,422,669

106 78,498

107 664,579

108 5,761,455

1021 21,127,269,486,018,731,928

From Driscoll, P.J., Gross, R., Michaels, J., Nelsen, R.B., and Wilson, B., Algebra, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 103.

© 2004 by CRC Press LLC

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5-7

General Engineering and Mathematics

Reliability 1. The reliability of a product is the probability that the product will function within specified limits for at least a specified period of time. 2. A series system is one in which the entire system will fail if any of its components fail. 3. A parallel system is one in which the entire system will fail only if all of its components fail. 4. Let Ri denote the reliability of the ith component. 5. Let Rs denote the reliability of a series system. 6. Let Rp denote the reliability of a series system. The product law of reliabilities states n

Rs =

’R

i

i =1

The product law of unreliabilities states n

Rp = 1 -

’ (1 - R ) i

i =1

From Mascagni, M., Rinaman, W.C., Sousa, M., and Strauss, M.T., Probability and statistics, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 653.

Conversion: Metric to English Multiply centimeters cubic meters cubic meters grams kilograms kilometers liters meters meters milliliters milliliters square centimeters square meters square meters

By

To Obtain

0.3937008 1.307951 35.31467 0.03527396 2.204623 0.6213712 0.2641721 1.093613 3.280840 0.03381402 0.06102374 0.1550003 1.195990 10.76391

inches cubic yards cubic feet ounces pounds miles gallons (US) yards feet fluid ounces cubic inches square inches square yards square feet

From Gross, R., Katz, V.J., and Strauss, M.T., Miscellaneous, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 796.

Conversion: English to Metric Multiply cubic feet cubic inches cubic yards feet fluid ounces gallons (US) inches miles mils

© 2004 by CRC Press LLC

By 0.02831685 16.38706 0.7645549 0.3048000 29.57353 3.785412 2.540000 1.609344 25.4

To Obtain cubic meters milliliters cubic meters meters milliliters liters centimeters kilometers micrometers

1587_Book.fm Page 8 Monday, September 1, 2003 7:17 PM

5-8

CRC Handbook of Engineering Tables

Conversion: English to Metric (continued) Multiply ounces pounds square feet square inches square yards yards

By

To Obtain

28.34952 0.4535924 0.09290304 6.451600 0.8361274 0.9144000

grams kilograms square meters square centimeters square meters meters

From Gross, R., Katz, V.J., and Strauss, M.T., Miscellaneous, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, p. 797.

Interpretations of Powers of 10 10–15 10–11 10–10 10–9 10–6 100 101 102 105 106 107 108 109 1010 1015 1016 1018 1019 1021 1024 1028 1033 1050 1078

the radius of the hydrogen nucleus (a proton) in meters the likelihood of being dealt 13 top honors in bridge the radius of a hydrogen atom in meters the number of seconds it takes light to travel one foot the likelihood of being dealt a royal flush in poker the density of water is 1 gram per milliliter the number of fingers that people have the number of sable elements in the periodic table the number of hairs on a human scalp the number of possible chess board positions after 4 moves the number of seconds in a year the speed of light in meters per second the number of heartbeats in a lifetime for most mammals the number of people on the earth the surface area of the earth in square meters the age of the universe in seconds the volume of water in the earth’s oceans in cubic meters the number of possible positions of Rubik’s cube the volume of the earth in cubic meters the number of grains of sand in the Sahara desert the mass of the earth in grams the mass of the solar system in grams the number of atoms in the earth the volume of the universe in cubic meters

From Gross, R., Katz, V.J., and Strauss, M.T., Miscellaneous, in CRC Standard Mathematical Tables and Formulae, 31st ed., Zwillinger, D., Ed., CRC Press, Boca Raton, FL, 2003, pp. 798–799.

Typical Values for Coefficients of Static Friction Materials Metal on ice Wood on wood Leather on wood Leather on metal Aluminum on aluminum

ms 0.03–0.05 0.30–0.70 0.20–0.50 0.30–0.60 1.10–1.70

From Hibbeler, R.C., Force-system resultants and equilibrium, in the Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 8.

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5-9

General Engineering and Mathematics

Properties of Plane Areas Figure

Centroid

Area Moments of Inertia

y Circular area

Ix = I y =

r

—

x

C

Iz =

y

y=

C r

y

4r 3p

x y

x=y=

4r 3p

Area of circular sector

r a x a

C

x

x=

2 r sina 3 a

pr4 16

4ˆ Êp Ix = I y = Á - ˜r 4 Ë 16 9p ¯

x

y

p r4 4

Ix = I y =

C y

p r4 8

Êp 8 ˆ Ix = Á - ˜r 4 Ë 8 9p ¯ Iz =

Quarter-circular area x

r

p r4 2

Ix = I y =

Semicircular area

p r4 4

Iz =

p r4 8

Ix =

r4 Ê 1 ˆ Á a - sin 2a˜ ¯ 4Ë 2

Iy =

r4 Ê 1 ˆ Á a + sin 2a˜ ¯ 4Ë 2

1 I z = r 4a 2 Rectangular area

C

h

— x

b Triangular x1 area

a y x

C y b

h x

x= y=

a+b 3 h 3

y

b

x

Area of elliptical quadrant C y x a

x=

4a 3p

4b y= 3p

Ix =

bh3 3

Ix =

bh3 12

Iz =

bh 2 2 (b + h ) 12

Ix =

bh3 12

Ix =

bh3 36

I x1 =

bh3 4

Ix =

p ab3 4ˆ Êp , I x = Á - ˜ ab3 Ë 16 9p ¯ 16

Iy =

p a3b 4ˆ Êp , I y = Á - ˜ a3b Ë 16 9p ¯ 16

Iz =

pab 2 2 a +b 16

(

)

From Meriam, J.L., Moments of inertia, in The Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 30. Originally from Meriam, J. L. and Kraige, L. G. 1992. Engineering Mechanics, 3rd ed. John Wiley & Sons, New York.

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5-10

CRC Handbook of Engineering Tables Moments of Inertia of Homogeneous Solids (m = Mass of Body Shown) Mass Center

Body

r

Circular cylindrical shell

l 2

l 2

1 1 I xx = mr 2 + ml 2 2 12 —

G

z

1 1 I x1x1 = mr 2 + ml 2 2 3 I zz = mr 2

x

x1

Mass Moments of Inertia

I xx = I yy Half cylindrical shell

l 2

l 2

G

z x1

y

r y1 x

1 1 = mr 2 + ml 2 2 12 2r x= p

I x1x1 = I y1y1 1 1 = mr 2 + ml 2 2 3 I zz = mr 2 4ˆ Ê I zz = Á1 - 2 ˜ mr 2 Ë p ¯

r

Circular cylinder

l 2

l 2 G

1 1 I xx = mr 2 + ml 2 4 12 —

z

1 I zz = mr 2 2

x

x1

1 1 I x1x1 = mr 2 + ml 2 4 3

I xx = I yy

l 2

l 2

Semicylinder

r

y1

x1

I x1x1 = I y1y1 4r x= 3p

G

z

1 1 = mr 2 + ml 2 4 12

y x

1 1 = mr 2 + ml 2 4 3 1 I zz = mr 2 2 Ê 1 16 ˆ I zz = Á - 2 ˜ mr 2 Ë 2 9p ¯

l 2

l 2

Rectangular parallelepiped

b

—

G

z a

y1

y2 x

© 2004 by CRC Press LLC

y

I xx =

1 m a2 + l 2 12

(

)

I yy =

1 m b2 + l 2 12

(

)

I zz =

1 m a2 + b2 12

(

)

I y1y1 =

1 1 mb2 + ml 2 12 3

(

1 I y2 y2 = m b2 + l 2 3

)

1587_Book.fm Page 11 Monday, September 1, 2003 7:17 PM

5-11

General Engineering and Mathematics Moments of Inertia of Homogeneous Solids (m = Mass of Body Shown) (continued) Mass Center

Body Spherical shell

G r

z

—

r G G

z

Hemispherical shell y

r x= 2

x

Mass Moments of Inertia

2 I zz = mr 2 3

2 I xx = I yy = I zz = mr 2 3 I yy = I zz =

5 mr 2 12

Sphere G

—

r

z

r

Hemisphere

G

z

3r x= 8

y x

l 2

l 2

Uniform slender rod

I yy = I zz =

83 mr 2 320

1 2 ml 12

1 I y1y1 = ml 2 3

y

y1

2 I xx = I yy = I zz = mr 2 5

I yy = —

G

2 I zz = mr 2 5

x

Quartercircular rod x=y

y G

=

x

2r p

1 I xx = I yy = mr 2 2 I zz = mr 2

r

y

z

l 2

l 2 b

G —

z

1 1 I yy = mb2 + ml 2 4 12

(

1 I zz = m a2 + b2 4

a y1

© 2004 by CRC Press LLC

1 1 I xx = ma2 + ml 2 4 12

Elliptical cylinder

y x

)

1 1 I y1y1 = mb2 + ml 2 4 3

1587_Book.fm Page 12 Monday, September 1, 2003 7:17 PM

5-12

CRC Handbook of Engineering Tables Moments of Inertia of Homogeneous Solids (m = Mass of Body Shown) (continued) Mass Center

Body

1 1 I yy = mr 2 + mh2 4 2

Conical shell

r G

2h z= 3

z h

Mass Moments of Inertia

y

y1

1 1 I y1y1 = mr 2 + mh2 4 6 1 I zz = mr 2 2 1 1 I yy = mr 2 + mh2 4 18 I xx = I yy 1 1 = mr 2 + mh2 4 2

Half conical shell y

G

z x1

h

r y1

x

x=

4r 3p

z=

2h 3

I x1x1 = I y1y1 1 1 = mr 2 + mh2 4 6 1 I zz = mr 2 2 Ê 1 16 ˆ I zz = Á - 2 ˜ mr 2 Ë 2 9p ¯

Right-circular cone

r G

3h z= 4

z h

y

y1

I yy =

3 3 mr 2 + mh2 20 5

I y1y1 =

3 1 mr 2 + mh2 20 10

I zz =

3 mr 2 10

I yy =

3 3 mr 2 + mh2 20 80

I xx = I yy = Half cone

G

z r x1

y

h y1

x

x=

r p

3h z= 4

3 3 mr 2 + mh2 20 5

I x1x1 = I y1y1 = I zz =

3 1 mr 2 + mh2 20 10 3 mr 2 10

1ˆ Ê 3 I zz = Á - 2 ˜ mr 2 Ë 10 p ¯

© 2004 by CRC Press LLC

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5-13

General Engineering and Mathematics Moments of Inertia of Homogeneous Solids (m = Mass of Body Shown) (continued) Mass Center

Body

Mass Moments of Inertia

(

)

(

)

(

)

1 I xx = m b2 + c 2 5 2

y2

z2

x + + =1 a2 b2 c2

x a

1 I yy = m a2 + c 2 5

z

G

z=

b

3c 8

1 Ê 19 ˆ I xx = mÁ b2 + c 2 ˜ 5 Ë 64 ¯

c Semiellipsoid

y

1 I zz = m a2 + c 2 5

1 Ê 19 ˆ I yy = mÁ a2 + c 2 ˜ 5 Ë 64 ¯ 1 1 I xx = mb2 + mc 2 6 2 z x2 y2 + = c a2 b2 b z

y

1 1 I yy = ma2 + mc 2 6 2

Elliptic paraboloid z=

G

2c 3

a

)

1 Ê 1 ˆ I xx = mÁ b2 + c 2 ˜ 6 Ë 3 ¯

x

c

(

1 I zz = m a2 + b2 6

1 Ê 1 ˆ I yy = mÁ a2 + c 2 ˜ 6 Ë 3 ¯

z Rectangular tetrahedron c

G x

a x= 4 b y= 4

a

c z= 4

b y

x

1 m b2 + c 2 10

(

)

I yy =

1 m a2 + c 2 10

(

)

I zz =

1 m a2 + b2 10

(

)

I xx =

3 m b2 + c 2 80

(

)

I yy =

3 m a2 + c 2 80

(

)

I zz =

3 m a2 + b2 80

(

)

z Half torus G

a 2 + 4R 2 x= 2pR

y

a

I xx =

R

R

1 5 I xx = I yy = mR 2 + ma2 2 8 3 I zz = mR 2 + ma2 4

From Meriam, J.L., Moments of inertia, in The Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 35–38.

© 2004 by CRC Press LLC

1587_Book.fm Page 14 Monday, September 1, 2003 7:17 PM

5-14

CRC Handbook of Engineering Tables Dynamic Viscosity of Liquids (m) (mPa ◊ s) -25∞C

Liquid Water Mercury Methanol Isobutyl acetate Toluene Styrene Acetic acid Ethanol Ethylene glycol

0∞C

25∞C

50∞C

75∞C

1.793

0.890 1.526 0.544 0.676 0.560 0.695 1.056 1.074 16.1

0.547 1.402

0.378 1.312

0.493 0.424 0.507 0.786 0.694 6.554

0.370 0.333 0.390 0.599 0.476 3.340

1.258

0.793

1.165

0.778 1.050

3.262

1.786

100∞C

0.286 0.270 0.310 0.464 1.975

From Braun, E.R. and Wang, P.-L., Boundary layers, in The Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 401.

Resistor Color Code

Color Black Brown Red Orange Yellow Green Blue Violet Gray White Silver Gold None a

First Band,a Significant Figure

Second Band, Significant Figure

Third Band, Multiplier

Fourth Band,b Tolerance (%)

Fifth Band,b Failure Rate (%/1000 h)

0 1 2 3 4 5 6 7 8 9 — — —

0 1 2 3 4 5 6 7 8 9 — — —

1 10 102 103 104 105 106 107 108 109 0.01 0.1 —

— — — — — — — — — — 10 5 20

— 1 0.1 0.01 0.001 — — — — — — — —

The first band is the one closest to one end of the resistor. A first band wider than the others indicates a wire-wound resistor. b Certain MIL parts. From Domingoes, H., Passive components, in The Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 1113.

© 2004 by CRC Press LLC

1587_Book.fm Page 15 Friday, September 26, 2003 12:10 PM

5-15

General Engineering and Mathematics

Acquisition Cost

Poor Cost Management

System design and development, production and/or construction

System Operating Cost Technical Data Cost

Operating personnel, facilities, utilities, energy, taxes, etc.

Distribution Cost Materials handling, packaging, shipping, transportation, distribution

Operating and maintenance manuals, procedures, instructions, field failure reports

Disposal Cost

Maintenance Cost

Customer service, field service, Phaseout and retirement, disassembly depot/supplier maintenance and recovery, (corrective/preventive maintenance) decontamination, recycling

Computer Resources Cost Operating and maintenance, computers, auxiliaries, software, and databases/documentation

Supply Support Cost Spares, repair parts, and related inventories (provisioning/inventory maintenance)

Training Cost

Test and Support Equipment Cost

Operator and maintenance training, training facilities, equipment, aids, data/documentation

Test equipment, monitoring equipment, special handling equipment

The problem of total cost visibility. From Fabrycky, W.J. and Blanchard, B.S., Life-cycle costing, in The Engineering Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1996, p. 1969.

Trigonometry Triangles In any triangle (in a plane) with sides a, b, and c and corresponding opposite angles A, B, and C, a b c = = sin A sin B sin C

(Law of sines)

a2 = b2 + c 2 - 2cb cos A

(Law of cosines)

a + b tan ( A + B) = a - b tan ( A - B)

(Law of tangents)

1 2 1 2

1 (s - b) 1 sin A = where s = (a + b + c) 2 bc 2 1 cos A = 2

s(s - a)(s - c) bc

1 (s - b)(s - c) tan A = 2 s(s - a) 1 Area = bc sin A 2 = s(s - a)(s - b)(s - c) If the vertices have coordinates (x1, y1), (x2, y2), (x3, y3), the area is the absolute value of the expression

© 2004 by CRC Press LLC

1587_Book.fm Page 16 Monday, September 1, 2003 7:17 PM

5-16

CRC Handbook of Engineering Tables

Trigonometry (continued) x1 1 x2 2 x3

y1 y2 y3

1 1 1

Trigonometric Functions of an Angle With reference to the following figure, P(x, y) is a point in any one of the four quadrants and A is an angle whose initial side is coincident with the positive x axis and whose terminal side contains the point P(x, y). The distance from the origin P(x, y) is denoted by r and is positive. The trigonometric functions of the angle A are defined as: sin A = sine A

=y r

cos A = cosine A

=x r

tan A = tangent A

=y x

ctn A = cotangent A = x y sec A = secant A

=r x

csc A = cosecant A

=r y

Angles are measured in degrees or radians; 180˚ = p radians; 1 radian = 180/p degrees. Y (II)

(I) P(x,y) r

A

X

0

(IV)

(III)

The trigonometric point. Angle A is taken to be positive when the rotation is counterclockwise and negative when the rotation is clockwise. The plane is divided into quadrants as shown. The trigonometric functions of 0˚, 30˚, 45˚, and integer multiples of these are directly computed. 0∞

30∞

45∞

60∞

1 2 3 2 3 3

2 2 2 2

3 2 1 2

1

3

120∞

135∞

3 2 1 2

2 2 2 2

•

- 3

-1

3 3

0

-

3 3

-1

2

2

•

-2

2

2 3 3

1

2 3 3

sin

0

cos

1

tan

0

ctn

•

3

1

sec

1

2 3 3

csc

•

2

© 2004 by CRC Press LLC

90∞ 1 0

- 2 2

150∞

180∞

1 2

0

3 2 3 3

-1

- 3

•

-

-

0

2 3 3

-1

2

•

1587_Book.fm Page 17 Monday, September 1, 2003 7:17 PM

5-17

General Engineering and Mathematics

Trigonometry (continued) Trigonometric Identities sin A =

1 csc A

cos A =

1 sec A

tan A =

sin A 1 = ctn A cos A

csc A =

1 sin A

sec A =

1 cos A

ctn A =

cos A 1 = tan A sin A

sin 2 A + cos2 A = 1 1 + tan 2 A = sec 2 A 1 + ctn 2 A = csc 2 A sin( A ± B) = sin A cos B ± cos A sin B cos( A ± B) = cos A cos B m sin A sin B tan( A ± B) =

tan A ± tan B 1 m tan A tan B

sin 2 A = 2 sin A cos A sin 3 A = 3sin A - 4 sin3 A sin nA = 2 sin(n - 1)A cos A - sin(n - 2)A cos 2 A = 2 cos2 A - 1 = 1 - 2 sin 2 A cos 3 A = 4 cos3 A - 3cos A cos nA = 2 cos(n - 1)A cos A - cos(n - 2)A 1 1 sin A + sin B = 2 sin ( A + B)cos ( A - B) 2 2 1 1 sin A - sin B = 2 cos ( A + B)sin ( A - B) 2 2 1 1 cos A + cos B = 2 cos ( A + B)cos ( A - B) 2 2 1 1 cos A - cos B = -2 sin ( A + B)sin ( A - B) 2 2 tan A ± tan B =

sin( A ± B) cos A cos B

ctn A ± ctn B = ±

sin( A ± B) sin A sin B

1 1 sin A sin B = cos( A - B) - cos( A + B) 2 2

© 2004 by CRC Press LLC

1587_Book.fm Page 18 Tuesday, September 2, 2003 3:25 PM

5-18

CRC Handbook of Engineering Tables

Trigonometry (continued) 1 1 cos A cos B = cos( A - B) + cos( A + B) 2 2 1 1 sin A cos B = sin( A + B) + sin( A - B) 2 2

tan

sin

A 1 - cos A =± 2 2

cos

A 1 + cos A =± 2 2

A 1 - cos A sin A 1 - cos A = = =± 2 sin A 1 + cos A 1 + cos A 1 sin 2 A = (1 - cos 2 A) 2 1 cos2 A = (1 + cos 2 A) 2 1 sin3 A = (3sin A - sin 3 A) 4 1 cos3 A = (cos 3 A + 3cos A) 4

(

)

1 sin ix = i e x - e - x = i sinh x 2 cos ix =

(

)

1 x -x e + e = cosh x 2

tan ix =

(

i e x - e-x e x + e-x

) = i tanh x

e x +iy = e x (cos y + i sin y) (cos x ± i sin x)n = cos nx ± i sin nx

Inverse Trigonometric Functions The inverse trigonometric functions are multiple valued, and this should be taken into account in the use of the following formulas. sin -1 x = cos -1 1 - x 2 = tan -1 = sec -1

x 1- x

2

1 1 - x2

1 - x2 x

= ctn -1 = csc -1

1 x

= - sin -1(- x) cos -1 x = sin -1 1 - x 2 = tan -1 = sec -1

1 - x2 x = ctn -1 x 1 - x2 1 1 = csc -1 x 1 - x2

= p - cos -1(- x)

© 2004 by CRC Press LLC

1587_Book.fm Page 19 Monday, September 1, 2003 7:17 PM

5-19

General Engineering and Mathematics

Trigonometry (continued) tan -1 x = ctn -1 = sin -1

1 x x

1

= cos -1

1 + x2

= sec -1 1 + x 2 = csc -1

1 + x2 1 + x2 x

= - tan -1(- x) From Dorf, R.C., Ed., The Engineering Handbook, CRC Press, Boca Raton, FL, 1996, pp. 2037–2041.

Series Bernoulli and Euler Numbers A set of numbers, B1, B3, . . . , B2n – 1 (Bernoulli numbers) and B2, B4, . . . , B2n (Euler numbers), appears in the series expansions of many functions. A partial listing follows; these are computed from the following equations: B2n -

2n(2n - 1) 2n(2n - 1)(2n - 2)(2n - 3) B2n-2 + B2n- 4 - L + (-1)n = 0 2! 4!

and 22n (22n - 1) (2n - 1)(2n - 2)(2n - 3) B2n-1 = (2n - 1)B2n-2 B2n- 4 + L + (-1)n-1 2n 3! B1 = 1 6

B2 = 1

B3 = 1 30

B4 = 5

B5 = 1 42

B6 = 61

B7 = 1 30

B8 = 1385

B9 = 5 66

B10 = 50, 521

B11 = 691 2730

B12 = 2, 702, 765

B13 = 7 6

B14 = 199, 360, 981

M

M

Series of Functions In the following, the interval of convergence is indicated; otherwise it is all x. Logarithms are to the base e. Bernoulli and Euler numbers (B2n - 1 and B2n) appear in certain expressions. (a + x ) n = a n + na n -1 x + (a - bx ) -1 =

n(n - 1) n - 2 2 n(n - 1)(n - 2) n - 3 3 n! a x + a x +L + a n- j x j + L 2! 3! (n - j)! j!

ù 1 È bx b 2 x 2 b 3 x 3 + 2 + 3 + Lú Í1 + aÎ a a a û

(1 ± x ) n = 1 ± nx +

n(n - 1) 2 n(n - 1)(n - 2)x 3 x ± +L 2! 3!

(1 ± x ) - n = 1 m nx +

© 2004 by CRC Press LLC

n(n + 1) 2 n(n + 1)(n + 2) 3 x m x +L 2! 3!

[x [b x 2

2

]

2

]

[x < 1] 2

[x < 1] 2

1587_Book.fm Page 20 Tuesday, September 2, 2003 3:25 PM

5-20

CRC Handbook of Engineering Tables

Series (continued)

(1 ± x )1 2 = 1 ±

[x < 1]

1◊ 3 ◊ 5 1 1 2 1◊ 3 xx ± x3 x 4 ±L 2 ◊4 ◊6 2 ◊4 ◊6 ◊8 2 2 ◊4

2

(1 ± x ) -1 2 = 1 m

1 1◊ 3 2 1◊ 3 ◊ 5 3 1◊ 3 ◊ 5 ◊ 7 4 x+ x m x + x ±L 2 2 ◊4 2 ◊4 ◊6 2 ◊4 ◊6 ◊8

[x < 1]

(1 ± x 2 )1 2 = 1 ±

1◊ 3 ◊ 5 1 2 x4 1◊ 3 x ± x6 x 8 ±L 2 ◊4 ◊6 ◊8 2 2 ◊4 2 ◊4 ◊6

[x < 1] [x < 1] [x < 1]

2

2

(1 ± x ) -1 = 1 m x + x 2 m x 3 + x 4 m x 5 + L

2

(1 ± x ) -2 = 1 m 2 x + 3 x 2 m 4 x 3 + 5 x 4 m L e x = 1+ x +

2

x2 x3 x4 + + +L 2! 3! 4!

2

e -x = 1- x 2 +

x4 x6 x8 + -L 2! 3! 4!

a x = 1 + x log a +

(x log a ) 2 (x log a ) 3 + +L 2! 3!

1 1 log x = (x - 1) - (x - 1)2 + (x - 1)3 - L 2 3 2

log x =

[0 < x < 2]

3

x - 1 1 Ê x - 1ˆ 1 Ê x - 1ˆ + Á ˜ + Á ˜ +L x 2Ë x ¯ 3Ë x ¯

1ù È Íx > 2 ú Î û

ÈÊ x - 1 ˆ 1 Ê x - 1 ˆ 3 1 Ê x - 1 ˆ 5 log x = 2 ÍÁ ˜ +L ˜+ Á ˜ + Á ÍÎË x + 1 ¯ 3 Ë x + 1 ¯ 5 Ë x + 1 ¯

[x > 0]

1 1 1 log(1 + x) = x - x 2 + x 3 - x 4 + L 2 3 4

[x < 1]

1 3 1 5 1 7 Ê1+ x ˆ È ù log Á ˜ = 2Íx + x + x + x + L ú Ë1- x ¯ 3 5 7 Î û

[x < 1]

È 1 1 Ê 1 ˆ3 1 Ê 1 ˆ 5 Ê x + 1ˆ log Á ˜ = 2Í + Á ˜ + Á ˜ + L Ë x - 1¯ ÍÎ x 3 Ë x ¯ 5 Ë x ¯

[x > 1]

sin x = x -

x3 x5 x7 + +L 3! 5! 7!

cos x = 1 -

x2 x4 x6 + +L 2! 4! 6!

tan x = x +

ctn x =

© 2004 by CRC Press LLC

ù ú úû

2

ù ú úû

2 2n (2 2n - 1)B 2n -1 x 2n -1 x 3 2 x 5 17 x 7 + + +L+ 3 15 315 (2n)!

B (2 x ) 2 n 1 x x 3 2x 5 - - L - 2n -1 -L (2n)! x x 3 45 945

2

2

È 2 p2 ù Íx < ú 4 û Î

[x

2

< p2

]

1587_Book.fm Page 21 Monday, September 1, 2003 7:17 PM

5-21

General Engineering and Mathematics

Series (continued)

csc x =

(

)

2 2 2n +1 - 1 1 x 7 x 3 31x 5 B x 2n +1 + L + + + +L+ x 3! 3 ◊ 5! 3 ◊ 7! (2n + 2)! 2n +1

[x

2

< p2

]

sin -1 x = x +

x 3 (1◊ 3)x 5 (1◊ 3 ◊ 5)x 7 + + +L 6 (2 ◊ 4)5 (2 ◊ 4 ◊ 6)7

[x < 1]

tan -1 x = x -

1 3 1 5 1 7 x + x - x +L 3 5 7

[x < 1] 2

[x > 1]

p 1 1◊ 3 1◊ 3 ◊ 5 1 - -L 2 x 6 x 3 (2 ◊ 4)5 x 5 (2 ◊ 4 ◊ 6)7 x 7

sec -1 x =

sinh x = x +

x3 x5 x7 + + +L 3! 5! 7!

cosh x = 1 +

x2 x4 x6 x8 + + + +L 2! 4! 6! 8!

(

)

tanh x = 2 2 - 1 2 2 B1

(

)

(

2

)

x x3 - 2 4 - 1 2 4 B3 2! 4!

+ 2 6 - 1 2 6 B5

È 2 p2 ù Íx < ú 4 û Î

x5 -L 6!

ˆ 2 2 B1 x 2 2 4 B 3 x 4 2 6 B 5 x 6 1Ê 1+ + - L˜ Á 2! 4! 6! xË ¯

ctnh x =

sech x = 1 csch x =

2

[x

< p2

]

È 2 p2 ù Íx < ú 4 û Î

B2 x 2 B4 x 4 B6 x 6 + +L 2! 4! 6!

(

2

[x

)

1 x x3 - (2 - 1)2 B1 + 2 3 - 1 2 B 3 -L 2! 4! x

2

< p2

]

sinh -1 x = x -

1 x 3 1◊ 3 x 5 1◊ 3 ◊ 5 x 7 + +L 2 3 2 ◊4 5 2 ◊4 ◊6 7

[x < 1]

tanh -1 x = x +

x3 x5 x7 + + +L 3 5 7

[x < 1] 2

[x > 1]

ctnh -1 x =

1 1 1 + + +L x 3x 3 5x 5

csch -1x =

1 1 1◊ 3 1◊ 3 ◊ 5 + +L x 2 ◊ 3x 3 2 ◊ 4 ◊ 5x 5 2 ◊ 4 ◊ 6 ◊ 7 x 7

Úe x

0

-t 2

2

2

[x > 1] 2

x5 x7 1 +L dt = x - x 3 + 3 5 ◊ 2! 7 ◊ 3!

Error Function The following function, known as the error function, erf x, arises frequently in applications: erf x =

e pÚ

2

x

-t 2

dt

0

The integral cannot be represented in terms of a finite number of elementary functions; therefore, values of erf x have been compiled in tables. The following is the series for erf x:

© 2004 by CRC Press LLC

1587_Book.fm Page 22 Monday, September 1, 2003 7:17 PM

5-22

CRC Handbook of Engineering Tables

Series (continued) erf x =

ù 2 È x3 x5 x7 + + Lú Íx 3 5 ◊ 2! 7 ◊ 3! pÎ û

There is a close relation between this function and the area under the standard normal curve. For evaluation it is convenient to use z instead of x; then erf z may be evaluated from the area F(z) by use of the relation erf z = 2 F

( 2 z)

Example erf (0.5) = 2 F[(1.414)(0.5)] = 2 F(0.707) By interpolation, F(0.707) = 0.260; thus, erf(0.5) = 0.520.

Series Expansion The expression in parentheses following certain series indicates the region of convergence. If not otherwise indicated, it is understood that the series converges for all finite values of x. Binomial (x + y)n = x n + nx n-1 y + (1 ± x)n = 1 ± nx +

n(n - 1) n-2 2 n(n - 1)(n - 2) n-3 3 x y + x y +L 2! 3!

2

< x2

]

[x < 1]

n(n - 1)x 2 n(n - 1)(n - 2)x 3 ± +L 2! 3!

(1 ± x)- n = 1 m nx +

[y

2

[x < 1]

n(n + 1)x 2 n(n + 1)(n + 2)x 3 +L m 2! 3!

2

[x < 1] [x < 1]

(1 ± x)-1 = 1 m x + x 2 m x 3 + x 4 m x 5 + L

2

(1 ± x)-2 = 1 m 2 x + 3x 2 m 4 x 3 + 5x 4 m 6 x 5 + L

2

Reversion of Series Let a series be represented by y = a1x + a2 x 2 + a3 x 3 + a4 x 4 + a5 x 5 + a6 x 6 + L

(a

1

π 0)

To find the coefficients of the series x = A1 y + A2 y 2 + A3 y 3 + A4 y 4 + L a2 a13

(

1 a1

A4 =

1 5a1a2a3 - a12a4 - 5a23 a17

A5 =

1 6a2a a + 3a12a32 + 14a24 - a13a5 - 21a1a22a3 a19 1 2 4

A6 =

1 7 a3a a + 7 a13a3a4 + 84a1a23a3 - a14a6 - 28a12a22a4 - 28a12a2a32 - 42a25 a111 1 2 5

A7 =

1 8a 4a a + 8a14a3a5 + 4a14a42 + 120a12a23a4 + 180a12a22a32 + 132a26 - a15a7 -36a13a22a5 - 72a13a2a3a4 - 12a13a33 - 330a1a24a3 a113 1 2 6

A2 = -

(

(

(

(

© 2004 by CRC Press LLC

A3 =

1 2a22 - a1a3 a15

)

A1 =

) ) ) )

1587_Book.fm Page 23 Monday, September 1, 2003 7:17 PM

5-23

General Engineering and Mathematics

Series (continued) Taylor 1. f (x) = f (a) + (x - a) f ¢(a) +

(x - a)2 (x - a)3 (x - a)n (n) f ¢¢(a) + f ¢¢¢(a) + L + f (a) + L 2! 3! n!

(Taylor’s series)

(Increment form) 2. f (x + h) = f (x) + hf ¢(x) +

h2 h3 f ¢¢(x) + f ¢¢¢(x) + L 2! 3!

x2 x3 f ¢¢(h) + f ¢¢¢(h) + L 2! 3! 3. If f(x) is a function possessing derivatives of all orders throughout the interval a £ x £ b, then there is a value X, with a < X < b, such that = f (h) + xf ¢(h) +

f (b) = f (a) + (b - a) f ¢(a) + f (a + h) = f (a) + hf ¢(a) +

(b - a)2 (b - a)n-1 (n-1) (b - a)n (n) f ¢¢(a) + L + f (a) + f (X ) (n - 1)! n! 2!

h2 hn-1 (n-1) h n (n) f ¢¢(a) + L + f f (a + qh), b = a + h, 0 < q < 1 (a) + (n - 1)! 2! n!

or f (x) = f (a) + (x - a) f ¢(a) +

(x - a)2 f (n-1)(a) f ¢¢(a) + L + (x - a)n-1 + Rn (n - 1)! 2!

where f (n)[a + q ◊ (x - a)]

Rn =

n!

(x - a)n ,

0 < q < 1.

The above forms are known as Taylor’s series with the remainder term. 4. Taylor’s series for a function of two variables: Ê ∂ ∂ f (x , y) ∂ f (x , y) ∂ ˆ If Á h + k ˜ f (x , y) = h +k ; ∂x ¯ ∂x ∂y Ë ∂x 2

2 Ê ∂ ∂ ˆ ∂ 2 f (x , y) 2 ∂ 2 f (x , y) 2 ∂ f (x , y) + 2hk +k Á h ∂ x + k ∂ y ˜ f (x , y) = h 2 ∂x ∂ y ∂x ∂ y2 Ë ¯

etc., and if n

Ê ∂ ∂ ˆ Á h ∂ x + k ∂ y ˜ f (x , y) Ë ¯ x =a y =b

where the bar and subscripts mean that after differentiation we are to replace x by a and y by b, n

Ê ∂ ∂ ˆ 1Ê ∂ ∂ ˆ f (a + h, b + k) = f (a, b) + Á h + k ˜ f (x , y) + L + Á h + k ˜ f (x , y) + L n ! x y¯ ∂y¯ ∂ ∂ Ë ∂x Ë x =a x =a y =b

y =b

MacLaurin f (x) = f (0) + xf ¢(0) +

x2 x3 f (n-1)(0) f ¢¢(0) + f ¢¢¢(0) + L + x n-1 + Rn 2! 3! (n - 1)!

where Rn =

© 2004 by CRC Press LLC

x n f (n)(qx) , n!

0 < q <1

1587_Book.fm Page 24 Monday, September 1, 2003 7:17 PM

5-24

CRC Handbook of Engineering Tables

Series (continued) Exponential e =1+

1 1 1 1 + + + +L 1! 2! 3! 4!

ex = 1+ x +

x 2 x3 x 4 + + +L 2! 3! 4!

(all real values of x)

(x log a) + (x log a) 2

a x = 1 + x log e a +

3

e

e

2!

3!

+L

È ù (x - a)2 (x - a)3 e x = e a Í1 + (x - a) + + + Lú 2! 3! Î û Logarithmic 2

log e x =

3

x - 1 1 Ê x - 1ˆ 1 Ê x - 1ˆ + Á ˜ + Á ˜ +L 2Ë x ¯ 3Ë x ¯ x

1 1 log e x = (x - 1) - (x - 1)2 + (x - 1)3 - L 2 3 È x - 1 1 Ê x - 1ˆ 3 1 Ê x - 1ˆ 5 ù log e x = 2 Í + Á ˜ + Á ˜ + Lú Ë ¯ Ë ¯ 5 x +1 ÍÎ x + 1 3 x + 1 úû 1 1 1 log e (1 + x) = x - x 2 + x 3 - x 4 + L 2 3 4

1ˆ Ê Áx > ˜ Ë 2¯ (2 ≥ x > 0) (x > 0) (-1 < x £ 1)

1 1 È1 ù log e (n + 1) - log e (n - 1) = 2 Í + 3 + 5 + Lú 5n Î n 3n û 3 5 È x ù 1Ê x ˆ 1Ê x ˆ log e (a + x) = log e a + 2 Í + Á ˜ + Á ˜ + Lú ÍÎ 2a + x 3 Ë 2a + x ¯ 5 Ë 2a + x ¯ úû

log e

È ù 1+ x x3 x 5 x 2n-1 = 2Íx + + +L+ + Lú 1- x 3 5 2 n 1 Î û

log e x = log e a +

© 2004 by CRC Press LLC

(x - a) (x - a)2 (x - a)3 + -L a 2a 2 3a3

(a > 0, -a < x < +•)

(-1 < x < 1) (0 < x £ 2a)

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Series (continued) Trigonometric sin x = x -

x3 x 5 x 7 + +L 3! 5! 7!

(all real values of x)

cos x = 1 -

x2 x 4 x6 + +L 2! 4! 6!

(all real values of x)

tan x = x +

x 3 2 x 5 17 x 7 62x 9 + + + +L 3 15 315 2835

+

(

(2n)!

(x cot x =

)

(-1)n-122n 22n - 1 B2n 2

x 2n-1 + L

< p 2 4 , and Bn represents the nth Bernoulli number

)

1 x x 2 2x 5 x7 - -L x 3 45 945 4725 -

(-1)n+122n B2n x 2n-1 + L (2n)!

(x

2

< p 2 , and Bn represents the nth Bernoulli number

)

From Dorf, R.C., Ed., The Engineering Handbook, CRC Press, Boca Raton, FL, 1996, pp. 2041–2048.

© 2004 by CRC Press LLC

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Differential Calculus Notation For the following equations, the symbols f(x), g(x), etc., represent functions of x. The value of a function f (x) at x = a is denoted f (a). For the function y = f (x) the derivative of y with respect to x is denoted by one of the following: dy , dx

f ¢(x),

Dx y ,

y¢

Higher derivatives are as follows: d 2 y d Ê dy ˆ d = f ¢(x) = f ¢¢(x) Á ˜= dx 2 dx Ë dx ¯ dx d3 y d Ê d 2 y ˆ d = = f ¢¢(x) = f ¢¢¢(x) dx 3 dx ÁË dx 2 ˜¯ dx M and values of these at x = a are denoted f ≤(a), f (a), and so on.

Slope of a Curve The tangent line at point P(x, y) of the curve y = f (x) has a slope f ¢(x) provided that f ¢(x) exists at P. The slope at P is defined to be that of the tangent line at P. The tangent line at P(x1, y1) is given by y - y1 = f ¢( x1 )( x - x1 ) The normal line to the curve at P(x1, y1) has slope –1/f ¢(x1) and thus obeys the equation

[

]

y - y1 = -1 f ¢( x1 ) ( x - x1 ) (The slope of a vertical line is not defined.)

Angle of Intersection of Two Curves Two curves, y = f1(x) and y = f2(x), that intersect at a point P(X, Y) where derivatives f 1¢(X), f 2¢(X) exist, have an angle (a) of intersection given by tan a =

f 2¢( X ) - f1¢( X ) 1 + f 2¢( X ) ◊ f1¢( X )

If tan a > 0, then a is the acute angle; if tan a < 0, then a is the obtuse angle.

Radius of Curvature The radius of curvature R of the curve y = f (x) at the point P(x, y) is

{1 + [ f ¢(x)] } R= 2

3/2

f ¢¢(x)

In polar coordinates (q, r) the corresponding formula is 3/2

2 È Ê dr ˆ ù Ír 2 + Á ˜ ú Ë dq ¯ ú Í û R= Î 2 dr d 2r Ê ˆ r 2 + 2Á ˜ - r 2 Ë dq ¯ dq

The curvature K is 1/R.

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Differential Calculus (continued) Relative Maxima and Minima The function f has a relative maximum at x = a if f (a) ≥ f (a + c) for all values of c (positive or negative) that are sufficiently near zero. The function f has a relative minimum at x = b if f(b) £ f(b + c) for all values of c that are sufficiently close to zero. If the function f is defined on the closed interval x1 £ x £ x2 and has a relative maximum or minimum at x = a, where x1 < a < x2, and if the derivative f ¢(x) exists at x = a, then f ¢(a) = 0. It is noteworthy that a relative maximum or minimum may occur at a point where the derivative does not exist. Further, the derivative may vanish at a point that is neither a maximum nor a minimum for the function. Values of x for which f ¢(x) = 0 are called “critical values.” To determine whether a critical value of x, say xc, is a relative maximum or minimum for the function at xc, one may use the second derivative test: 1. If f ≤(xc) is positive, f(xc) is a minimum. 2. If f ≤(xc) is negative, f(xc) is a maximum. 3. If f ≤(xc) is zero, no conclusion may be made. The sign of the derivative as x advances through xc may also be used as a test. If f ¢(x) changes from positive to zero to negative, then a maximum occurs at xc, whereas a change in f ¢(x) from negative to zero to positive indicates a minimum. If f ¢(x) does not change sign as x advances through xc, then the point is neither a maximum nor a minimum.

Points of Inflection of a Curve The sign of the second derivative of f indicates whether the graph of y = f (x) is concave upward or concave downward: f ≤(x) > 0: concave upward f ≤(x) < 0: concave downward

P

Point of inflection. A point of the curve at which the direction of concavity changes is called a point of inflection. Such a point may occur where f ≤(x) = 0 or where f ≤(x) becomes infinite. More precisely, if the function y = f (x) and its first derivative y¢ = f ¢(x) are continuous in the interval a £ x £ b, and if y≤ = f ≤(x) exists in a < x < b, then the graph of y = f(x) for a < x < b is concave upward if f ≤(x) is positive and concave downward if f ≤(x) is negative.

Taylor’s Formula If f is a function that is continuous on an interval that contains a and x, and if its first (n + 1) derivatives are continuous on this interval, then f (x) = f (a) + f ¢(a)(x - a) +

f ¢¢(a) f ¢¢¢(a) f (n)(a) (x - a)2 + (x - a)3 + L + (x - a)n + R 2! 3! n!

where R is called the remainder. There are various common forms of the remainder:

Lagrange’s Form R = f (n+1)(b) ◊

(x - a)n+1 , (n + 1)!

b between a and x

Cauchy’s Form R = f (n+1)(b) ◊

© 2004 by CRC Press LLC

(x - B)n (x - a) , n!

b between a and x

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Differential Calculus (continued) Integral Form R=

Ú

x

a

(x - t )n (n+1) f (t )dt n!

Indeterminant Forms If f(x) and g(x) are continuous in an interval that includes x = a, and if f(a) = 0 and g(a) = 0, the limit limxÆa [f(x)/g(x)] takes the form “0/0,” called an indeterminant form. L’Hôpital’s rule is lim x Æa

f (x) f ¢(x) = lim g (x) x Æa g ¢(x)

Similarly, it may be shown that if f (x) Æ • and g(x) Æ • as x Æ a, then lim x Æa

f (x) f ¢(x) = lim g (x) x Æa g ¢(x)

(The above holds for x Æ •.)

Examples lim x Æ0

sin x cos x = lim =1 x Æ0 x 1

x2 2x 2 = lim x = lim x = 0 x Æ• e x x Æ• e x Æ• e lim

Numerical Methods 1. Newton’s method for approximating roots of the equation f (x) = 0: A first estimate x1 of the root is made; then, provided that f ¢ (x1) π 0, a better approximation is x2: x 2 = x1 -

f (x) f ¢ ( x1 )

The process may be repeated to yield a third approximation, x3, to the root: x3 = x 2 -

f (x2 )

f ¢( x 2 )

provided f ¢ (x2) exists. The process may be repeated. (In certain rare cases the process will not converge.) 2. Trapezoidal rule for areas: For the function y = f (x) defined on the interval (a, b) and positive there, take n equal subintervals of width Dx = (b - a)/n. The area bounded by the curve between x = a and x = b [or definite integral of f (x)] is approximately the sum of trapezoidal areas, or 1 ˆ Ê1 A ~ Á y0 + y1 + y2 + L + yn-1 + yn ˜ (D x) Ë2 2 ¯ Estimation of the error (E) is possible if the second derivative can be obtained: E= where c is some number between a and b.

© 2004 by CRC Press LLC

b-a f ¢¢(c)(Dx)2 12

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General Engineering and Mathematics

Differential Calculus (continued) y

y

y

0

n x

0

a

b

Dx

Trapezoidal rule for area.

Functions of Two Variables For the function of two variables, denoted z = f (x, y), if y is held constant, say at y = y1, then the resulting function is a function of x only. Similarly, x may be held constant at x1, to give the resulting function of y.

The Gas Laws A familiar example is afforded by the ideal gas law relating the pressure p, the volume V, and the absolute temperature T of an ideal gas: pV = nRT where n is the number of moles and R is the gas constant per mole, 8.31 (J ◊ K-1 ◊ mole-1). By rearrangement, any one of the three variables may be expressed as a function of the other two. Further, either one of these two may be held constant. If T is held constant, then we get the form known as Boyle’s law: p = kV -1

(Boyle’s law)

where we have denoted nRT by the constant k and, of course, V > 0. If the pressure remains constant, we have Charles’ law: V = bT

(Charles’ law)

where the constant b denotes nR/p. Similarly, volume may be kept constant: p = aT where now the constant, denoted a, is nR/V.

Partial Derivatives The physical example afforded by the ideal gas law permits clear interpretations of processes in which one of the variables is held constant. More generally, we may consider a function z = f (x, y) defined over some region of the xy plane in which we hold one of the two coordinates, say y, constant. If the resulting function of x is differentiable at a point (x, y), we denote this derivative by one of the notations fx ,

d f dx ,

d z dx

called the partial derivative with respect to x. Similarly, if x is held constant and the resulting function of y is differentiable, we get the partial derivative with respect to y, denoted by one of the following: fy,

d f dy ,

d z dy

Example. Given z = x y - y sin x + 4y, then 4 3

dz dx = 4(xy)3 - y cos x dz dy = 3x 4 y 2 - sin x + 4 From Dorf, R.C., Ed., The Engineering Handbook, CRC Press, Boca Raton, FL, 1996, pp. 2048–2052.

© 2004 by CRC Press LLC

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Integral Calculus Indefinite Integral If F(x) is differentiable for all values of x in the interval (a, b) and satisfies the equation dy/dx = f(x), then F(x) is an integral of f(x) with respect to x. The notation is F(x) = Ú f(x) dx or, in differential form, dF(x) = f (x) dx. For any function F(x) that is an integral of f(x), it follows that F(x) + C is also an integral. We thus write

Ú f (x) dx = F(x) + C Definite Integral Let f(x) be defined on the interval [a, b] which is partitioned by points x1, x2, . . . , xj, . . . , xn–1 between a = x0 and b = xn. The jth interval has length Dxj = xj - xj–1, which may vary with j. The sum nj = 1 f(uj )Dxj , where uj is arbitrarily chosen in the jth subinterval, depends on the numbers x0, . . . , xn and the choice of the v as well as f; but if such sums approach a common value as all Dx approach zero, then this value is the definite integral of f over the interval (a, b) and b is denoted Úa f(x)dx. The fundamental theorem of integral calculus states that

S

Ú f (x)dx = F(b) - F(a), b

a

where F is any continuous indefinite integral of f in the interval (a, b).

Properties

Ú [ f (x) + f (x) + L + f (x)]dx = Ú f (x) dx + Ú f (x)dx + L + Ú f (x) dx b

a

b

1

j

2

b

1

a

a

Ú cf (x) dx = c Ú f (x) dx, b

b

2

a

j

b

a

if c is a constant

a

Ú f (x) dx = -Ú f (x) dx b

a

a

b

Ú f (x) dx = Ú f (x) dx + Ú f (x) dx b

b

c

a

c

a

Common Applications of the Definite Integral Area (Rectangular Coordinates) Given the function y = f (x) such that y > 0 for all x between a and b, the area bounded by the curve y = f (x), the x axis, and the vertical lines x = a and x = b is A=

Ú f (x) dx b

a

Length of Arc (Rectangular Coordinates) Given the smooth curve f (x, y) = 0 from point (x1, y1) to point (x2, y2), the length between these points is L=

Ú

x2

L=

Ú

y2

x1

y1

1 + (dy dx ) dx 2

1 + (dx dy ) dy 2

Mean Value of a Function The mean value of a function f(x) continuous on [a, b] is 1 (b - a)

© 2004 by CRC Press LLC

Ú f (x)dx b

a

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Integral Calculus (continued) Area (Polar Coordinates) Given the curve r = f (q), continuous and nonnegative for q1 £ q £ q2, the area enclosed by this curve and the radial lines q = q1 and q = q2 is given by A=

Ú

q2

q1

1 2

[ f (q)] dq 2

Length of Arc (Polar Coordinates) Given the curve r = f (q) with continuous derivative f ¢ (q) on q1 £ q £ q2, the length of arc from q = q1 to q = q2 is L=

q2

Ú

q1

[ f (q)] + [ f ¢(q)] dq 2

2

Volume of Revolution Given a function y = f(x) continuous and nonnegative on the interval (a, b), when the region bounded by f(x) between a and b is revolved about the x axis, the volume of revolution is V =p

Ú [ f (x)] dx b

2

a

Surface Area of Revolution (Revolution about the x Axis, Between a and b) If the portion of the curve y = f (x) between x = a and x = b is revolved about the x axis, the area A of the surface generated is given by the following: A=

Ú 2pf (x){1 + [ f ¢(x)] } b

2

12

dx

a

Work If a variable force f (x) is applied to an object in the direction of motion along the x axis between x = a and x = b, the work done is W=

Ú f (x) dx b

a

Cylindrical and Spherical Coordinates 1. Cylindrical coordinates: x = r cos q y = r sin q Element of volume dV = r dr dq dz. 2. Spherical coordinates: x = r sin f cos q y = r sin f sin q z = r cos f Element of volume dV = r2 sin f dr df dq.

© 2004 by CRC Press LLC

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Integral Calculus (continued) z

z

P

r P

j

z

y

y q

q

r x

x

Cylindrical coordinates.

Spherical coordinates.

Double Integration The evaluation of a double integral of f (x, y) over a plane region R,

ÚÚ f (x, y)dA R

is practically accomplished by iterated (repeated) integration. For example, suppose that a vertical straight line meets the boundary of R in at most two points so that there is an upper boundary, y = y2(x), and a lower boundary, y = y1(x). Also, it is assumed that these functions are continuous from a to b (see figure below). Then Ê

ÚÚ f (x, y)dA = Ú ÁË Ú b

a

R

y2 ( y)

y1( x )

ˆ f (x , y)dy˜ dx ¯

If R has left-hand boundary, x = x1(y), and right-hand boundary, x = x2(y), which are continuous from c to d (the extreme values of y in R), then Ê

ÚÚ f (x, y)dA = Ú ÁË Ú d

c

R

x 2 ( y)

x1( y )

ˆ f (x , y)dx ˜ dy ¯

Such integrations are sometimes more convenient in polar coordinates, x = r cos q, y = r sin q, dA = r dr dq. y

y2 (x)

y1 (x)

a

© 2004 by CRC Press LLC

b

x

Region R bounded by y2(x) and y1(x).

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Integral Calculus (continued) Surface Area and Volume by Double Integration For the surface given by z = f (x, y), which projects onto the closed region R of the xy plane, one may calculate the volume V bounded above by the surface and below by R, and the surface area S by the following: V=

ÚÚ zdA = ÚÚ f (x, y)dx dy R

S=

R

ÚÚ ÈÎÍ1 + (dz dx) + (dz dy) ùûú 2

2

1/2

dx dy

R

[In polar coordinates, (r, q ), we replace d A by r d r d q.]

Centroid The centroid of a region R of the xy plane is a point (x¢, y¢) where x¢ =

1 A

ÚÚ xd A,

y¢ =

R

1 A

ÚÚ yd A R

and A is the area of the region. Example. For the circular sector of angle 2a and radius R, the area A is aR2; the integral needed for x¢, expressed in polar coordinates, is a

ÚÚ xdA = Ú Ú (r cos q)rdrdq R

-a 0

+a

È R3 ù 2 = Í sin qú = R3 sin q 3 Î û -a 3 and thus, 2 3 R sin a 2 sin a x¢ = 3 = R a 3 aR 2 Centroids of some common regions are shown in the following table.

© 2004 by CRC Press LLC

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Integral Calculus (continued) Centroids Area Rectangle y

x¢

y¢

bh

b/2

h/2

bh/2

b/2

h/3

pR2/2

R

4R/3p

pR2/4

4R/3p

4R/3p

R 2A

2R sin A/3A

0

(rectangle)

h x

b Isosceles triangle* y

(isos. triangle)*

h x

b Semicircle y

(semicircle)

x

R Quarter circle y

(quarter circle)

R

x

Circular sector y

(circular sector)

R A

x

* y¢ = h/3 for any triangle of altitude h. From Dorf, R.C., Ed., The Engineering Handbook, CRC Press, Boca Raton, FL, 1996, pp. 2053–2057.

© 2004 by CRC Press LLC

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General Engineering and Mathematics

Special Functions Hyperbolic Functions sinh x =

e x - e-x 2

csch x =

1 sinh x

cosh x =

e x + e-x 2

sech x =

1 cosh x

tanh x =

e x - e-x e x + e-x

ctnh x =

1 tanh x

sinh(- x) = - sinh x

ctnh (- x) = -ctnh x

cosh(- x) = cosh x

sech (- x) = sech x

tanh(- x) = - tanh x

csch (- x) = -csch x

tanh x =

sinh x cosh x

ctnh x =

cosh x sinh x

cosh2 x - sinh2 x = 1

1 cosh2 x = (cosh 2 x + 1) 2

1 sinh2 x = (cosh 2 x - 1) 2

ctnh2 x - csch2 x = 1

csch2 x - sech2 x = csch2 x sech2 x

tanh2 x + sech2 x = 1

sinh(x + y) = sinh x cosh y + cosh x sinh y cosh(x + y) = cosh x cosh y + sinh x sinh y sinh(x - y) = sinh x cosh y - cosh x sinh y cosh(x - y) = cosh x cosh y - sinh x sinh y tanh(x + y) =

tanh x + tanh y 1 + tanh x tanh y

tanh(x - y) =

tanh x - tanh y 1 - tanh x tanh y

Bessel Functions Bessel functions, also called cylindrical functions, arise in many physical problems as solutions of the differential equation

(

)

x 2 y ¢¢ + xy ¢ + x 2 - n 2 y = 0 which is known as Bessel’s equation. Certain solutions, known as Bessel functions of the first kind of order n, are given by J n (x) =

•

Â k =0

J - n (x) =

(-1)k Ê xˆ Á ˜ k! G(n + k + 1) Ë 2 ¯

•

n+ 2k

Â k!G(-n + k + 1) ÊÁË 2 ˆ˜¯ (-1)k

x

- n+ 2k

k =0

In the above it is noteworthy that the gamma function must be defined for the negative argument q : G(q) = G(q + 1)/q, provided that q is not a negative integer. When q is a negative integer, 1/G(q) is defined to be zero. The functions J-n (x) and Jn (x) are solutions of Bessel’s equation for all real n. It is seen, for n = 1, 2, 3, . . . , that J - n (x) = (-1)n J n (x) and, therefore, these are not independent; hence, a linear combination of these is not a general solution. When, however, n is not a positive integer, a negative integer, or zero, the linear combination with arbitrary constants c1 and c2,

© 2004 by CRC Press LLC

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Special Functions (continued) y = c1 J n ( x ) + c 2 J - n ( x ) is the general solution of the Bessel differential equation. The zero-order function is especially important as it arises in the solution of the heat equation (for a “long” cylinder): x2 x4 x6 + +L 22 2242 224262

J 0 (x) = 1 -

while the following relations show a connection to the trigonometric functions: 1/2

È 2 ù J1/2(x) = Í ú sin x Î px û 1/2

È 2 ù J -1/2(x) = Í ú cos x Î px û The following recursion formula gives Jn+1 (x) for any order in terms of lower-order functions: 2n J (x) = J n-1(x) + J n+1(x) x n

Legendre Polynomials If Laplace’s equation, —2V = 0, is expressed in spherical coordinates, it is r 2 sin q

d 2V dV d 2V dV 1 d 2V + 2r sin q + sin q 2 + cos q + =0 2 dq sin q df2 dr dr dq

and any of its solutions, V(r, q, f), are known as spherical harmonics. The solution as a product V (r , q, f) = R(r )Q(q) which is independent of f, leads to

[

]

sin 2 q Q ¢¢ + sin q cos q Q ¢ + n(n + 1)sin 2 q Q = 0 Rearrangement and substitution of x = cos q leads to

(1 - x ) ddxQ - 2x ddxQ + n(n + 1)Q = 0 2

2

2

known as Legendre’s equation. Important special cases are those in which n is zero or a positive integer, and, for such cases, Legendre’s equation is satisfied by polynomials called Legendre polynomials, Pn(x). A short list of Legendre polynomials, expressed in terms of x and cos q, is given below. These are given by the following general formula: L

Pn (x) =

Â 2 j!(n - j)!(n - 2 j)! x (-1) j (2n - 2 j)!

n

j =0

where L = n/2 if n is even and L = (n - 1)/2 if n is odd. P0(x) = 1 P1(x) = x 1 P2(x) = (3x 2 - 1) 2 P3(x) =

© 2004 by CRC Press LLC

(

1 5x 3 - 3x 2

)

n-2 j

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General Engineering and Mathematics

Special Functions (continued)

(

)

P4(x) =

1 35x 4 - 30x 2 + 3 8

P5(x) =

1 63x 5 - 70x 3 + 15x 8

(

)

P0(cos q) = 1a P1(cos q) = cos q 1 P2(cos q) = (3cos 2 q + 1) 4 1 P3(cos q) = (5cos 3 q + 3cos q) 8 P4(cos q) =

1 (35cos 4 q + 20 cos 2q + 9) 64

Additional Legendre polynomials may be determined from the recursion formula (n + 1)Pn+1(x) - (2n + 1)xPn (x) + nPn-1(x) = 0

(n = 1, 2,K)

or the Rodrigues formula Pn (x) =

(

)

n 1 dn 2 x -1 2 n! dx n n

Laguerre Polynomials Laguerre polynomials, denoted Ln(x), are solutions of the differential equation xy ¢¢ + (1 - x)y ¢ + ny = 0 and are given by n

Ln (x) =

Â j =0

(-1) j C x j (n = 0, 1, 2,K) j! (n, j)

Thus, L0(x) = 1 L1(x) = 1 - x 1 L2(x) = 1 - 2 x + x 2 2 3 1 L3(x) = 1 - 3x + x 2 - x 3 2 6 Additional Laguerre polynomials may be obtained from the recursion formula (n + 1)Ln+1(x) - (2n + 1 - x)Ln (x) + nLn-1(x) = 0

Hermite Polynomials The Hermite polynomials, denoted Hn(x), are given by 2

H 0 = 1,

H n (x) = (-1)n e x

2

d ne - x , dx n

(n = 1, 2,K)

and are solutions of the differential equation y ¢¢ - 2 xy ¢ + 2ny = 0

© 2004 by CRC Press LLC

(n = 0, 1, 2K)

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Special Functions (continued) The first few Hermite polynomials are H0 = 1

H1(x) = 2 x

H 2 (x) = 4 x - 2

H3(x) = 8 x 3 - 12x

2

H 4(x) = 16x 4 - 48x 2 + 12 Additional Hermite polynomials may be obtained from the relation H n+1(x) = 2 xH n (x) - H n¢ (x) where prime denotes differentiation with respect to x.

Orthogonality A set of functions { fn(x)} (n = 1, 2, . . .) is orthogonal in an interval (a, b) with respect to a given weight function w(x) if

Ú w(x) f (x)f (x)dx = 0 b

m

a

n

when m π n

The following polynomials are orthogonal on the given interval for the given w(x): Pn (x)

Legendre polynomial s:

w(x) = 1 a = -1, b = 1

Ln (x)

Laguerre polynomial s:

w(x) = exp(- x) a = 0, b = •

H n (x)

Hermite polynomial s:

( )

w(x) = exp - x 2 a = -•, b = •

The Bessel functions of order n, Jn(l1x), Jn(l 2 x), . . . , are orthogonal with respect to w(x) = x over the interval (0, c) provided that the li are the positive roots of Jn(lc) = 0:

Ú xJ (l x) J (l x)dx = 0 c

0

where n is fixed and n ≥ 0.

© 2004 by CRC Press LLC

n

j

n

k

( j π k)

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General Engineering and Mathematics

Special Functions (continued) Functions with x2/a2 ± y2/b2 Elliptic Paraboloid

(

z = c x 2 a2 + y 2 b2

)

x 2 a2 + y 2 b2 - z c = 0

(a)

(b)

Elliptic paraboloid. (a) a = 0.5, b = 1.0, c = –1.0; viewpoint = (5, –6, 4). (b) a = 1.0, b = 1.0, c = –2.0; viewpoint = (5, –6, 4).

Hyperbolic Paraboloid (Commonly Called Saddle)

(

z = c x 2 a2 - y 2 b2

)

x a - y b -z c =0 2

(a)

2

2

2

(b)

Hyperbolic paraboloid. (a) a = 0.50, b = 0.5, c = 1.0; viewpoint = (4, –6, 4). (b) a = 1.00, b = 0.5, c = 1.0; viewpoint = (4, –6, 4).

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CRC Handbook of Engineering Tables

Special Functions (continued) Elliptic Cylinder 1 = x 2 a2 + y 2 b2 x 2 a2 + y 2 b2 - 1 = 0

Elliptic cylinder. a = 1.0, b = 1.0; viewpoint = (4, –5, 2).

Hyperbolic Cylinder 1 = x 2 a2 - y 2 b2 x 2 a2 - y 2 b2 - 1 = 0

Hyperbolic cylinder. a = 1.0, b = 1.0; viewpoint = (4, –6, 3).

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General Engineering and Mathematics

Special Functions (continued) Functions with (x 2/a 2 + y 2/b 2 ± c2)1/2 Sphere

(

z = 1 - x2 - y2

)

1/2

x2 + y2 + z2 -1 = 0

Sphere. Viewpoint = (4, –5, 2).

Ellipsoid

(

z = c 1 - x 2 a2 - y 2 b2

)

1/2

x 2 a2 + y 2 b2 + z 2 c 2 - 1 = 0

(a)

(b)

Ellipsoid. (a) a = 1.00, b = 1.00, c = 0.5; viewpoint = (4, –5, 2). (b) a = 0.50, b = 0.50, c = 1.0; viewpoint = (4, –5, 2). Special cases:

© 2004 by CRC Press LLC

a =b>c

gives oblate spheroid

a =b
gives prolate spheroid

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CRC Handbook of Engineering Tables

Special Functions (continued) Cone

(

z = x2 + y2

)

1/2

x2 + y2 - z2 = 0

Cone. Viewpoint = (4, –5, 2).

Elliptic Cone (Circular Cone if a = b)

(

z = c x 2 a2 + y 2 b2

)

1/2

x 2 a2 + y 2 b2 - z 2 c 2 = 0

(a)

(b)

Elliptic cone. (a) a = 0.5, b = 0.5, c = 1.00; viewpoint = (4, –5, 2). (b) a = 1.0, b = 1.0, c = 0.50; viewpoint = (4, –5, 2).

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General Engineering and Mathematics

Special Functions (continued) Hyperboloid of One Sheet

(

)

z = c x 2 a2 + y 2 b2 - 1

1/2

x 2 a2 + y 2 b2 - z 2 c 2 - 1 = 0

(a)

(b)

Hyperboloid of one sheet. (a) a = 0.1, b = 0.1, c = 0.2; ±z = c 15 ; viewpoint = (4, –5, 2). (b) a = 0.2, b = 0.2, c = 0.2; ±z = c 15 ; viewpoint = (4, –5, 2).

Hyperboloid of Two Sheets

(

)

z = c x 2 a2 + y 2 b2 + 1

1/2

x 2 a2 + y 2 b2 - z 2 c 2 + 1 = 0

(a)

(b)

Hyperboloid of two sheets. (a) a = 0.125, b = 0.125, c = 0.2; ±z = c 17; viewpoint = (4, –5, 2). (b) a = 0.25, b = 0.25, c = 0.2; ±z = c 17; viewpoint = (4, –5, 2). From Dorf, R.C., Ed., The Engineering Handbook, CRC Press, Boca Raton, FL, 1996, pp. 2058–2066.

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1000

Analog ICs Discrete ICs

100 Nanoscale ICs Novel Basics and Physics

10

Novel Basic Physics

1 0.1

1990

2000

2010 Year

2020

IC Fabrication Facility Cost ($ Billions)

Electrons per Device

CRC Handbook of Engineering Tables

100 10 1 0.1

1990

2000

2010

2020

Year

Moore’s laws. (From Lyshevski, S.E., Nanocomputer architectures and nanotechnology, in Handbook of Nanoscience, Engineering, and Technology, Goddard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 6-5.)

Approximate Current Densities in Electrons per Second per Square Nanometer Calculated from Experimental Data for Selected Molecular Electronic and Macroscopic Metal Devices Molecular Electronic Device 1,4-Dithiol Benzene

3-Ring Polyphenylene Wire

Poly-phenylene RTD (5 rings)

Carbon Nanotube

Copper Wire

1 2 ¥ 10–8

1 3.2 ¥ 10–5

1.4 (peak) 1.4 ¥ 10–11

1 1 ¥ 10–7

2 ¥ 10–3 (10 cm wire) 1 (approx.)

Amperes Electrons per Sec nm2

2 ¥ 10–8 1.2 ¥ 1011

3.2 ¥ 10–8 2.0 ¥ 1011

1.4 ¥ 10–14 8.7 ¥ 104

1 ¥ 10–7 6.2 ¥ 1011

– –

~0.05

~0.05

~0.05

~3.1 (Radius ª 1 nm)

~3.1 ¥ 1012 (Radius ª 1 mm)

Electrons per Sec-nm2

~2 ¥ 1012

~4 ¥ 1012

~2 ¥ 106

~2 ¥ 1011

~2 ¥ 106

(7)

(8)

(5,6)

(4)

Quantity Applied Voltage Current Measured in Experiment Current Inferred per Molecule Estimated CrossSectional Area per Molecule Current Density

Units Volts Amperes

Reference

Conversion factor for amperes to electrons per second is 1 Ampere ∫ 1 Coulomb/sec = (1.6 ¥ 10-19)-1 electrons/sec = 6.2 ¥ 10 electrons/sec. b In order to estimate the current densities per molecule from the published data on the room temperature nanopore measurements in References 5, 6, and 8, it was determined that the samples in the monolayer in the nanopore contained on the order of 1000 molecules per monolayer. This estimate is based on an average nanopore diameter of 30 nm and an estimated molecular diameter on the order of approximately 1 nm. c Common copper wire generally is regarded as being highly conductive. Therefore, data for 10 cm of 1mm diameter (18 gauge) copper wire is included only for comparison as a familiar, conductive, macroscopic reference system. A current on the order of 1 ampere is the maximum recommended for such wire to avoid undue heating and danger of fire. Sources of current measurements: (4) S.J. Tans et al., Individual single-wall carbon nanotubes as quantum wires, Nature, 386, 474–477, 1997; (5) M.A. Reed, Electrical Properties of Molecular Devices, presented at 1997 DARPA ULTRA Program Review Conference, Santa Fe, NM, October, 1997; (6) M.A. Reed, Molecular-scale electronics, Proc. IEEE, 87, 652–658, 1999; (7) C. Thou, M.R. Deshpande, M.A. Reed, and J.M. Tour, Nanoscale metal/self-assembled monolayer/metal heterostructures, Appl. Phys. Lett., 71, 611–613, 1997; (8) C. Zhou, Atomic and Molecular Wires, Ph.D. dissertation, Yale University, 1999. With permission. From Ellenbogen, J.C. and Love, J.C., Architectures for molecular electronic computers, in Handbook of Nanoscience, Engineering, and Technology, Goodard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 7-6. a

18

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General Engineering and Mathematics

Comparison of Memory Technologies for the Year 2011 CMOS Technology

DRAM

Flash

SRAM

MRAM

Reference Generation at Introduction Circuit Speed Feature Size Access Time Write Time Erase Time Retention Time Endurance Cycles Operating Voltage (V) Voltage to Switch State Cell Size

SIA 1999 64 GB 150 MHz 50 nm 10ns 10 ns <1 ns 2–4 s Infinite 0.5–0.6 V 0.2 V 2.5 F2*/bit 0.0005 mm2

SIA 1999 64 GB 150 MHz 50 nm 10 ns 10 ms 10 ms 10 years 105 5V 5V 2F2/bit

SIA 1999 180 MB/cm2 913 MHz 35 nm 1.1 ns 1.1 ns 1.1 ns N/A Infinite 0.5–0.6 V 0.5–0.6 V 12F2/bit

64 GB >500 MHz <50 nm <2 ns <10 ns N/A Infinite Infinite <1 V <50 mV 2F2/bit

* F = minimal lithographic feature size. From Wolf, S.A., Chtchelkanova, A.Y., and Treger, D., Spintronics — Spin-based electronics, in Handbook of Nanoscience, Engineering, and Technology, Goodard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 8-6.

Size and scale of naturally occurring structures as compared with human-made structures. (From Bashir, R., Biologically mediated assembly of artificial nanostructures and microstructures, in Handbook of Nanoscience, Engineering, and Technology, Goddard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 15-2.)

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CRC Handbook of Engineering Tables

# of Neurons in the Human Brain 3 (in 15 cm ) SIA Roadmap

CMOS Technology 1.E+12

1000

# of Transistors/ DRAMChip

1.E+10 2

DRAM

1.E+09

256Mb

1.E+08 16Mb

DRAM Bits/mm2

1.E+07

1Mb 1.E+06

100

# of Transistors/DRAM Chip

1.E+11

Minimum Feature Size(nm)

DRAM Bits/mm

Minimum Feature Size (nm)

10000

64Kb 1.E+05 Areal Neuron Density in Human 2 Brain (# N/mm )

4Kb

1.E+04 1.E+03

10 1970

1980

1990

2000

2010

2020

Year

Trends in miniaturization of integrated circuits in the last 25 years. (From Bashir, R., Biologically mediated assembly of artificial nanostructures and microstructures, in Handbook of Nanoscience, Engineering, and Technology, Goddard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 15-3.)

© 2004 by CRC Press LLC

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General Engineering and Mathematics

Civilizations, technology periods (ages), and historical revolutions as a function of time. (From Tomalia, D.A., Mardel, K., Henderson, S.A., Holan, G., and Estard, R., Dendrimers — An enabling synthetic science to controlled organic nanostructures, in Handbook of Nanoscience, Engineering, and Technology, Goddard, III, W.A., Brenner, D.W., Lyshevski, S.E., and Iafrate, G.J., Eds., CRC Press, Boca Raton, FL, 2003, p. 20-3.)

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Abbreviations AAAS ACS AGI AIChE AIME AIP AMA API ASCE ASME BET DOD DOE e.g. eng., engr. erf esp. est. etc. exp(x) ff. i.e. ISO LH ln log MTBF MTTF n.a. n.d. NAE NAS NASA NBS NIST NIH NSF NTP NUC NYPL TMA

American Association for Advancement of Science American Chemical Society American Geological Institute American Institute of Chemical Engineers American Institute of Mining, Metallurgical and Petroleum Engineers American Institute of Physics actual mechanical advantage American Petroleum Institute American Society of Civil Engineers American Society of Mechanical Engineers Brunauer-Emmet-Teller Department of Defense (U.S.) Department of Energy (U.S.) for example engineer, engineering error function especially estimate(d) and so forth (x) is the exponent of e and following that is International Standards Organization latent heat logarithm to the base e logarithm to the base 10 mean time before failure (same as) mean time to failure not available no date; or undated National Academy of Engineering (U.S.) National Academy of Sciences (U.S.) National Aeronautics and Space Administration (U.S.) National Bureau of Standards (presently NIST) National Institute of Standards and Technology (U.S.) National Institutes of Health (U.S.) National Science Foundation (U.S.) normal temperature and pressure (25O C at 1 atm.) National Union Catalogue New York Public Library theoretical mechanical advantage

From Hall, C.W., Laws and Models: Science, Engineering, and Technology, CRC Press, Boca Raton, FL, 2000, p. xxvii.

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General Engineering and Mathematics

Boiling Point Law, General The decrease in vapor pressure of a nonvolatile solvent at the boiling point is proportional to the increase in mole fraction of solute as related to the moles of solute present. Thus: –dp = –p dx/x where p = vapor pressure x = mole of solute

Triple point for water.

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Hall Effect (1879) When a steady current is flowing in a steady magnetic field, electromotive forces (voltages) are developed at right angles both to the magnetic force and to the current, and these are proportional to the product of the intensity of the current, the magnetic force, and the sine of the angle between the directions of these quantities.

Ideal Mixtures, Law of The property of a mixture of gases and some solids and some liquids is an additive function of the same property of the components, an assumption which in many cases is far from correct: W A = W 1 A1 + W 2 A2 + W 3 A3 + …

Large Numbers, Law of (1689) (1713); Bernoulli Theorem (1713) Various statements are used to represent the law of large numbers, but the idea is the same for each. If the size of a sample of statistically independent variables is increased indefinitely, good sample estimates of population parameters will tend to concentrate more and more closely about the true value. There are strong laws and weak laws of large numbers. Strong laws are concerned with showing that a variable, x, converges to a value m with a probability of one. The strong law of large numbers is represented by the Borel theorem. Weak laws consider conditions under which the probability that |x – m| is greater than some given epsilon, e, tends to zero. The weak law of large numbers is represented by the Bernoulli theorem. For the Bernoulli theorem, we have the following relationship: lim P (|x – m| > e) = 0 as N Æ • where x = sample means m = population N = number of trials S. Poisson gave the name of the law of large numbers to J. Bernoulli.

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General Engineering and Mathematics

Maxwell Electromagnetic Field Equations (1864) Maxwell, who was born in 1831, the year that Faraday published his discovery of electromagnetic induction, expressed Faraday’s discoveries mathematically in field theory in 1855–1857, followed by his major work in four electromagnetic field equations, expressed in vector form as follows: 1. 2. 3. 4.

— ◊ D = r, where D is electric displacement. The electric flux lines, if they end, will end on electric charges. — ◊ b = 0, where b is magnetic flux density. Those magnetic flux lines never terminate. — ◊ E = – db/dt, which is a form of the Faraday law of induction, where E is the electric field density. — ◊ H = i + dD/dt, where H is magnetic field density. Based on the work by Ampere on steady currents, it shows that the line integral of magnetic intensity around a closed curve equals the current encircled, i.

Moore Law (1964) Integrated circuits and microelectronics will double in density every other year (or every one and half years, by some references), according to a binary growth curve, and the design cost and number of functions per circuit will keep pace with complexity (on a 1960 to 1985 time frame). Elements per chip = 2(years/t) where t is 1, 2, 3, … years.

Newton Laws of Motion (Three Laws) (1687); Laws of Dynamics These three basic laws form the basis of classical mechanics; that is, for mechanical problems not involving atomic particles or smaller, and speeds not involving the speed of light. The first law is a restatement of the discovery by Galileo that no force is required for steady, unchanging motion. First Law (Law of Inertia) A body at rest remains at rest, a body in motion continues in motion at constant speed along a straight line, unless the body, whether at rest or moving, is acted upon by an unbalanced force. Second Law (Law of Constant Acceleration) An unbalanced force acting on a body causes the body to accelerate in the direction of the force, with the acceleration directly proportional to the mass (m) of the body: F = m a = W/g a where F = unbalanced force m = mass of the body W = weight of the body a = acceleration g = gravitational constant Third Law [Law of Conservation of Momentum (Motion)] For every action there is an equal and opposite reaction, applies to all forces—electrical, gravitational, magnetic, etc.

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Normal Law; Normal Law of Error; Normal or Gaussian Distribution Law; Gauss Error Curve; Probability Curve The Gaussian distribution and the normal law of error are both often expressed as the same relationship. The Gaussian distribution law is the theoretical frequency distribution for a set of data of any normal, repetitive function, due to chance, represented by a bell-shaped curve symmetrical about a mean. The relationship of the number of events occuring and frequency when the events occur are due to chance only. The probability for distributions that occur due to chance is: f(x) = p = h/(p)1/2 exp(–h2x2) where p = the probability, often written as y = p h = a constant that depends on spread of the data or is a measure of precision x = distance, plus or minus, from the center

Gaussian distribution and normal distribution.

Photoelectric Effect, Laws of (1888)(1924); (Published in 1930) 1. For a given frequency of incident light, the kinetic energy of ejected photoelectrons does not change, but their number increases in direct proportion to the light intensity. 2. When the frequency of incident light changes (increases), no electrons are emitted until a certain threshold frequency is reached (depending on the metal). For higher frequencies, the energy of photoelectrons increases in direct proportion to the difference of the frequency used and the threshold frequencies. This is represented by the Einstein equation: W=hg–f where W = maximum kinetic energy given off by electrons h = Planck constant g = frequency f = minimum energy to remove an electron from a solid (can also be applied to a gas)

Shannon Law or Formula or Theorem (1948) The information transmitted from a message source over a communications system is represented by: C = W log2(1 + P/N) where C = channel capacity in bits per second W = bandwidth P = signal power N = gaussian noise power, N = kTW where k = Boltzmann constant and T = temperature

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General Engineering and Mathematics

Skin Effect In any current carrying conductor the current tends to concentrate toward the outer surface as a result of eddy currents. An alternating current flowing through a pipe produces a magnetic field which produces eddy currents. Eddy current losses, the heat generated by eddy currents is given by: Pe = Ke f 2 bm2 Vol where Pe = power loss by eddy current Ke = eddy current loss constant f = frequency of electricity bm = maximum flux density (webers/m2) Vol = volume of pipe (conductor)

Snell Law (1613*, 1621); Snell Law of Refraction; Descartes Law The relationship of the angle of incidence, the angle of refraction, the velocity light in a first medium, and the velocity in the second medium, gives the index of refraction: n = sin i/sin r

i = v/v´

where n = index of refraction i = angle of incidence r = angle of refraction v = velocity in first medium v´ = velocity in second medium Although the relationship was discovered in 1621, as stated above, and one author claims 1613*, the phenomenon was known at the time of Ptolemy (Claudius) in about the year A.D. 75.

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Thermodynamics, Laws of (1847, 1850, 1851, 1906) The First and Second Laws were stated by R. Clausius in 1850, based on previous work, and were further developed by W. Thomson in 1851. Zeroth Law of Thermodynamics. For systems in equilibrium, there is an intrinsic property: internal energy. Any two bodies or systems in equilibrium with a third body are in equilibrium with each other. A function of the state of a substance that takes on the same value for all substances in thermal equilibrium, which is the temperature. For closed systems, changes in the internal energy are: dU = dQ – dW where dU = change internal energy dQ = heat transferred to system W = external work First Law of Thermodynamics (1842*, 1847). The total energy change of any system together with its surroundings is zero; also called the Law of Conservation of Energy. The energy, including that equivalent to mass, of the universe is constant. The First law was expressed by H. Helmholtz and R. Clausius, was based on work by J. von Mayer (1842), and is an extension of the work of J. Joule. The statement of the first law is: DU = Q + W where DU = the change in internal energy of the system Q = heat absorbed by the system W = work done on the system Second Law of Thermodynamics (1850). A general law of the natural tendency in which the entropy of the universe and of systems in the universe is tending to a maximum, also called Law of Entropy. All processes in nature tend to occur with an increase in entropy; the flow of heat is always from higher to lower temperature. Not all forms of energy are equally interchangeable, with other forms of energy tending to go to heat. The Carnot theorem, DS ≥ 0, published in 1824, provides a working equation embodying the principles of the second law, which was expressed by Lord Kelvin (William Thomson) and by R. Clausius, who coined the word entropy. L. Boltzmann provided the statistical foundation of the second law (1877). Third Law of Thermodynamics (1906). Solutions and gases are excluded from the third law. The Nernst heat theorem, also identified as the third law of thermodynamics, was extended by Planck by adding the postulate that the absolute entropy of a pure solid or a pure liquid approaches zero at 0 K: lim S Æ 0 T Æ0

The entropy is related to thermodynamic probability by: S = k ln W where

S = entropy k = Boltzmann constant W = statistical probability

Thus, the more random the molecules are arranged, the greater the values of W and S. For a completely ordered system, W = 1 and S = 1. An exception is for a crystalline structure, for which quantum theory shows that the entropy at 0° abs. is not zero, because the crystal may exist in more than one state and have entropy residues from nuclear spin.

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Young Modulus, E The Young modulus applies to an elastic material and is the ratio of unit stress to elastic strain, produced in tension or compression: E = Ds/De The Young modulus for aluminum is 10 ¥ 106 psi; steel, 30 ¥ 106 psi; wood, concrete (compression), 5000 psi (34.5 MPa). Elastic materials obey the Hooke law. The Young modulus by stretching of a wire or rod is: M = mgL/pr2 e where M = modulus m = mass L = length

r = radius e = elongation

The modulus of rigidity for twisting of a bar is: M = CL/pr4 q where

C = couple, C = mgx q = twist, radians

L = length r = radius

From Hall, C.W., Laws and Models: Science, Engineering, and Technology, CRC Press, Boca Raton, FL, 2000.

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Types of Manufacturing — Characteristics and Examples Volume Variety Flexibility 1. Job-shop production

2. Mass production

3. Continuous production

Very low Highest Highest

High Low Low

Highest Lowest Lowest

Tool and die making Casting (foundry) Baking (bakery) Auto assembly Bottling Apparel manufacturing Paper milling Refining Extrusion

From Schonberger, R.J., Types of manufacturing, in The Technology Management Handbook, Dorf, R.C., Ed., CRC Press, Boca Raton, FL, 1999, p. 13-2.

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General Engineering and Mathematics

Coefficient of Friction—Identical Metals* Courtesy of Edmond E. Bisson and Donald H. Buckley The following table gives coefficients of kinetic sliding friction for polycrystalline pure metals in contact with themselves. Coefficient of Friction Lubricated Oil or Grease†

Metal

Unlubricated

Solid Film MoS2

Dry-Sliding in Air

Vacuum, with Surfaces Cleaned

1.0 1.0 1.2 0.3 0.4 (4)

Seizure (2) Seizure Seizure 3.0 (3) —

1.2–1.5 0.8 1.5 2.0 (8) 1.0 1.2 0.4 0.4 2.0

Seizure (6) Seizure Seizure Seizure Seizure Seizure 3.0–5.0 (6) 4.0 —

0.4 0.4 0.4 0.6 0.6 0.4 0.3 0.3 0.3 0.5 0.8 0.9

0.5 0.6 0.3 1.2 0.5 0.3 0.6 0.5 0.4 0.4

Body-Centered Cubic Iron on iron Tantalum on tantalum Molybdenum on molybdenum Tungsten on tungsten Chromium on chromium

0.15 0.1 0.1 0.1 0.34

.04–.08 .04–.08 .04–.08 .04–.08 .04–.08

Face-Centered Cubic Copper on copper Nickel on nickel Silver on silver Gold on gold Aluminum on aluminum Platinum on platinum Rhodium on rhodium Iridium on iridium Lead on lead

0.08 0.28 0.55 0.2 0.12 0.25 0.1 0.1 0.1

Beryllium on beryllium Magnesium on magnesium Lanthanum on lanthanum Titanium on titanium Zirconium on zirconium Rhenium on rhenium Osmium on osmium Ruthenium on ruthenium Thallium on thallium Cobalt on cobalt Cadmium on cadmium Zinc on zinc

0.1 0.08 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.05 0.04

.04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 — —

Hexagonal .04–.08 .04–.08 — .04–.08 .04–.08 .04–.08 — — — .04–.08 .04–.08 —

(6) (7) (7)

(6)

(6) (6) (6) (6) (6) (6) (6) (6) (6) (6)

(4) (4)

— —

(4)

—

Rhombohedral Bismuth

—

—

0.9

†Paraffinic oil plus 1% lauric acid.

Metal Copper on copper Steel on steel

© 2004 by CRC Press LLC

Surface Film Oxide Sulfide Oxide Fe2O3 Fe3O4 Sulfide (FeS) Chloride (FeCl2) Oleic Acid Graphite Telfon (PTFE)

Coefficient of Friction 0.8 0.7

(4) (4)

0.6 0.4 0.5 0.1 0.1 0.1 0.04

(9) (9) (9) (9) (9) (9) (4)

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Coefficient of Friction—Identical Metals* (continued) * Values are principally from Reference 1 and NASA data, except where indicated by other reference numbers in parentheses. References 1. “The Friction and Lubrication of Solids,” F.P. Bowden and D. Tabor, Parts I and II, Oxford Press, Part I: 1958, Part II: 1964. 2. “Influence of Chemisorbed Films on Adhesion and Friction of Clean Iron,” D.H. Buckley, NASA TN D–4775, 1968. 3. “Influence of Chemisorbed Films of Various Gases on Adhesion and Friction of Tungsten,” D.H. Buckley, J. Appl. Phys., 39(9): 4224–4233, 1968. 4. “Friction and Wear,” I.V. Kragelskii, Butterworths, 1965; available as an English translation. 5. “The Influence of Crystal Structure. Orientation and Solubility on the Adhesion and Sliding of Various Metal Single Crystals in Vacuum (10–11 Torr),” D.H. Buckley, ASTM SP–431, 1968, pp. 248–271. 6. “The Influence of Crystal Structure and Some Properties of Hexagonal Metals on Friction and Adhesion,” D.H. Buckley and R.L. Johnson, Wear, 11:405–419, 1968. 7. “Friction and Wear of Materials,” E. Rabinowicz, John Wiley & Sons, 1965. 8. “The Lubrication of Gold,” M. Antler, Wear, 6: 44–65, 1963. 9. “Advanced Bearing Technology,” E.E. Bisson and W.J. Anderson, NASA SP-38, 1964 From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 610–611.

Coefficient of Friction—Identical Alloy Pairs Courtesy of Edmond E. Bisson and Donald H. Buckley Coefficients of Kinetic Sliding Friction for Pairs of Identical Metal Alloys Coefficient of Friction* Lubricated

Unlubricated

Alloy

Oil or Grease†

Solid Film MoS2

Dry-Sliding in Air

Vacuum, with Surface Cleaned

1020 steel on 1020 steel 52100 steel on 52100 steel 440–C S.S. on 440–C S.S. 304 S.S. on 304 S.S. Cast iron on cast iron M-1 tool steel on M-1 tool steel Brass on brass Rene 41 on Rene 41 Inconel on Inconel Hastelloy D on Hastelloy D Cermet K 162 B on Cermet K 162 B Stellite Star J on Stellite Star J Co-25 Mo on Co-25 Mo Ti-12 Sn on Ti-12 Sn Ti-16 Al on Ti-16 Al

0.1 0.1 0.1 0.1 0.1 0.1 0.1 (2) 0.1 0.1 0.1 0.1 0.1 0.08 — —

.04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 (2) .04–.08 .04–.08 — .04–.08 .04–.08 0.04 — —

0.5 (1) 0.5 (1) 0.4 (1) 0.9 (1) 0.3 (4) 0.5 (1) 0.4 (4) 0.4 (1) 0.8 (1) 0.7 (1) 0.2 (1) 0.3 (1) 0.5 (3) 0.8 (1) 0.5 (3)

Seizure 5.0 (1) 2.5 Seizure — — — 4.0 Seizure Seizure 1.0 0.5 (1) 0.3 0.6 (3) 0.3 (3)

† Lubricated with a mineral oil containing oxidation and corrosion inhibitors. * Data from NASA—Lewis Research Center, except where indicated by reference numbers in parentheses. References 1. “Advanced Bearing Technology,” E.E. Bisson and W.J. Anderson, NASA SP-38, 1964. 2. “Friction and Wear,” I.V. Kragelskii, Butterworths, 1965; available as an English translation. 3. “Friction and Wear of Hexagonal Metals and Alloys as Related to Crystal Structure and Lattice Parameters in Vacuum,” D.H. Buckley and R.L. Johnson, ASLE Trans., 9: 121–135, 1966. 4. “Friction and Wear of Materials,” E. Rabinowicz, John Wiley & Sons, 1965. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 611.

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Coefficient of Friction—Dissimilar Metals Courtesy of Edmond E. Bisson and Donald H. Buckley Following are coefficients of kinetic sliding friction for dissimilar pure metals in contact with each other. Coefficient of Friction* Lubricated

Unlubricated

Metal Couple

Oil or Grease†

Solid Film MoS2

Dry-Sliding in Air

Vacuum, with Surface Cleaned

Aluminum on iron Aluminum on zinc Cadmium on aluminum Cadmium on bismuth Cadmium on iron Cadmium on zinc Cobalt on iron Cobalt on copper Cobalt on aluminum Copper on cadmium Copper on zinc Copper on iron Copper on nickel Copper on tungsten Nickel on tungsten Zinc on iron Zinc on antimony Zinc on bismuth

0.1 0.1 (1) 0.1 (1) 0.1 (1) 0.1 0.1 (1) 0.1 0.1 0.1 (1) 0.1 (1) 0.1 (1) 0.1 0.1 0.1 0.1 0.1 (1) 0.1 (1) 0.1 (1)

.04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08 .04–.08

1.1 (2) 0.8 (2) 0.6 (2) 0.8 (2) 0.6 (2) 0.6 (2) 0.5 (2) 0.9 (2) 1.0 (2) 0.9 (2) 0.9 (2) 1.0 (2) 1.2 (4) 0.4 (4) 0.3 (4) 0.9 (2) 0.9 (2) 0.7 (2)

Seizure — — — — — 0.7 (3) — — — — 5.0 (1) 2.0 (4) 0.5 (4) 4.0 (4) — — —

†Lubricated with mineral oil containing oxidation and corrosion inhibitors. Coefficient of Friction* Material Combination Hard steel on Babbitt (ASTM 1) Hard steel on Babbitt (ASTM 8) Hard steel on Babbitt (ASTM 10) Monel on SAE 52100 bearing steel Beryllium copper on SAE 52100 bearing stgeel Brass on SAE 52100 bearing steel Bronze on SAE 52100 bearing steel Gray cast iron on SAE 52100 bearing steel Nodular iron on SAE 52100 bearing steel Nichrome V on SAE 52100 bearing steel 24ST-aluminum on SAE 52100 bearing steel

Dry-Sliding

Boundary Lubrication‡

0.33 (6) 0.35 (6) — 0.4 (5) 0.8 (5) 0.5 (5) 0.3 (5) 0.6 (5) 0.5 (5) 0.3 (5) 0.3 (5)

0.16 (6) 0.14 (6) 0.13 (6) 0.33 (5) 0.10 (5) 0.12 (5) 0.17 (5) 0.29 (5) 0.17 (5) 0.13 (5) 0.17 (5)

‡ Paraffinic oil with oxidation and corrosion inhibitor. * Values from NASA data, except where indicated by reference numbers in parentheses. References 1. “Friction and Wear,” I.V. Kragelskii, Butterworths, 1965; available as an English translation. 2. “Surface Friction of Clean Metals—A Basic Factor in the Metal Cutting Process,” H. Ernst and M.E. Merchant, Proc. Conf. Friction and Surface Finish, MIT, June 1940, pp. 76–101. 3. “Marked Influence of Crystal Structure on the Friction and Wear Characteristics of Cobalt and Cobalt Base Alloys in Vacuum to 10–9 Millimeter of Mercury,” D.H. Buckley and R.L. Johnson, NASA TN D–2523, 1964. 4. “The Influence of Crystal Structure, Orientation and Solubility on the Adhesion and Sliding of Various Metal Single Crystals in Vacuum (10–11 Torr),” D.H. Buckley, ASTM SP–431, pp. 248–271, 1968. 5. “Investigation of Wear and Friction Properties Under Sliding Conditions of Some Materials, Suitable for Cages of Rolling-Contact Bearings,” R.L. Johnson, M.A. Swikert, and E.E. Bisson, NACA Report 1062, 1952. 6. “Studies in Boundary Lubrication,” W.E. Campbell, Trans. ASME, 61(7): 633–641, 1939. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 612.

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Coefficient of Friction—Single Crystals* Courtesy of Edmond E. Bisson and Donald H. Buckley The following tables give coefficients of kinetic sliding friction for single crystals—metals and non-metals. Metals Coefficient of Friction Metal Single crystal copper on single crystal copper Single crystal cobalt on polycrystalline cobalt Single crystal magnesium on polycrystalline magnesium Single crystal rhenium on polycrystalline rhenium Single crystal beryllium on polycrystalline beryllium Single crystal titanium on polycrystalline titanium Single crystal tungsten on single crystal tungsten

Atomic Plane

In Air, 20˚C

In Vacuum, Clean

(100) (110) (111) (0001) (1010) (0001) (1010) (0001) (1010) (0001) (1010) (0001) (1010) (100) (110) (210)

0.60 0.40 0.21 0.40 — 0.30 — 0.20 0.25 0.45 0.46 0.48 0.25 0.60 0.41 0.40

>40 >40 21.0 0.35 0.80 0.40 0.90 0.29 0.38 0.48 0.51 0.56 0.36 3.0 (2) 1.9 (2) 1.3 (2)

Non-Metals Coefficient of Friction Material Diamond on diamond

Sapphire on sapphire

Diamond on magnesium oxide Diamond on lithium fluoride Diamond on potassium fluoride Diamond on sodium chloride Diamond on potassium bromide

Atomic Plane and Direction (100) (100) (111) (0001) (0001) (1010) (1010) (100) (100) (100) (100) (100)

<100> <110> — <1120> <1010> <1120> <0001> <100> <110> <110> <110> <110>

In Air, 20˚C 0.15 (3,4) 0.05 (3,4) 0.05 (3,4) 0.15 — 0.20 — 0.07 0.24 0.71 0.47–0.70 0.85

In Vacuum, Clean — — 0.9 (4) 0.50 0.96 0.93 1.00 — 0.80 — — —

* Data from Reference 1 unless otherwise indicated by reference numbers in parentheses. References 1. “The Influence of the Atomic Nature of Crystalline Materials on Friction,” D.H. Buckley, ASLE Trans., 2:89–100, 1968. 2. “Influence of Film of Various Gases on Adhesion and Friction of Tungsten,” D.H. Buckley, J. Appl. Phys., 39(9): 4224–4233, 1968. 3. “The Abrasion of Diamond,” M. Seal, Roy. Soc. Proc., Series A, 248:379–393, 1958. 4. “The Friction and Lubrication of Solids,” F.P. Bowden and D. Tabor, Part I, Oxford University Press, 1958. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 613.

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Coefficient of Friction—Non-Metals* Courtesy of Edmond E. Bisson and Donald H. Buckley Listed below are coefficients of kinetic sliding friction for plastics and other non-metals in identical pairs and on steel. Coefficient of Friction Dry-Sliding in Air

Vacuum, with Clean Surface

Material

On Itself

On Steel

On Itself

On Steel

Teflon (PTFE) Nylon Perspex Polystyrene PCFE Polyimide Bakelite Titanium carbide Glass Diamond Sapphire Mica Carbon Graphite

0.1 0.15–0.25 0.8 0.5 0.2 — 0.3 0.2 1.0 0.1 (2) 0.2 (3) 1.0 0.2 0.1

0.04 0.2 0.5 0.3 0.08 0.25 (7) 0.30 (8) 0.5 0.6 0.1 0.15 (4) — 0.15 0.1

— — — — — 0.5 (7) — 0.9 — 0.9 0.8 (5) — — 0.8

.2–.3 (7) — — — 0.3 (7) 0.2 (7) — — — — 0.2 (5) — 0.4 (6) 0.3 (6)

* Data from Reference 1 unless otherwise indicated by reference numbers in parentheses. References 1. “The Friction and Lubrication of Solids,” F.P. Bowden and D. Tabor, Part I, Oxford University Press, 1954. 2. “The Abrasion of Diamond,” M. Seal, Roy. Soc. Proc., Series A, 248:379–393, 1958. 3. “Friction and Wear of Single Crystals,” R.P. Steijn, Wear-Usure-Verschleiss, 7(1): 48–66, 1964. 4. “Friction and Wear of Single-Crystal Sapphire Sliding on Steel,” S.J. Duwell, J. Appl. Phys., 33: 2691–2698, 1962. 5. “Friction Characteristics in Vacuum of Single and Polycrystalline Aluminum Oxide in Contact with Themselves and with Various Metals,” D.H. Buckley, ASLE Trans., 10: 134–145, 1965. 6. “Mechanism of Lubrication for Solid Carbon Materials in Vacuum to 10–9 Millimeters of Mercury,” D.H. Buckley and R.L. Johnson, ASLE Trans., 7(1): 91–100, 1964. 7. “Degradation of Polymeric Composition in Vacuum to 10–9 mm Hg in Evaporation and Sliding Friction Experiments,” D.H. Buckley and R.L. Johnson, SPE Trans., 4(4): 1–9, 1964. 8. M.B. Peterson and J.F. Murray, Requirements of Materials for Sliding and Rolling Contacts, “Boundary Lubrication,” American Society of Mechanical Engineers, 1969, Chapter 9. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 614.

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Coefficient of Friction—Lubricating Powders Courtesy of Edmond E. Bisson and Donald H. Buckley Listed below are coefficients of kinetic sliding friction for steel on steel (SAE 4620 on SAE 1020) with various powders between the surfaces. Powder Cadmium iodide, CdI2 Cadmium chloride, CdCl2 Tungsten disulfide, WS2 Silver sulfate, Ag2SO4 Lead iodide, PbI2

Coefficient of Friction†

Powder

Coefficient of Friction†

0.06 0.07 0.08 0.14 0.28

Zinc stearate, Zn (C18H35O2)2 Cobalt chloride, CoCl2 Mercury iodide, HgI2 Copper bromide, CuBr2 Silver iodide, AgI

0.11 0.10 0.18 0.06 0.25

† Data compiled from: “Advanced Bearing Technology,” E.E. Bisson and W.J. Anderson, NASA SP-38, 1964. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 614.

Coefficients of Static and Sliding Friction Reference letters indicate the lubricant used; numbers in parentheses give sources (see References). Key to Lubricants Used; a = oleic acid b = Atlantic spindle oil (light mineral) c = caster oil d = lard oil e = Atlantic spindle oil plus 2% oleic acid f = medium mineral oil g = medium mineral oil plus 1/2% oleic acid h = stearic acid i = grease (zinc oxide base) j = graphite k = turbine oil plus 1% graphite l = turbine oil plus 1% stearic acid

m = turbine oil (medium mineral) n = olive oil p = palmitic acid q = ricinoleic acid r = dry soap s = lard t = water u = rape oil v = 3-in-1 oil w = octyl alcohol x = triolein y = 1% lauric acid in paraffin oil Static

Materials

Dry

Hard steel on hard steel

0.78 (1)

Mild steel on mild steel

0.74 (19)

Hard steel on graphite Hard steel on Babbitt (ASTM 1)

0.21 (1) 0.70 (11)

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Sliding Greasy

Dry

Greasy

0.11 (1, a) 0.23 (1, b) 0.15 (1, c) 0.11 (1, d) 0.0075 (18, p) 0.0052 (18, h)

0.42 (2)

0.029 (5, h) 0.081 (5, c) 0.080 (5, i) 0.058 (5, j) 0.084 (5, d) 0.105 (5, k) 0.096 (5, l) 0.108 (5, m) 0.12 (5, a) 0.09 (3, a) 0.19 (3, u)

0.57 (3) 0.09 (1, a) 0.23 (1, b) 0.15 (1, c) 0.08 (1, d) 0.085 (1, e)

0.33 (6)

0.16 (1, b) 0.06 (1, c) 0.11 (1, d)

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Coefficients of Static and Sliding Friction (continued) Static Materials Hard steel on Babbitt (ASTM 8)

Dry 0.42 (11)

Hard steel on Babbitt (ASTM 10)

Mild steel on cadmium silver Mild steel on phosphor bronze Mild steel on copper lead Mild steel on cast iron Mild steel on lead Nickel on mild steel Aluminum on mild steel Magnesium on mild steel Magnesium on magnesium Teflon on Teflon Teflon on steel Tungsten carbide on tungsten carbide Tungsten carbide on steel Tungsten carbide on copper Tungsten carbide on iron Bonded carbide on copper Bonded carbide on iron Cadmium on mild steel Copper on mild steel Nickel on nickel Brass on mild steel Brass on cast iron Zinc on cast iron Magnesium on cast iron Copper on cast iron Tin on cast iron Lead on cast iron Aluminum on aluminum Glass on glass

Sliding Greasy

0.17 (1, b) 0.11 (1, c) 0.09 (1, d) 0.08 (1, e) 0.25 (1, b) 0.12 (1, c) 0.10 (1, d) 0.11 (1, e)

Dry

Greasy

0.35 (11)

0.14 (1, b) 0.065 (1, c) 0.07 (1, d) 0.08 (11, h) 0.13 (1, b) 0.06 (1, c) 0.055 (1, d)

0.34 (3)

0.95 (11)

0.183 (15, c) 0.5 (1, f)

0.61 (8) 0.6 (22) 0.04 (22) 0.04 (22) 0.2 (22) 0.5 (22) 0.325 (23) 0.8 (23) 0.35 (23) 0.8 (23)

0.08 (22, y) 0.04 (22, f ) 0.04 (22, f ) 0.12 (22, a) 0.08 (22, a)

0.53 (8) 1.10 (16) 0.51 (8) 0.85 (16) 1.05 (6)

1.05 (16) 0.94 (8)

0.23 (6) 0.95 (11) 0.64 (3) 0.47 (3) 0.42 (3)

0.01 (10, p) 0.005 (10, g)

0.46 (3) 0.36 (3) 0.53 (3) 0.44 (6) 0.30 (6) 0.21 (7) 0.25 (7) 0.29 (7) 0.32 (7) 0.43 (7) 1.4 (3) 0.40 (3)

Carbon on glass Garnet on mild steel Glass on nickel Copper on glass Cast iron on cast iron

0.78 (8) 0.68 (8) 1.10 (16)

0.18 (3) 0.39 (3) 0.56 (3) 0.53 (3) 0.15 (9)

Bronze on cast iron Oak on oak (parallel to grain)

0.62 (9)

0.22 (9) 0.48 (9)

Oak on oak (perpendicular) Leather on oak (parallel) Cast iron on oak Leather on cast iron Laminated plastic on steel Fluted rubber bearing on steel

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0.54 (9) 0.61 (9)

0.097 (2, f ) 0.173 (2, f ) 0.145 (2, f ) 0.133 (2, f ) 0.3 (11, f ) 0.178 (3, x)

0.32 (9) 0.52 (9) 0.49 (9) 0.56 (9) 0.35 (12)

0.18 (17, a) 0.12 (3, w)

0.09 (3, a) 0.116 (3, v)

0.070 (9, d) 0.064 (9, n) 0.077 (9, n) 0.164 (9, r) 0.067 (9, s) 0.072 (9, s) 0.075 (9, n) 0.36 (9, t) 0.13 (9, n) 0.05 (12, t) 0.05 (13, t)

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Coefficients of Static and Sliding Friction (continued) References (1) Campbell, Trans. ASME, 1939; (2) Clarke, Lincoln, and Sterrett, Proc. API, 1935; (3) Beare and Bowden, Phil. Trans. Roy. Soc., 1935; (4) Dokos, Trans. ASME, 1946; (5) Boyd and Robertson, Trans. ASME, 1945; (6) Sachs, zeit. f. angew. Math. und Mech., 1924; (7) Honda and Yamala, Jour. I of M, 1925; (8) Tomlinson, Phil. Mag., 1929; (9) Morin, Acad. Roy. des Sciences. 1838; (10) Claypoole, Trans. ASME, 1943; (11) Tabor, Jour. Applied Phys., 1945; (12) Eyssen, General Discussion on Lubrication. ASME, 1937; (13) Brazier and Holland-Bowyer, General Discussion on Lubrication, ASME, 1937; (14) Burwell, Jour. SAE, 1942; (15) Stanton, “Friction,” Logmans; (16) Ernst and Merchant, Conference on Friction and Surface Finish, M.I.T., 1940; (17) Gongwer, Conference on Friction and Surface Finish, M.I.T., 1940; (18) Hardy and Bircumshaw, Proc. Roy. Soc., 1925; (19) Hardy and Hardy, Phil. Mag., 1919; (20) Bowden and Young, Proc. Roy. Soc., 1951; (21) Hardy and Doubleday, Proc. Roy. Soc., 1923; (22) Bowden and Tabor, “The Friction and Lubrication of Solids,” Oxford; (23) Shooter, Research, 4, 1951. From Bolz, R.E. and Tuve, G.L., Friction and lubrication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 621–622.

The Greek Alphabet Greek Letter

Greek Name

English Equivalent

Greek Letter

Greek Name

English Equivalent

A B

a b

Alpha Beta

(ä) (b)

N X

v x

Nu Xi

(n) (ks)

G D E

g d e

Gamma Delta Epsilon

(g) (d) (e)

O P R

o p r

Omicron Pi Rho

(o) (p) (r)

Z H

z h

Zeta (z) Eta

(z) – (a)

S T

s V t

Sigma Tau

(s) (t)

Q

q

Theta

(th)

U

u

Upsilon

(ü, oo )

I K

i k

Iota Kappa

– (e) (k)

F C

f c

Phi Chi

(f) (H)

L M

l m

Lambda Mu

(l) (m)

Y W

y w

Psi Omega

(ps) (o)

From Bolz, R.E. and Tuve, G.L., Communication, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 793.

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Units and Their Conversion Policy of this Edition In each table in this handbook, the numerical values are preferably expressed in those units most commonly used by U.S. engineers working in the specific field, but SI metric units have also been added. In some cases two tables are given, one in English units, one in metric. In other tables parallel columns showing figures in both units are used, or the conversion factors are listed. In a general engineering handbook complete consistency in units, abbreviations, and symbols is hardly possible, or even desirable. Such consistency would quickly defeat the objective of providing quick access to numbers of maximum immediate usefulness. Within each special field of engineering, the technical societies and industry associations have developed certain uniform practices and standards; if tables and data are given only in units that are foreign to these prevailing standards, convenience is sacrificed. In any case the practical demands of compilation and new typesetting costs, and the usual requirement of a copyright owner that reprinted material should not be changed, may well govern the units used in any given table. The present edition of this handbook reflects the changes in abbreviations, symbols, and forms that are resulting from the efforts to reduce the diversity of practices from one specialty to another and from one nation to another. Recommendations of the International Organization for Standardization (ISO–R 1000) and of the “Metric Practice Guide,” adopted by ASTM, NBS, APL, and others, have focused attention on the diversity of so-called standards. Since the United States is the only major industrial nation that has not yet converted to metric units, some legal requirements in that direction are to be expected. It is now a contradiction to speak of the “English” system of units, and for some time to come U.S. engineers must accommodate to a wide use of conversions from one set of units to another. The extensive conversion tables that follow are offered with this expectation. In spite of major efforts to unify engineering practices, there are many good reasons for retaining several means of expressing a physical quantity. For ease of learning and communication a descriptive name is better than one arbitrarily assigned, such as Hz for cps, celsius for centigrade, and torr for mm Hg; an opposite trend is prevalent at this time. Numerical scales directly related to the physical phenomena and to the method of their measurement have an advantage in the laboratory or field and will not soon be abandoned. Examples are barometric pressure in mm or in. of mercury, viscosity in seconds Saybolt, the calorie or the Btu, and even the “coefficients” of expansion, friction, diffusion, attenuation, and reflection. Symbols, abbreviations, and even the units themselves are not infrequently subject to change; note, for example, the now preferred dB in place of the well-established db; elimination of widely used abbreviations, such as kwh, cps, gpm, cc, and psi; and revised values for the second, the calorie, or the atomic weights. Users of this handbook are invited to call attention to places where consistency could be improved without sacrificing the objectives. Of the many named units that might have more than one value, this book uses (unless otherwise stated) the thermochemical gram-calorie (4.184 J), the thermochemical Btu (1 054.35 J), the avoirdupois pound and ounce, the statue mile (5 280 ft), the short ton (2 000 lb), the U.S. liquid gallon (231 in.3), and the electrical horsepower (746 W). Rather than present a special and condensed table of engineering conversion factors, the editors have chosen to reprint the large table that has been developed over the years for the Handbook of Chemistry and Physics. Certain specialized conversion factors and tables have been included. The Metric International System (SI) Moves toward an international system of metric units are now following each other in quick succession, so a table of conversion factors for the most common units is given herewith. Perhaps the most definite are the moves toward the SI standards already initiated by the National Bureau of Standards, the various military services, the National Aeronautics and Space Administration, and other U.S. Government research groups. The American Society for Testing and Materials has declared in favor of SI units and will give other units only a secondary place in all newly issued ASTM Standards. a Other major engineering societies have committees to explore the adoption of SI units and are holding many meetings for discussion among members. Whatever the decisions about converting to the metric system, the actual process will require many years, as can readily be seen from the experiences of other countries; in Great Britain, for example, even the single conversion to decimal monetary units and coinage moves very slowly. The practices and standards among the metric-system countries are far from uniform; no real international system exists among them. Mere conversion of present U.S. specifications, drawings, tools, machines, and stock sizes, to equivalent metric units (so-called “soft” conversion) will not in any sense result in an “international” system. Instead, a “hard” conversion representing the abandonment of the 1/2-fractional system in favor of a 1/10-fractional system is necessary to attain the real advantages of the metric system. This means re-sizing of all round and sheet stock, lumber, bolts, screws, nails, wires, gears, containers, modules, and sub-assemblies, plus all the tools and machines related thereto. A long period of doublestocking must follow. The entire change is made the more difficult by the great penetration of U.S. products and materials into the markets of the world, e.g., airplanes and military equipment, production, and construction machinery. This is not to mention the problem of the individual engineer, technician, and user, who visualizes all his size relationships in inches

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Units and Their Conversion (continued) and feet and his weights in pounds. Realistically, more than one generation will be required for the educational conversion alone. In presenting data in international standard metric units throughout this edition, the practices and forms used in the “Metric Practice Guide” have been carefully followed.a Certain conventions used in the “Metric Practice Guide” are not consistent with those originally adopted for this handbook, nor with ANSI standards. Special attention is directed to the following conventions: 1. For degrees Kelvin the degree symbol is omitted; for example, 50 K, not 50˚K. 2. For multiplication a center point is used; for example, the unit of dynamic viscosity is abbreviated as N·s/m 2, not N s/m2 or N ¥ s/m2. 3. Symbols for SI units are not capitalized unless the unit is derived from a proper name, as N for Sir Isaac Newton; however, unabbreviated units are not capitalized, such as newton, kelvin, hertz.

To Convert Acceleration feet/second2 Area square feet Energy Btu (mean) calorie (mean) electron volt foot-pound watthour Force dyne kilogram pound Length foot mil mile (U.S. statute) Mass pound slug ton (2000 lb) a

To

Conversion Factors to SI Standard Units Multiply by To Convert To

meters/second2

0.3048

square meters

0.09290304

joule joule joule joule joule Newton Newton Newton meter meter meter

kilogram kilogram kilogram

1055.87 4.19002 1.60210 ¥ 10–19 1.355818 3600. 0.00001 9.80665 4.448222 0.3048000 0.0000254 1609.344

0.4535924 14.59390 907.1847

Power Btu/second foot-pounds/ second horsepower Pressure atmosphere bar kilograms/cm2 pounds/in.2 torr (mm Hg. 0°C) Viscosity centipoise pounds/foot second Volume cubic foot gallon (U.S. liquid)

watt watt watt

Multiply by 1054.350 1.355818 746.

newtons/meter2 newtons/meter2 newtons/meter2 newtons/meter2 newtons/meter2

101325.0 100000. 98066.50 6894.757 133.322

newton-second/ meter2 newton-second/ meter2

0.001

1.488164

cubic meter cubic meter

0.02831685 0.003785412

See “Metric Practice Guide,” ASTM Standard E 380–70, American Society for Testing and Materials, 1970. From Bolz, R.E. and Tuve, G.L., Units and conversion factors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 803–804.

© 2004 by CRC Press LLC

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General Engineering and Mathematics

International System (SI) Metric Units Basic Units–MKS Length Mass Time

meter kilogram second

m kg s

Electric current Thermodynamic temperature Luminous intensity

ampere kelvin candela

Derived Units Property

Unis†

Abbreviations and Dimensions

Acceleration Activity (of radioactive source) Angular acceleration Angular velocity Area

meter per second squared 1 per second radian per second squared radian per second square meter

m/s2 s–1 rads/s–1 rad/s m2

Density Dynamic viscosity Electric capacitance Electric charge Electric field strength

kilogram per cubic meter newton-second per sq meter farad coulomb volt per meter

kg/m3 N·s/m2 F C V/m

Electric resistance Entropy Force Frequency Illumination

ohm joule per kelvin newton hertz lux

J/K N hz lx

Inductance Kinematic viscosity Luminance Luminous flux Magnetomotive force

henry sq meter per second candela per sq meter lumen ampere

H m2/s cd/m2 lm A

Magnetic field strength Magnetic flux Magnetic flux density Power Pressure

ampere per meter weber tesla watt newton per square meter

A/m Wb T W N/m2

Radiant intensity Specific heat Thermal conductivity Velocity Volume

watt per steradian joule per kilogram kelvin watt per meter kelvin meter per second cubic meter

W/sr J/kg K W/m K m/s m3

Voltage, potential difference, electromotive force Wave number Work, energy, quantity of heat

volt

V

(W/A)

1 per meter joule

m–1 J

(N·m)

© 2004 by CRC Press LLC

(A·s/V) (A·s)

(V/A) (kg·m/s2) (s–1) (lm/m2) (V·s/A)

(cd·sr)

(V·s) (Wb/m2) (J/s)

A K cd

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CRC Handbook of Engineering Tables

International System (SI) Metric Units (continued) Prefix Names of Multiples and Submultiples of Units Decimal Equivalent

Prefix

Pronunciation

Symbol

Exponential Expression

1,000,000,000,000 1,000,000,000 1,000,000 1,000 100

tera giga mega kilo hecto

tˇer¢a· j ˇi¢ga· mˇeg¢a· kˇil¢o– hˇek¢to–

T G M k h

10+12 10+9 10+6 10+3 10+2

10 0.1 0.01 0.001 0.000 001

deka deci centi milli micro

dˇek¢a· dˇes¢ˇi sˇent¢ˇi m ˇil¢ˇi – mi¢kro–

da d c m m

10 10–1 10–2 10–3 10–6

0.000 000 001 0.000 000 000 001 0.000 000 000 000 001 0.000 000 000 000 000 001

nano pico femto atto

naˇ n¢o– pˇe¢ko– feˇm¢to– aˇ t¢to–

n p f a

10–9 10–12 10–15 10–18

Definitions of the Most Important International System (SI) Units The ampere (unit of electric current) is the constant current that, if maintained in two straight parallel conductors of infinite length, of negligible circular sections, and placed 1 meter apart in a vacuum, will produce between these conductors a force equal to 2 ¥ 10–7 newton per meter of length. The candela is the luminous intensity, in the direction of the normal, of a blackbody surface 1/600,000 square meter in area, at the temperature of solidification of platinum under a pressure of 101,325 newtons per square meter. The coulomb (unit of quantity of electricity) is the quantity of electricity transported in 1 second by a current of 1 ampere. The ephemeris second (unit of time) is exactly 1/31 556 925.974 7 of the tropical year of 1900, January, 0 days, and 12 hours ephemeris time. The fraud (unit of electric capacitance) is the capacitance of a capacitor between the plates of which there appears a difference of potential of 1 volt when it is charged by a quantity of electricity equal to 1 coulomb. The henry (unit of electric inductance) is the inductance of a closed circuit in which an electromotive force of 1 volt is produced when the electric current in the circuit varies uniformly at a rate of 1 ampere per second. The International Practical Kelvin Temperature Scale of 1960 and the International Practical Celsius Temperature Scale of 1960 are defined by a set of interpolation equations based on the following reference temperatures:

Oxygen, liquid-gas equilibrium Water, solid-liquid equilibrium Water, solid-liquid-gas equilibrium Water, liquid-gas equilibrium Zinc, solid-liquid equilibrium Sulfur, liquid-gas equilibrium Silver, solid-liquid equilibrium Gold, solid-liquid equilibrium

K

Deg C

90.18 273.15 273.16 373.15 692.655 717.75 1233.95 1336.15

–182.97 0.00 0.01 100.00 419.505 444.6 960.8 1063.0

The joule (unit of energy) is the work done when the point of application of 1 newton is displaced a distance of 1 meter in the direction of the force. The kelvin (unit of thermodynamic temperature) is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The decision was made at the 13th General Conference on Weights and Measures on October 13, 1967, that the name of the unit of thermodynamic temperature would be changed from degree Kelvin (symbol: ˚K) to kelvin (symbol: K). The name (kelvin) and symbol (K) are to be used for expressing temperature intervals. The former convention that expressed a temperature interval in degrees Kelvin or, abbreviated, deg K is dropped. However, the old designations are acceptable temporarily as alternatives to the new ones. One may also express temperature intervals in degrees Celsius.

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General Engineering and Mathematics

5-69

International System (SI) Metric Units (continued) The kilogram (unit of mass) is the mass of a particular cylinder of platinum iridium alloy, called the International Prototype Kilogram, which is preserved in a vault at Sèvres, France, by the International Bureau of Weights and Measures. Length: The name micron, for a unit of length equal to 10–6 meter, and the symbol m that has been used for it were dropped by action of the 13th General Conference on Weights and Measures on October 13, 1967. The symbol m is to be used solely as an abbreviation for the prefix micro-, standing for the multiplication by 10–6. Thus the length previously designated as 1 micron should be designated 1 mm. The lumin (unit of luminous flux) is the luminous flux emitted in a solid angle of 1 steradian by a uniform point source having an intensity of 1 candela. The newton (unit of force) is that force that gives to a mass of 1 kilogram an acceleration of 1 meter per second. The ohm (unit of electric resistance) is the electric resistance between two points of a conductor when a constant difference of potential of 1 volt, applied between these two points, produces in this conductor a current of 1 ampere, this conductor not being the source of any electromotive force. The meter (unit of length) is the length of exactly 1 650 763.73 wavelengths of the radiation in vacuum corresponding to the unperturbed transition between the levels 2p10 and 5d5 of the atom of krypton 86, the orange-red line. The second is the unit of time of the International System of Units. The definition adopted at the October 13, 1967, meeting of the 13th General Conference on Weights and measures is: “The second is he duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental state of the atom of cesium 133.” The frequency (9 192 631 770 hz), which the definition assigns to the cesium radiation, was carefully chosen to make it impossible, by any existing experimental evidence, to distinguish the new second from the ephemeris second based on the earth’s motion. Therefore no changes need to be made in data stated in terms of the old standard in order to convert them to the new one. The atomic definition has two important advantages over the previous definition: (1) it can be realized (i.e., generated by a suitable clock) with sufficient precision, ± 1 part per hundred billion (1011) or better, to meet the most exacting demands of modern metrology; and (2) it is available to anyone who has access to or who can build an atomic clock controlled by the specified cesium radiation.‡ In addition one can compare other high-precision clocks directly with such a standard in a relatively short time — an hour or so compared against years with the astronomical standard. Laboratory-type atomic clocks are complex and expensive, so that most clocks and frequency generators will continue to be calibrated against a standard such as the NBS Frequency Standard, controlled by a cesium atomic beam, at the Radio Standards Laboratory in Boulder, Colorado. In most cases the comparison will be by way of the standard-frequency and timeinterval signals broadcast by NBS radio stations WWV, WWVH, WWVB, and WWVL. The volt (unit of electric potential difference and electromotive force) is the difference of electric potential between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these points is equal to 1 watt. The watt (unit of power) is the power that gives rise to the production of energy at the rate of 1 joule per second. The weber (unit of magnetic flux) is the magnetic flux that, linking a circuit of one turn, produces in it an electromotive force of 1 volt as it is reduced to zero at a uniform rate in 1 second. † According to SI terminology, the following should be treated as obsolete: angstrom (now 100 picometers or 0.1 nanometer) liter (now cubic decimeter) bar (now 100 kilonewtons/meter2) metric ton (now megagram) kiloliter (now cubic meter) micron (now micrometer) kiloton (now gigagram) ‡ A description of such clocks is given in “Atomic Frequency Standards,” NBS Tech. News Bull., 45:8–11, January 1961. For more developments and technical details, see R.E. Bechler, R.C. Mockler, and J.M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1:114–131, July 1965. From Bolz, R.E. and Tuve, G.L., Units and conversion factors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 805–807.

© 2004 by CRC Press LLC

International Metric System This table can be used for conversion of any quantity in English units to corresponding SI units to give significant figures (without the use of a calculator). Exact values are shown in boldface. Unless otherwise stated, values are in thermochemical calorie, thermochemical Btu, and avoirdupois mass units.a Instruction: Shift decimal as required for each digit in the original quantity and add the converted results. Example: Convert an acceleration of 15.30 ft/s2 to m/s2. Solution: From first line of table, 3.048 0 + 1.524 0 + 0.091 44 = 4.663 4 m/s2. 1 ACCELERATION foot/second2 to meter/ second2, m/s2 g’s (free fall, standard to meter/second2, m/s2 inch/second2 to meter/ second2, m/s2

4

5

6

7

8

9

0.304 8

0.609 6

0.914 4

1.219 2

1.524 0

1.828 8

2.133 6

2.438 4

2,743 2

9.806 65

19.613

29.420

39.227

49.033

58.840

68.647

78.453

88.260

0.025 4

0.050 8

0.076 2

0.101 6

0.127 0

0.152 4

0.177 8

0.203 2

0.228 6

4 046.856 5.067 075 ¥ 10–10 0.092 903 04 0.000 645 16 2 589 988

8 093.7 10.134 ¥ 10–10 0.185 81 0.001 290 32 5 180 000

12 141 15.201 ¥ 10–10 0.278 71 0.001 935 48 7 770 000

16 187 20.268 ¥ 10–10 0.371 61 0.002 580 64 10 360 000

20 234 25.335 ¥ 10–10 0.464 52 0.003 225 80 12 950 000

24 281 30.402 ¥ 10–10 0.557 42 0.003 870 96 15 540 000

28 328 35.470 ¥ 10–10 0.650 32 0.004 516 12 18 130 000

32 375 40.537 ¥ 10–10 0.743 22 0.005 161 28 20 720 000

36 422 45.604 ¥ 10–10 0.836 13 0.005 806 44 23 310 000

0.836 127 36

1.672 3

2.508 4

3.344 5

4.180 6

5.016 8

5.852 9

6.689 0

7.525 1

0.014 123

0.021 185

0.028 246

0.035 308

0.042 369

0.049 431

0.056 492

0.063 554

0.225 97

0.338 95

0.451 94

0.564 92

0.677 91

0.790 89

0.903 88

1.016 9

2.711 6

4.067 5

5.423 3

6.779 1

8.134 9

9.490 7

10.847

12.202

0.034 236

0.051 354

0.068 472

0.085 590

0.102 71

0.119 83

0.136 94

0.154 06

14.978

22.467

29.957

37.446

44.935

52.424

59.913

67.402

BENDING MOMENT OR TORQUE ounce-force-inch to 0.007 061 552 newton-meter, N·m pound-force-inch to 0.112 984 8 newton-meter, N·m pound-force-foot to 1.355 818 newton-meter, N·m DENSITY (MASS/VOLUME) 0.017 118 06 grain/gallon to kilogram/ meter3, kg/m3 ounce/gallon to kilogram/ 7.489 152 meter3, kg/m3

© 2004 by CRC Press LLC

3

CRC Handbook of Engineering Tables

AREA acre to meter2, m2 circular mil to meter2, m2 foot2 to meter2, m2 inch2 to meter2, m2 mile2 (U.S. statute) to meter2, m2 yard2 to meter2, m2

2

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Conversions to SI Units

5 190.0

6 920.0

8 650.0

10 380

12 110

13 840

15 570

16.018 46

32.037

48.055

64.074

80.092

96.111

112.13

128.15

144.17

27 679.90

55 360

83 040

110 720

138 400

166 080

193 760

221 440

249 120

119.826 4

239.65

359.48

479.31

599.13

718.96

838.78

958.61

1 078.4

515.378 8

1 030.8

1 546.1

2 061.5

2 576.9

3 092.3

3 607 7

4 123.0

4 638.4

7 200 192 970

10 800 289 460

14 400 385 950

18 000 482 440

21 600 578 920

25 200 675 410

28 800 771 900

32 400 868 380

0.000 2 1.591 5 159.15

0.000 3 2.387 3 238.73

0.000 4 3.183 1 318.31

0.000 5 3.978 9 397.89

0.000 6 4.774 6 477.46

0.000 7 5.570 4 557.04

0.000 8 6.366 2 636.62

0.000 9 7.162.0 716.20

2.513 3 ¥ 10–7

3.769 9 ¥ 10–7

5.026 5 ¥ 10–7

6.283 2 ¥ 10–7

7.539 8 ¥ 10–7

8.796 5 ¥ 10–7

10.053 ¥ 10–7

11.310 ¥ 10–7

1 054.350

2 108.7

3 163.1

4 217.4

5 271.8

6 326.1

7 380.5

8 434.8

9 489.2

1 055.056

2 220.1

3 165.2

4 220.2

5 275.3

6 330.3

7 385.4

8 440.4

9 495.5

4.184 4.186 8 1.602 10 ¥ 10–19 1.355 818 3 600 000 2 684 520

8.368 8.373 6 3.204 2 ¥ 10–19 2.711 6 7 200 000 5 369 039

12.552 12.560 4 4.806 3 ¥ 10–19 4.067 5 10 800 000 8 053 559

16.736 16.747 2 6.408 4 ¥ 10–19 5.423 3 14 400 000 10 738 078

20.920 20.934 0 8.010 5 ¥ 10–19 6.779 1 18 000 000 13 422 598

25.104 25 120 8 9.612 6 ¥ 10–19 8.134 9 21 600 000 16 107 117

29.288 29.307 6 11.215 ¥ 10–19 9.490 7 25 200 000 18 791 637

33.472 33.494 4 12.817 ¥ 10–19 10.847 28 800 000 21 476 156

37.656 37.681 2 14.419 ¥ 10–19 12.202 32 400 000 24 160 676

0.000 471 947 4

0.000 943 89

0.001 415 8

0.001 887 8

0.002 359 7

0.002 831 7

0.003 303 6

0.003 775 6

0.004 247 5

0.028 316 85

0.056 634

0.084 951

0.113 27

0.141 58

0.169 90

0.198 22

0.226 53

0.254 85

4.381 264 ¥ 10–8

8.762 ¥ 10–8

13.144 ¥ 10–8

17.525 ¥ 10–8

21.906 ¥ 10–8

26.288 ¥ 10–8

30.669 ¥ 10–8

35.050 ¥ 10–8

39.431 ¥ 10–8

ELECTRICITY AND MAGNETISM ampere-hour to coulomb, C 3 600 faraday (based on C-12) to 96 487.00 coulomb, C gauss to tesla, T 0.000 1 gilbert to ampere-turn 0.795 774 7 oersted to ampere-meter, 79.577 47 A/m unit pole to weber, Wb 1.256 637 ¥ 10–7 ENERGY AND WORK British thermal unit to joule, J British thermal unit (IT) to joule, Ja calorie to joule, J calorie (IT) to joule, Ja electron volt to joule, J foot-pound-force to joule, J kilowatt-hour to joule, J horsepower-hour to joule, J FLOW RATE foot3/minute to meter3/ second, m3/s foot3/second to meter3/ second, m3/s gallon (U.S. liquid)/day to meter3/second, m3/s

© 2004 by CRC Press LLC

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3 460.0

5-71

1 729.994

General Engineering and Mathematics

ounce/inch3 to kilogram/ meter3, kg/m3 pound-mass/foot3 to kilogram/meter3, kg/m3 pound-mass/inch3 to kilogram/meter3, kg/m3 pound-mass/gallon to kilogram/meter3, kg/m3 slug/foot3 to kilogram/ meter3, kg/m3

1 gallon (U.S. liquid)/minute to meter3/second, m3/s pound-mass/hour to kilogram/second, kg/s pound-mass/minute to kilogram/second, kg/s

3

4

5

6

7

8

9

0.000 189 27

0.000 252 36

0.000 315 45

0.000 378 54

0.000 441 63

0.000 504 72

0.000 567 81

0.000 125 997 9

0.000 252 00

0.000 377 99

0.000 503 99

0.000 629 99

0.000 755 99

0.000 881 99

0.001 007 98

0.001 133 98

0.007 559 873

0.015 120

0.022 680

0.030 239

0.037 799

0.045 359

0.052 919

0.060 479

0.068 039

19.613 0.556 03 8.896 4

29.420 0.834 04 13.345

39.227 1.112 1 17.793

49.033 1.390 1 22.241

58.840 1.668 1 26.689

68.647 1.946 1 31.138

78.453 2.224 1 35.586

88.260 2.502 1 40.034

8 368

12 552

16 736

20 920

25 104

29 288

33 472

37 656

8 373.6

12 560.4

16 747.2

20 934.0

25 120.8

29 307.6

33 494.4

37 681.2

8 368

12 552

16 736

20 920

25 104

29 288

33 472

37 656

4 648.9

6 973.3

9 287.8

11 622

13 947

16 271

18 596

20 920

4 652

6 978

9 304

11 630

13 956

16 282

18 608

20 934

8 368

12 552

16 736

20 920

25 104

29 288

33 472

37 656

HEAT SPECIFIC HEAT CAPACITY British thermal unit/ 4 184 pound-mass-deg F to joule/kilogram-kelvin, J/kg·K 4 186.8 British thermal unit (IT)/ pound-mass-deg F to joule/kilogram-kelvin, J/kg·Ka calorie/gram-deg C to joule/ 4 184 kilogram-kelvin, J/kg·K ENERGY/MASS (ENTHALPY, ETC.) British thermal unit/ 2 324.444 pound-mass to joule/ kilogram, J/kg 2 326 British thermal unit (IT)/ pound-mass to joule/ kilogram, J/kga calorie/gram to joule/ 4 184 kilogram, J/kg

CRC Handbook of Engineering Tables

0.000 063 090 20 0.000 126 18

FORCE kilogram-force to newton, N 9.806 65 ounce-force to newton, N 0.278 014 0 pound-force to newton, N 4.448 222

© 2004 by CRC Press LLC

2

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Conversions to SI Units (continued)

THERMAL DIFFUSIVITY foot2/hour to meter2/ second, m2/s THERMAL RESISTANCE deg F-hour foot2/British thermal unit to kelvinmeter2/watt, K·m2/W

6.918 3

8.647 9

10.377

12.107

13.837

15.566

3.461 5

5.192 2

6.922 9

8.653 7

10.384

12.115

13.846

15.577

0.288 26

0.432 39

0.576 53

0.720 66

0.864 79

1.008 9

1.153 1

1.297 2

0.288 46

0.432 68

0.576 91

0.721 14

0.865 37

1.009 60

1.153 82

1.298 05

836.8

1 255.2

1 673.6

2 092.0

2 510.4

2 928.8

3 347.2

3 765.6

22 698

34 047

45 396

56 745

68 094

79 443

90 791

102 140

836 80

125 520

167 360

209 200

251 040

292 880

334 720

376 560

0.000 025 806 4

0.000 051 612 8 0.000 077 419 2 0.000 103 256

0.000 129 032

0.000 154 838 4 0.000 180 644 8 0.000 206 451 2 0.000 232 257 6

0.176 228 0

0.352 46

0.528 68

0.704 91

0.881 14

1.057 4

1.233 6

1.409 8

1.586 1

11.349

17.023

22.698

28.372

34.047

39.721

45.396

51.070

40 856

61 284

81 712

102 140

122 570

143 000

163 420

183 850

5-73

THERMAL CONDUCTANCE British thermal unit/hour- 5.674 466 foot2-deg F to watt/meter2kelvin, W/m2·K British thermal unit/ 20 428.08 second-foot2-deg F to watt/ meter2-kelvin, W/m2·K

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5.188 7

1587_Book.fm Page 73 Tuesday, September 2, 2003 3:25 PM

ENERGY PER UNIT AREA British thermal unit/foot2 to 11 348.93 joule/meter2, J/m2 calorie/centimeter2 to joule/ 41 840 meter2, J/m2

3.459 2

General Engineering and Mathematics

THERMAL CONDUCTIVITY British thermal unit/hour- 1.729 577 foot-deg F to watt/meterkelvin, W/m·K 1.730 735 British thermal unit (IT)/ hour-foot-deg F to watt/ meter-kelvin, W/m·Ka British thermal unit-inch/ 0.144 131 4 hour-foot2-deg F to watt/ meter-kelvin, W/m·K 0.144 227 9 British thermal unit (IT)inch/hour-foot2-deg F to watt/meter-kelvin, W/m·Ka calorie second-centimeter- 418.4 deg C to watt/meter-kelvin, W/m·K

1

4

5

6

7

8

9

83 680

125 520

167 360

209 200

251 040

292 880

334 720

376 560

0.000 254 1.828 8 0.304 8 0.025 4 9.460 550 ¥ 1015 0.000 025 4 1 852

0.000 508 3.657 6 0.609 6 0.050 8 18.921 ¥ 1015 0.000 050 8 3 704

0.000 762 5.486 4 0.914 4 0.076 2 28.382 ¥ 1015 0.000 076 2 5 556

0.001 016 7.315 2 1.219 2 0.101 6 37.842 ¥ 1015 0.000 101 6 7 408

0.001 270 9.144 0 1.524 0 0.127 0 47.303 ¥ 1015 0.000 127 0 9 260

0.001 524 10.972 8 1.828 8 0.152 4 56.763 ¥ 1015 0.000 152 4 11 112

0.001 778 12.801 6 2.133 6 0.177 8 55.224 ¥ 1015 0.000 177 8 12 964

0.002 032 14.630 4 2.438 4 0.203 2 75.684 ¥ 1015 0.000 203 2 14 816

0.002 286 16.459 2 2.743 2 0.228 6 85.145 ¥ 1015 0.000 228 6 16 668

1 609.344

3 218.7

4 828.0

6 437.4

8 046.7

9 656.1

11 265

12 875

14 484

5.029 2 0.914 4

10.058 4 1.828 8

15.087 6 2.743 2

20.116 8 3.657 6

25.146 0 4.572 0

30.175 2 5.486 4

35.204 4 6.400 8

40.233 6 7.315 2

45.262 8 8.229 6

0.000 064 798 91 0.000 129 60 0.028 349 52 0.056 699 0.031 103 48 0.062 207

0.000 194 40 0.085 049 0.093 310

0.000 259 20 0.113 40 0.124 41

0.000 324 00 0.141 75 0.155 52

0.000 388 80 0.170 10 0.186 62

0.000 453 60 0.198 45 0.217 72

0.000 518 40 0.226 80 0.248 83

0.000 583 20 0.255 15 0.279 93

0.453 592 37 0.373 241 7

0.907 18 0.746 48

1.360 8 1.119 7

1.814 4 1.493 0

2.268 0 1.866 2

2.721 6 2.239 5

3.175 1 2.612 7

3.628 7 2.985 9

4.082 3 3.359 2

14.593 90 1 016.047

29.188 2 032.1

43.782 3 048.1

58.376 4 064.2

72.970 5 080.2

87.563 6 096.3

102.16 7 112.3

116.75 8 128.4

131.35 9 144.4

907.184 7

1 814.4

2 721 6

3 628.7

4 535.9

5 443.1

6 350.3

7 257.5

8 164.7

calorie/second-centimeter - 41 840 deg C to watt/meter2kelvin, W/m·K LENGTH caliber to meter, m fathom to meter, m foot to meter, m inch to meter, m light year to meter, m mil to meter, m mile (U.S. nautical) to meter, m mile (U.S. statute) to meter, m rod to meter, m yard to meter, m MASS grain to kilogram, kg ounce-mass to kilogram, kg ounce-mass (troy or apothecary) to kilogram, kg pound-mass to kilogram, kg pound-mass (troy or apothecary) to kilogram, kg slug to kilogram, kg ton (long, 2 240 lbm) to kilogram, kg ton (short, 2 000 lbm) to kilogram, kg

© 2004 by CRC Press LLC

2

CRC Handbook of Engineering Tables

3

2

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5-74

Conversions to SI Units (continued)

2 108.7

3 163.1

4 217.4

5 271.8

6 326.1

7 380.5

8 434.8

9 489.2

17.572 50

35.145

52.718

70.290

87.863

105.44

123.01

140.58

158.15

0.292 875 1

0.585 75

0.878 63

1.171 5

1.464 4

1.757 3

2.050 1

2.343 0

2.635 9

0.293 071 1

0.586 14

0.879 21

1.172 3

1.465 4

1.758 4

2.051 5

2.344 6

2.637 6

4.184 0.069 733 33 1.355 818

8.368 0.139 47 2.711 6

12.552 0.209 20 4.067 5

16.736 0.278 93 5.423 3

20.920 0.348 67 6.779 1

25.104 0.418 40 8.134 9

29.288 0.488 13 9.490 7

33.472 0.557 87 10.847

37.656 0.627 60 12 202

0.022 596 97

0.045 194

0.067 791

0.090 388

0.112 98

0.135 58

0.158 18

0.180 78

0.203 37

0.,000 376 616 1

0.000 753 23

0.001 129 8

0.001 506 5

0.001 883 1

0.002 259 7

0.002 636 3

0.003 012 9

0.003 389 5

745.699 9

1 491.4

2 237.1

2 982.8

3 728.5

4 474.2

5 219.9

5 965.6

6 711.3

746.

1 492.

2 238.

2 984.

3 730.

4 476.

5 222.

5 968.

6 714.

3 516.853

7 033.7

10 551

14 067

17 584

21 101

24 618

28 135

31 652

11 348.93

22 698

34 047

45 396

56 745

68 094

79 443

90 791

102 140

189.148 9

378.30

567.45

756.60

945.74

1 134.9

1 324.0

1 513.2

1 702.3

3.152 481

6.305 0

9.457 4

12.610

15.762

18.915

22.067

25.220

28.372

1 634 246

3 268 500

4 902 700

6 537 000

8 171 200

9 805 500

11 440 000

13 074 000

14 708 000

697.333 3

1 394.7

2 092.0

2 789.3

3 486.7

4 184.0

4 881.3

5 578.7

6 276.0

5-75

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1587_Book.fm Page 75 Monday, September 1, 2003 7:17 PM

POWER/AREA British thermal unit/foot2second to watt/meter2, W/m2 British thermal unit/foot2minute to watt/meter2, W/m2 British thermal unit/foot2hour to watt/meter2, W/m2 British thermal unit/inch2second to watt/meter2, W/m2 calorie/centimeter2-minute to watt/meter2, W/m2

1 0543.350

General Engineering and Mathematics

POWER British thermal unit/second to watt, W British thermal unit/minute to watt, W British thermal unit/hour to watt, W British thermal unit (IT)/ hour to watt, Wa calorie/second to watt, W calorie/minute to watt, W foot-pound-force/second to watt, W foot-pound-force/minute to watt, W foot-pound-force/hour to watt, W horsepower (550 ft·lbr/s) to watt, W horsepower (electric) to watt, W tons of refrigeration to watt, W

1

3

4

5

6

7

8

9

202 650

303 975

405 300

506 625

607 950

709 275

810 600

911 925

200 000 5 978.0

300 000 8 966.9

400 000 11 956

500 000 14 945

600 000 17 934

700 000 20 923

800 000 23 912

900 000 26 901

6 772.8

10 159

13 546

16 932

20 318

23 705

27 091

30 478

498.16

747.25

996.33

1 245.4

1 494.5

1 743.6

1 992.7

2 241.7

497.68

746.52

995.36

1 244.2

1 493.0

1 741.9

1 900.7

2 239.6

196 133

294 199.5

392 266

490 332.5

588 399

686 465.5

784 532

882 598.5

266.64

399.97

533.29

666.61

799.93

933.26

1 066.6

1 199.9

95.761

143.64

191.52

239.40

287.28

335.16

383.04

430.92

13 790

20 684

27 579

34 474

41 369

48 263

55 158

62 053

0.000 084 666 67 0.000 169 33

0.000 254 00

0.000 338 67

0.000 423 33

0.000 508 00

0.000 592 67

0.000 677 33

0.000 762 00

0.005 08

0.010 16

0.015 24

0.020 32

0.025 40

0.030 48

0.035 56

0.040 64

0.045 72

0.304 8

0.609 6

0.914 4

1.219 2

1.524 0

1.828 8

2.133 6

2.438 4

2.743.2

0.025 4

0.050 8

0.076 2

0.101 6

0.127 0

0.152 4

0.177 8

0.203 2

0.228 6

0.277 777 8

0.555 56

0.833 33

1.111 1

1.388 9

1.666 7

1.944 4

2.222 2

2.500 0

PRESSUSRE OR STRESS (FORCE/AREA) atmosphere (normal = 101 325 760 torr) to newton/ meter2, N/m2 bar to newton/meter2, N/m2 100 000 foot of water (39.2 F) to 2 988.980 newton/meter2, N/m2 inch of mercury (32 F) to 3 386.389 newton/meter2, N/m2 inch of water (39.2 F) to 249.082 0 newton/meter2, N/m2 inch of water (60 F) to 248.840 0 newton/meter2, N/m2 kilogram-force/centimeter2 98 006.5 to newton/meter2, N/m2 millimeter of mercury (0 C), 133.322 4 torr, to newton/meter2, N/m2 pound-force/foot2 to 47.880 26 newton/meter2, N/m2 pound-force/inch2 (psi) to 6 894.757 newton/meter2, N/m2 VELOCITY foot/hour to meter/second, m/s foot/minute to meter/ second, m/s foot/second to meter/ second, m/s inch/second to meter/ second, m/s kilometer/hour to meter/ second, m/s

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CRC Handbook of Engineering Tables

2

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5-76

Conversions to SI Units (continued)

1.028 9

1.543 3

2.057 8

2.572 2

3.086 7

3.601 1

4.115 6

4.630 0

0.447 04

0.894 08

1.341 12

1.788 16

2.235 20

2.682 24

3.129 28

3.576 32

4.023 36

26.822 4

53.644 8

80.467 2

107.289 6

134.112 0

160.934 4

187.756 8

214.587 92

241.401 6

1 609.344

3 218.7

4 828.0

6 437.4

8 046.7

9 656.1

11 265

12 875

14 484

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

2.976 3

4.464 5

5.952 7

7.440 8

8.929 0

10.417

11.905

13.393

95.761

143.64

191.52

239.40

287.28

335.16

383.04

430.92

95.761

143.64

191.52

239.40

287.28

335.16

383.04

430.92

2. ¥ 10–6

3. ¥ 10–6

4. ¥ 10–6

5. ¥ 10–6

6. ¥ 10–6

7. ¥ 10–6

8. ¥ 10–6

9. ¥ 10–6

0.185 81

0.278 71

0.371 61

0.464 52

0.557 42

0.650 32

0.743 22

0.836 12

1 233.482 0.158 987 3

2 467.0 0.217 97

3 700.4 0.476 96

4 933.9 0.635 95

6 167.4 0.794 94

7 400.9 0.953 92

8 634.4 1.112 9

9 867.9 1.271 9

11 101 1.430 9

0.002 359 737 0.035 239 07 0.028 316 85 0.003 785 412

0.004 719 5 0.070 478 0.056 634 0.,007 570 8

0.007 079 2 0.105 72 0.084 951 0.011 356

0.009 438 9 0.140 96 0.113 27 0.015 142

0.011 799 0.176 20 0.141.58 0.018 927

0.141 58 0.211 43 0.169 90 0.022 712

0.016 518 0.246 67 0.198 22 0.026 498

0.018 878 0.281 91 0.226 53 0.030 283

0.021 238 0.317 15 0.254 85 0.034 069

0.000 049 161

0.000 065 548

0.000 081 935

0.000 098 322

0.000 114 71

0.000 131 10

0.000 147 48

VISCOSITY DYNAMIC OR ABSOLUTE, m 0.001 centipoise to newtonsecond/meter2, N·s/m2 pound-mass/foot-second to 1.488 164 newton-second/meter2, N·s/m2 pound-force-second/foot2 47.880 26 to newton-second/meter2, N·s/m2 slug/foot-second to newton- 47.880 26 second/meter2, N·s/m2 KINEMATIC, n centistoke to meter2/second, 1. ¥ 10–6 m2/s foot2/second to meter2/ 0.092 903 04 second, m2/s VOLUME acre-foot to meter3, m3 barrel (oil, 42 gal) to meter3, m3 board foot to meter3, m3 bushel (U.S.) to meter3, m3 foot3 to meter3, m3 gallon (U.S. liquid) to meter3, m3 inch3 to meter3, m3

0.000 016 387 06 0.000 032 774

5-77

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1587_Book.fm Page 77 Monday, September 1, 2003 7:17 PM

0.514 444 4

General Engineering and Mathematics

knot (international) to meter/second, m/s mile/hour (U.S. statute) to meter/second, m/s mile/minute (U.S. statute) to meter/second, m/s mile/second (U.S. statute) to meter/second, m/s

1 ounce (U.S. fluid) to meter3, m3 peck (U.S.) to meter3, m3 quart (U.S. liquid) to meter3, m3 yard3 to meter3, m3

3

4

5

6

7

8

9

0.000 029 573 53 0.000 059 147

0.000 088 721

0.000 118 29

0.000 147 87

0.000 177 44

0.000 207 01

0.000 236 59

0.000 266 16

0.008 809 768 0.000 946 352 9

0.017 620 0.001 892 7

0.026 429 0.002 839 1

0.035 239 0.003 785 4

0.044 049 0.004 731 8

0.052 859 0.005 678 1

0.061 668 0.006 624 5

0.070 478 0.007 570 8

0.079 288 0.008 517 2

0.764 554 9

1.529 1

2.293 7

3.058 2

3.822 8

4.587 3

5.351 9

6.116 4

6.881 0

0.124 86

0.187 28

0.249 71

0.312 14

0.374 57

0.437 00

0.499 42

0.561 85

The thermochemical calorie is exactly 4.184 joules by definition. The international steam table (IT) calories is exactly 4.186 8 joules by definition. The thermochemical Btu is 1 054.350 joules. Each Btu is defined in terms of the corresponding calorie by 1 Btu/lbm·R ∫ 1 cal/g·K. From Bolz, R.E. and Tuve, G.L., Units and conversion factors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 808–816.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

VOLUME/MASS (SPECIFIC VOLUME) foot3/pound to meter3/ 0.062 427 96 kilogram, m3/kg a

2

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5-78

Conversions to SI Units (continued)

1587_Book.fm Page 79 Tuesday, September 2, 2003 3:25 PM

5-79

General Engineering and Mathematics

Fundamental Physical Constants B.N. Taylor, W.H. Parker, and D.N. Langenberg The numbers in parentheses are the standard deviation uncertainties in the last digits of the quoted value, computed on the basis of internal consistency.

Units Quantity

Symbol

Avogadro’s number Atomic mass unit Electron rest mass Proton rest mass Neutron rest mass Ratio of proton mass to electron mass Electron charge to mass ratio

1010 cm sec–1 10–3

10–19C

10–20 emu 10–10 esu 10–27 erg·sec 10–27 erg·sec 1023 mole–1 10–24 g 10–28 g 10–4 amu 10–24 g amu 10–24 g amu

R• a0

107 m–1 10–11 m

107 emu g–1 1017 esu g–1 10–7 G·cm2 10–7 erg·sec emu–1 10–17 erg·sec esu–1 erg sec g–1 erg sec g–1 103 emu mole–1 1014 esu mole–1 105 cm–1 10–9 cm

r0

2.817939(13)

4.6

10–15 m

10–13 cm

me/ms

1.0011596389(31) 0.0031

mB me gp gp/2p gp gp/2p mp/ms

9.274096(65) 9.284851(65) 2.65751270(82) 4.257597(13) 2.6751965(82) 4.257707(13) 1.52099312(10)

7.0 7.0 3.1 3.1 3.1 0.066

10–24 J T–1 10–24 J T–1 108 rad sec–1 T–1 107 Hz T–1 108 rad sec–1 T–1 107 Hz T–1 10–3

10–21 erg G–1 10–21 erg G–1 104 rad sec–1 FG–1 103 Hz G–1 104 rad sec–1 G–1 103 Hz G–1 10–3

mp/ms

1.52103264(46)

0.30

10–3

10–3

mp mp/mn

1.4106203(99) 2.792709(17)

7.0 6.2

10–26 J T–1

10–23 erg G–1

mp/mn mn lc lc/2p lc,p lc,p/2p lc,n lc,n/2p R0 k s c1

2.792782(17) 5.050951(50) 2.4263096(74) 3.861592(12) 1.3214409(90) 2.103139(14) 1.3196217(90) 2.100243(14) 8.321434(35) 1.380622(59) 5.66961(96) 4.992579(38)

6.2 10 3.1 3.1 6.8 6.8 6.8 6.8 42 43 170 7.6

10–27 J T–1 10–12 m 10–12 m 10–15 m 10–16 m 10–15 m 10–16 m 103 J kmole–1·K–1 10–23 J K–1 10–8 W m–2 K4 10–24 J·m

10–24 erg G–1 10–10 cm 10–10 cm 10–13 cm 10–14 cm 10–13 cm 10–14 cm 107 erg mole–1·K–1 10–16 erg K–1 10–5 erg sec–1 cm–2·K–4 10–15 erg·m

h h = h/2p N amu me me* Mp Mp* Mn Mn* Mp/me e/me

Quantum of circulation

h/2me h/me F

gp corrected for diamagnetism of H2O Magnetic moment of protons in H2O in Bohr magnetons Proton magnetic moment in Bohr magnetons Proton magnetic moment Magnetic moment of protons in H2O in nuclear magnetons mp /mn corrected for diamagnetism of H2O Nuclear magneton, [c](eh/2Mpc) Compton wavelength of the electron, h/me c Compton wavelength of the proton, h/Mp c Compton wavelength of the neutron, h/Mn c Gas constant Boltzmann’s constant, R0/N Stefan-Boltzmann constant, p2k4/60h3c2 First radiation constant, 8 phc

© 2004 by CRC Press LLC

cgs

108 m sec–1 10–3

Fo h/e

Rydberg constant, [m0c2/4p]2(mee4/4ph3c) Bohr radius, [m0c2/4p]–1(h2/mee2) = a/4pR• Classical electron radius, [m0c2/4p] (e2/mec2) = a3/4pR• Electron magnetic moment in Bohr magnetons Bohr magneton, [c](eh/2mec) Electron magnetic moment Gyromagnetic ratio of proton in H2O

SI

0.33 1.5 1.5 4.4 4.4 7.6 7.6 6.6 6.6 6.0 6.2 6.6 0.08 6.6 0.10 6.2 3.1 3.1 3.3 3.3 3.3 3.1 3.1 5.5 5.5 0.10 1.5

Magnetic flux quantum, [c]–1(hc/2e)

Faraday constant, Ne

Error, ppm

2.997250(10) 7.297351(11) 137.03602(21) 1.6021917(70) 4.803250(21) 6.626196(50) 1.0545919(80) 6.022169(40) 1.660531(11) 9.109558(54) 5.485930(34) 1.672614(11) 1.00727661(8) 1.674920(11) 1.00866520(10) 1836.109(11) 1.7588028(54) 5.272759(16) 2.0678538(69) 4.135708(14) 1.3795234(46) 3.636947(11) 7.273894(22) 9.648670(54) 2.892599(16) 1.09737312(11) 5.2917715(81)

Velocity of light c Fine-structure constant, [m0c2/4p](e2/hc) a a–1 Electron charge e Planck’s constant

Value

3.1

10–34 J·sec 10–34 J·sec 1016 kmole–1 10–27 kg 10–31 kg 10–4 amu 10–27 kg amu 10–27 kg amu 1011 C Kg–1 10–15 T·m2 10–15 J·sec C–1 10–4 J·sec kg–1 10–4 J·sec kg–1 107 C kmole–1

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CRC Handbook of Engineering Tables

Fundamental Physical Constants (continued) Units Quantity

Symbol

Second radiation constant, hc/k Gravitational constant kx-unit-to-angstrom conversion factor, L = l(Å)/l(kxu); l(CuKa1) = 1.537400 kxu Å*-to-angstrom conversion factor, L = l(Å)/l(Å*); l(WKa1) = 0.2090100 Å*

Value

Error, ppm

c2 G L

1.438833(61) 6.6732(31) 1.0020764(53)

43 460 5.3

L*

1.0000197(56)

5.6

SI

cgs

10–2 m·K 10–11 N·m2 Kg–2

cm·K 10–8 dyn·cm2g–2

* Note that the unified atomic mass scale 12C ∫ 12 has been used throughout, that amu = atomic mass unit, C = coulomb, G = gauss, Hz = hertz = cycles/sec, J = joule, K = kelvin (degrees kelvin), T = tesla (104 G), V = volt, and W = watt. In cases where formulas for constants are given (e.g., R•), the relations are written as the product of two factors. The second factor, in parentheses, is the expression to be used when all quantities are expressed in cgs units, with the electron charge in electrostatic units. The first factor, in brackets, is to be included only if all quantities are expressed in SI units. We remind the reader that with the exception of the auxiliary constants which have been taken to the exact, the uncertainties of these constants are correlated, and therefore the general law of error propagation must be used in calculating additional quantities requiring two or more of these constants. ENERGY CONVERSION FACTORS

Quantity 1 kg 1 amu Electron mass Proton mass Neutron mass 1 electron volt

Value

Unit

Error, ppm

5.609538(24) 931.4812(52) 0.5110041(16) 938.2592(52) 939.5527(52) 1.6021917(70)

1029 MeV MeV MeV MeV MeV 10–19 J 10–12 erg 1014 Hz 105 m–1 103 cm–1 104 K 10–6 eV·m 10–4 eV·cm 10–18 J 10–11 erg eV 1015 Hz 105 K 10–5 eV T–1 1010 Hz T–1 m–1·T–1 10–1 cm–1·T–1 K T–1 10–8 eV T–1 106 Hz T–1 10–2 m–1·T–1 10–4 cm–1·T–1 10–4 K T–1 10–2 m3·atm kmole–1·K–1 m3 kmole–1

4.4 5.5 3.1 5.5 5.5 4.4

2.4179659(81) 8.065465(27)

Energy-wavelength conversion

1.160485(49) 1.239854(41)

Rydberg constant, R•

2.179914(17)

Bohr magneton, ms

Nuclear magneton, mn

Gas constant, R0 Standard volume of ideal gas, V0

13.605826(45) 3.2898423(11) 1.578936(67) 5.788381(18) 1.3996108(43) 46.68598(14) 0.671733(29) 3.152526(21) 7.622700(42) 2.542659(14) 3.65846(16) 8.20562(35) 22.4136

3.3 3.3 42 3.3 7.6 3.3 0.35 43 3.1 3.1 3.1 43 6.8 5.5 5.5 44 42

From Bolz, R.E. and Tuve, G.L., Units and conversion factors, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 817–818. Originally from Rev. Mod. Phys., 41: 375, 1969. Reprinted by permission of the publisher, American Institute of Physics.

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1587_Section_5.fm Page 81 Tuesday, September 2, 2003 5:44 PM

5-81

General Engineering and Mathematics

Numerical Constants p Constants p= 1/p = p2 = loge p = log10 p =

3.14159 0.31830 9.86960 1.14472 0.49714 0.39908

2p =

log10

26535 98861 44010 98858 98726 99341

89793 83790 89358 49400 94133 79057

23846 67153 61883 17414 85435 52478

26433 77675 44909 34273 12682 25035

83279 26745 99876 51353 88290 91507

50288 02872 15113 05871 89887 69595

41971 40689 53136 16472 36516 02099

69399 19291 99407 94812 78324 34102

37510 48091 24079 91531 38044 92127

Logarithmic Constants e= 1/e = e2 = M = log10 e = 1/M = loge 10 = log10 M =

2. 71828 0. 36787 7. 38905 0. 43429 2. 30258 9. 63778

18284 94411 60989 44819 50929 43113

59045 71442 30650 03251 94045 00536

23536 32159 22723 82765 68401 78912

02874 55237 04274 11289 79914 29674

71352 70161 60575 18916 54684 98565

66249 46086 00781 60508 36420 —

77572 74458 31803 22943 76011 10

47093 11131 15570 97005 01488

69995 03176 55184 80366 62877

Miscellaneous p and e Constants p = ep = e–p = e1/2p = ii = e–1/2p = 4

22. 45915 23. 14069 0. 04321 4. 81047 0. 20787

77183 26327 39182 73809 95763

61045 79269 63772 65351 50761

47342 00572 24977 65547 90854

71522 90864 44177 30357 69556

Numerical Constants 2=

1.41421

35623

73095

04880

16887

24209

69807

85696

71875

37694

2= loge 2 = log10 2 = 3=

1.25992 0.69314 0.30102 1.73205

10498 71805 99956 08075

94873 59945 63981 68877

16476 30941 19251 29352

72106 72321 37388 74463

07278 21458 94724 41505

22835 17656 49302 87326

05702 80755 67681 69428

51464 00134 89881 05253

70150 36025 46210 81038

3= loge 3 = log10 3 =

1.44224 1.09861 0.47712

95703 22886 12547

07408 08109 19662

38232 69139 43729

16383 52452 50279

10780 36922 03255

10958 52570 11530

83918 46474 92001

69253 90557 28864

49935 82274 19069

3

3

Miscellaneous Euler’s Constant g = loge g = Golden Ratio f =

© 2004 by CRC Press LLC

0. 57721 –0. 54953 1. 61803

56649 93129 39887

01532 81644 49894

86061 82234 84820

45868

34365

63811

77203

09180

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5-82

CRC Handbook of Engineering Tables

Numerical Constants (continued) Numbers Containing p p = 3. 14159 26536 Number p 2p 3p 4p 8p p/2 p/3

3.1415 6.2831 9.4247 12.5663 25.1327 1.5707 1.0471

log10 p = 0. 49714 98727 Logarithm

927 853 780 706 412 963 976

0.4971 0.7981 0.9742 1.0092 1.4002 0.1961 0.0200

loge p = 1. 14472 98858 Number

p 2p2 4p2 1/p2 1/(2p2) 1/(4p2) 2

499 799 711 099 399 199 286

p

p/4

0.7853 982

9.8950 899 – 10

p/6

p § 4 or

0.5235 988

9.7189 986 – 10

p/8

p /2

0.3926 991

9.5940 599 – 10

2p/3

2.0943 951

0.3210 586

9.8696 19.7392 39.4784 0.1013 0.0506 0.0253 1.7724

044 088 176 212 606 303 539

Logarithm 0.9942 1.2953 1.5963 9.0057 8.7046 8.4036 0.2485

997 297 597 003 – 10 703 – 10 403 – 10 749

0.8862 269

9.9475 449 – 10

p /4

0.4431 135

9.6465 149 – 10

p§2

1.2533 141

0.0980 599

Number

Logarithm

4p/3 1/p 2/p

4.1887 902 0.3183 099 0.6366 198

0.6220 886 9.5028 501 – 10 9.8038 801 – 10

2§p p3

4/p

1.2732 395

0.1049 101

1§3 p

1/(2p)

0.1591 549

9.2018 201 – 10

3

1/(4p)

0.0795 775

8.9007 901 – 10

1/(6p)

0.0530 516

1/(8p) p/180 180/p

0.0397 887 0.0174 553 57.2957 795

3

p

Number

Logarithm

0.7978 846 31.0062 767 1.4645 919

9.9019 401 – 10 1.4914 496 0.1657 166

0.6827 841

9.8342 834 – 10

2.1450 294

0.3314 332

1§ p

0.5641 896

9.7514 251 – 10

8.7246 989 – 10

1 § 2p

0.3989 423

9.6009 101 – 10

8.5997 601 – 10 8.2418 774 – 10 1.7581 226

2§ p

1.1283 792

0.0524 551

p

2

Change of Base loga x = logb x/logb a log10 x = loge x/loge 10 loge x = log10 x/log10 e loge x = 1/M log10 x = 2.30258 50930 log10 x log10 x = M loge x = 0.43429 44819 loge x From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 877.

© 2004 by CRC Press LLC

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5-83

General Engineering and Mathematics

Mathematical Constants For Use on a Digital Computer Constant

Decimal (Base 10)

Octgal (Base 8) p Constants

p p–1 p p2 2p

3.14159 0.31830 1.77245 9.86960 2.5062

26355 98861 38509 44010 82746

89793 83790 05516 89358 31000

23846 67153 02729 61883 50241

3.1103 0.2427 1.6133 11.6751 2.4033

7552 6301 7611 7144 1143

4210 5562 0664 6762 7754

2643 3442 7366 1357 2340

0215 0251 5247 1322 5454

1423 2376 4703 2556 5371

(p/2)1/2 p–1/2 (2p)–1/2 p1/2 log10 p

1.25331 0.56418 0.39894 1.46459 0.49714

41373 95835 22804 18875 98726

15500 47756 01432 61523 94133

25120 28694 67793 26302 85435

1.2015 0.4406 0.3142 1.3556 0.3764

4461 7272 0424 7576 2466

7766 4041 6365 3461 6306

1160 2333 0331 0113 7216

2626 3210 2043 3612 7300

2574 6561 2077 7621 1457

1.14472 8.53973 1.15572 22.45915

98858 42226 73497 77183

49400 73567 90921 61045

17414

1.1120 10.4242 1.1175 26.3530

6404 6005 6677 5534

4347 5056 3047 1601

5033 5072 0733 0421

6413

6537

1613

1026

ln p pe p/e pe

47342

e Constants e e–1 ep e–p ep/2 log10 e

2.71828 0.36787 23.14069 0.4321 4.81407

18284 94411 26237 39182 73809

59045 71442 79269 63772 65351

23536 32159 00572 24977 65547

2.5576 0.2742 27.1100 0.0261 4.6367

0521 6530 2156 0021 5562

3050 6613 5411 1732 0526

5355 1674 1471 6307 2327

1246 6761 4754 3706 6476

5277 5272 6647 4257 2132

0.43429

44819

03251

82765

0.3362

6754

2511

5624

1614

5232

Numerical Constants 2 2 3 3 3 log10 2

1.41421 1.25992 1.73205 1.44224 0.30102

35623 10498 08075 95703 99956

73095 94873 68877 07408 63981

04880 16477 29641 38232 19251

1.3240

4746

3177

1674

6220

4262

1.5666

3656

4130

2312

5167

0145

ln 2 log10 3 ln 3 ln 10 log2 10

0.69314 0.47712 1.09861 2.30258

71805 12547 22886 50929

59945 19662 68109 94045

30941 43729 69139 68401

0.5427

1027

7575

0717

3632

5711

2.2327 3.24464

3067 741136

3552

5242

5405

5651

0.57721 1.78107 0.56145 –0.23866 –0.54953

56649 24179 94835 18912 93129

01532 90197 66885 16832 81644

86060 98522 16903 38945 82234

2147 2134 5717 4362 7233

7067 5261 0177 0631 6021

6660 1526 1345 1753 7532

6172 5761 7454 0063 2777

2321

3

Euler’s Constant: g g eg e–g logg ln g

0.4474 1.6177 0.4373 –0.1721 –0.4312

From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 878.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Derivatives In the following formulas u, v, w represent functions of x, while a, c, n represent fixed real numbers. All arguments in the trigonometric functions are measured in radians, and all inverse trigonmetric and hyperbolic functions represent principal values.†

1.

d (a ) = 0 dx

2.

d (x ) = 1 dx

3.

d (au) = a du dx dx

4.

d dv dw + (u + v - w) = du dx dx dx dx

5.

d dv du +v (uv ) = d dx dx dx

6.

d du dv + vw + uw (uvw) = uv dw dx dx dx dx v

du dv -u dx dx = 1 du - u dv v dx v 2 dx v2

7.

d Ê uˆ Á ˜= dx Ë v ¯

8.

d n du u = nu n-1 dx dx

9.

d dx

( )

( u ) = 2 1u dudx

10.

d Ê 1ˆ 1 du Á ˜ =- 2 dx Ë u ¯ u dx

11.

d Ê 1ˆ n du Á ˜ = - n+1 dx Ë u n ¯ u dx

12.

d Ê u n ˆ u n-1 Ê du dv ˆ = - mu ˜ Á nv dx ÁË v m ˜¯ v m+1 Ë dx dx ¯

13.

d n m dv ˆ Ê du + mu ˜ u v = u n-1v m-1 Á nv Ë dx dx dx ¯

14.

d d du f (u) = f (u) ◊ dx du dx

(

)

[ ]

[ ]

dy d[f(x)] - = ----------------- = f ' ( x ) define respectively a function and its derivative for any value x in their † Let y = f(x) and ----dx

dx

common domain. The differential for the function at such a value x is accordingly defined as

[ ]

dy = d f ( x ) =

[ ]

d f (x ) dy dx = dx = f ¢( x )dx dx dx

Each derivative formula has an associated differential formula. For example, formula 6 above has the differential formula d(uvw) = uv dw + vw du + uw dv

15.

df (u) d 2u d 2 f (u) Ê du ˆ d2 ◊ + ◊Á ˜ f (u) = 2 du dx 2 dx du 2 Ë dx ¯

16.

Ê nˆ d n v Ê nˆ d k v d n - k Ê nˆ d nu Ê nˆ dv d n-1u Ê nˆ d 2v d n-2u dn + Á ˜ 2 n-2 + L + Á ˜ k n-k + L + Á ˜ u n uv ] = Á ˜ v n + Á ˜ n [ n-1 dx Ë n¯ dx Ë k ¯ dx dx Ë 2¯ dx dx Ë 0¯ dx Ë 1¯ dx dx

[ ]

2

n! where ÊË nrˆ¯ = --------------------- the binomial coefficient, n non-negative integer and Ê nˆ = 1. Ë 0¯ r! ( n – r )!

© 2004 by CRC Press LLC

1587_Book.fm Page 85 Monday, September 1, 2003 7:17 PM

General Engineering and Mathematics

Derivatives (continued) 17.

du 1 = dx dx du

18.

d (loga u) = (loga e) u1 du dx dx

19.

d (loge u) = u1 du dx dx

20.

d u du a = au (log e a) dx dx

21.

d u du e = eu dx dx

22.

d v du dv + (log e u)u v u = vu v -1 dx dx dx

23.

d (sin u) = du (cos u) dx dx

24.

d (cos u) = du (sin u) dx dx

25.

d sec 2 u (tan u) = du dx dx

26.

d csc 2 u (cot u) = - du dx dx

27.

d sec u ◊ tan u (sec u) = du dx dx

28.

d csc u ◊ cot u (csc u) = - du dx dx

29.

d sin u (vers u) = du dx dx

30.

d pˆ Ê p , Á - £ arc sin u £ ˜ (arc sin u) = 1 2 du dx 2¯ 1 - u dx Ë 2

31.

d , (arc cos u) = - 1 2 du dx 1 - u dx

32.

d pˆ Ê p , Á - < arc tan u £ ˜ (arc tan u) = 1 +1u2 du dx dx Ë 2 2¯

33.

d , (arc cot u) = - 1 +1u2 du dx dx

34.

d p pˆ Ê , Á 0 £ arc sec u < , - p £ arc sec u < - ˜ (arc sec u) = 12 du dx 2 2¯ u u - 1 dx Ë

35.

d p pˆ Ê , Á 0 < arc csc u £ , - p < arc csc u £ - ˜ (arc csc u) = - 12 du Ë dx dx 2 2¯ u u -1

36.

d , (arc vers u) = 1 2 du dx 2u - u dx

37.

d (sinh u) = du (cosh u) dx dx

38.

d (cosh u) = du (sinh u) dx dx

if

dx π0 du

( ) ( )

( )

(

(

© 2004 by CRC Press LLC

) )

(0 £ arc cos u £ p)

(0 £ arc cot u £ p)

(0 £ arc vers u £ p)

5-85

1587_Book.fm Page 86 Monday, September 1, 2003 7:17 PM

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CRC Handbook of Engineering Tables

Derivatives (continued)

(

)

(

)

39.

d sec h2u (tanh u) = du dx dx

40.

d csc h2u (coth u) = du dx dx

41.

d (sec h u) = - du (sech u ◊ tanh u) dx dx

42.

d (csch u) = - du (csch u ◊ coth u) dx dx

43.

1 d d È Ê du ù sinh -1 u = log u + u 2 + 1 ˆ ú = ¯û dx dx ÍÎ Ë u 2 + 1 dx

44.

1 d d È Ê du ù cosh -1 u = log u + u 2 - 1 ˆ ú = , ¯û dx dx ÍÎ Ë u 2 - 1 dx

45.

d d È1 1+ u ù 1 du = tanh -1 u = log , dx dx ÍÎ 2 1 - u úû 1 - u 2 dx

46.

d d È1 u +1ù 1 du = coth -1 u = log , dx dx ÍÎ 2 u - 1 úû 1 - u 2 dx

47.

d d È 1 + 1 - u2 Ílog sech -1u = dx dx Í u Î

ù 1 du ú=, úû u 1 - u 2 dx

48.

d d È 1 + 1 + u2 Ílog csch -1u = dx dx Í u Î

ù 1 du ú=úû u 1 - u 2 dx

49.

d dq

Ú f (x)dx = f (q) , [ p constant ]

50.

d dp

Ú f (x)dx = - f ( p) , [q constant ]

d da

Ú f (x, a)dx = Ú ∂a [ f (x, a)]dx + f (q, a) da - f ( p, a) da

51.

(

)

(

)

(

)

(u < 1)

(

)

(u > 1)

(

)

(

)

(u > 1, cosh

-1

u>0

)

2

2

(0 < u < 1, sech

-1

u>0

)

q

p

q

p

q

q

p

p

∂

dq

dp

From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 884–887.

© 2004 by CRC Press LLC

1587_Book.fm Page 87 Tuesday, September 2, 2003 3:25 PM

5-87

General Engineering and Mathematics

Facts from Algebra Factors and Expansions (a ± b)2 = a2 ± 2ab + b2 (a ± b)3 = a3 ± 3a2b + 3ab2 ± b3 (a ± b)4 = a4 ± 4a3b + 6a2b2 ± 4 ab3 + b4 a2 – b2 = (a – b) (a + b) a2 + b2 = (a + b – 1) (a – b – 1) a3 – b3 = (a – b) (a2 + ab + b2) a3 + b3 = (a + b) (a2 – ab + b2) a4 + b4 = (a2 + ab 2 + b2) (a2 – ab 2 + b2) an – bn = (a – b) (an–1 + an–2b + … + bn–1) an – bn = (a + b) (an–1 – an–2b + … – bn–1), for even values of n an + bn = (a + b) (an–1 – an–2b + … + bn–1), for odd values of n a4 + a2b2 + b4 = (a2 + ab + b2) (a2 – ab + b2) (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc (a + b + c)3 = a3 + b3 + c3 + 3a2(b + c) + 3b2(a + c) + 3c2(a + b) + 6abc (a + b + c + d + …)2 = a2 + b2 + c2 + d2 + … + 2a(b + c + d + …) + 2b(c + d + …) + 2c(d + …) + … Powers and Roots a x ¥ a y = a(x+y) a0 = 1 [if a – 0] (ab)x = a x b x ax x- y = a( ) ay

(a ) x

y

a-x =

x

ax Ê aˆ Á ˜ = x Ë b¯ b

1 ax

1

= a xy

ax = x a

x

ab = x a x b

x x y

xy

a = a

y

a y = ax

x

x

a a = b xb

Proportion If

a c = , b d

then

a+b c +d a-b c -d = = , b d b d

a-b c -d = a+b c +d

From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 887.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Integrals—Elementary Forms 1. 2.

Ú a ◊ f (x)dx = aÚ f (x)dx

3.

Ú f( y)dx = Ú

4. 5.

f( y ) y¢

dy , where y ¢ =

Ú u dx dx = uv - Ú v dx dx

7.

Ú

x ndx =

8.

Ú

f (x )

9.

Ú x = log x

11. 12. 13. 14. 15. 16.

17.

18.

dy dx

Ú (u + v)dx = Ú udx + Ú vdx , where u and v are any functions of x Ú udv = uÚ dv - Ú vdu = uv – Ú vdu

6.

10.

© 2004 by CRC Press LLC

Ú adx = ax

dv

du

x n+1 , except n = –1 n +1

f ¢( x )dx

= log f ( x ) ,

(df (x ) = f ¢(x )dx )

dx

f ¢( x )dx

Ú2

Ú e dx = e Ú e dx = e x

(df (x ) = f ¢(x )dx )

x

ax

Úb

f (x ) ,

=

f (x )

ax

dx =

ax

a

bax , a log b

(b > 0)

Ú log x dx = x log x – x Ú a log adx = a , (a > 0) x

x

Ú a +x dx

2

Ú

Ú

2

=

1 x tan –1 a a

Ï1 -1 x Ô a tanh a Ô dx Ô or =Ì a2 – x 2 Ô a+x Ô1 ÔÓ 2a log a - x ,

(a

2

> x2

)

Ï 1 -1 x Ô- a coth a Ô dx Ô or =Ì 2 2 x –a Ô x-a Ô1 ÔÓ 2a log x + a ,

(x

2

> a2

)

1587_Book.fm Page 89 Monday, September 1, 2003 7:17 PM

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General Engineering and Mathematics

Integrals—Elementary Forms (continued)

19.

Ï -1 x Ôsin a Ô Ô dx =Ì or a2 – x 2 Ô Ô -1 x Ô- cos a , Ó

Ú

20.

Ú

21.

Úx

22.

Ú

dx x 2 ± a2 dx x 2 – a2

(a

2

> x2

)

= logÊ x + x 2 ± a2 ˆ Ë ¯ =

1 x sec -1 a a

1 Ê a + a2 ± x 2 = - logÁ a ÁË x x a2 ± x 2 dx

ˆ ˜˜ ¯

From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 888–889.

© 2004 by CRC Press LLC

1587_Book.fm Page 90 Monday, September 1, 2003 7:17 PM

5-90

CRC Handbook of Engineering Tables

Series The expression in parentheses following certain of the series indicates the region of convergence. If not otherwise indicated it is to be understood that the series converges for all finite values of x. Binomial

(x - y ) (1 ± x )

n

n

= x n + nx n-1 y + = 1 ± nx +

n(n - 1) 2!

n(n - 1)x 2 2!

±

n(n + 1)x 2

x n-2 y 2 +

3!

(1 ± x )

-1

= 1 m x + x 2 m x3 + x 4 m x 5 + L

(1 ± x )

-2

= 1 m 2 x + 3x 2 m 4 x 3 + 5x 4 m 6 x 5

m

(

x n-3 y 3 + L y 2 < x 2

3!

)

(x < 1)

+ Letc.

n(n + 1)(n + 2)x 3

-n

2!

3!

n(n - 1)(n - 2)x 3

(1 ± x )

= 1 m nx +

n(n - 1)(n - 2)

2

+ Letc.

(x < 1) 2

(x < 1) + L ( x < 1) 2

2

Reversion of Series Let a series be represented by y = a1x + a2 x 2 + a3 x 3 + a4 x 4 + a5 x 5 + a6 x 6 + L

(a

1

π 0)

to find the coefficients of the series x = A1 y + A2 y 2 + A3 y 3 + A4 y 4 + L a2 a13

(

1 a1

A4 =

1 5a1a2a3 - a12a4 - 5a23 a17

A5 =

1 6a2a a + 3a12a32 + 14a24 - a13a5 - 21a1a22a3 a19 1 2 4

A6 =

1 7 a3a a + 7 a13a3a4 + 84a1a23a3 - a14a6 - 28a12a22a4 - 28a12a2a32 - 42a25 a111 1 2 5

A7 =

1 8a 4a a + 8a14a3a5 + 4a14a42 + 120a12a23a4 + 180a12a22a32 a113 1 2 6

A2 = -

A3 =

1 2a22 - a1a3 a15

)

A1 =

(

)

(

)

(

)

(

+ 132a26 - a15a7 - 36a13a22a5 - 72a13a2a3a4 - 12a13a33 - 330a1a24a3

)

Taylor 1. f ( x ) = f (a) + ( x - a) f ¢(a) + +L+

( x - a)

n

n! (Increment form)

( x - a) 2!

2

f ¢¢(a) +

( x - a)

3

3!

f ¢¢¢(a)

n f ( ) (a) + L(Taylor's Series)

2. f ( x + h) = f ( x ) + hf ¢( x ) +

h2 h3 f ¢¢( x ) + f ¢¢¢( x ) + L 2! 3!

x3 x3 f ¢¢(h) + f ¢¢¢(h) + L 2! 3! 3. If f(x) is a function possessing derivatives of all orders throughout the interval a x b, then there is a value X, with a < X < b, such that = f (h) + xf ¢(h) +

© 2004 by CRC Press LLC

1587_Book.fm Page 91 Monday, September 1, 2003 7:17 PM

5-91

General Engineering and Mathematics

Series (continued) f (b) = f (a) + (b - a) f ¢(a) +

(b - a) (n - 1)!

n-1

+

2

2!

f ¢¢(a) + L

(b - a) f (n) X n-1 f ( ) (a ) + ( ) n! n

f (a + h) = f (a) + hf ¢(a) + +

(b - a)

h2 hn-1 (n-1) f ¢¢(a) + L + f (a ) n 2! ( - 1)!

hn (n-1) f (a + qh), b = a + h, 0 < q < 1 n!

or f ( x ) = f ( a ) + ( x - a ) f ¢( a ) +

( x - a) 2!

2

f ¢¢(a) + L + ( x - a)

n-1

n-1 f ( ) (a )

(n - 1)!

+ Rn

where

[

]

n f ( ) a + q ◊ ( x - a)

( x - a) , 0 < q < 1 n! The above forms are known as Taylor’s series with the remainder term. Rn =

n

4. Taylor’s series for a function of two variables ∂f ( x , y ) ∂f ( x , y ) Ê ∂ ∂ˆ + k ˜ f (x , y ) = h +k ; If Á h ∂y ¯ x ∂y Ë ∂x ∂2 f (x , y ) ∂2 f ( x , y ) 2 ∂2 f ( x , y ) Ê ∂ ∂ˆ + k ˜ f ( x , y ) = h2 +k + 2hk Áh 2 y¯ ∂x∂y ∂x ∂y 2 Ë ∂x 2

n

Ê ∂ ∂ˆ + k ˜ f ( x , y ) x =a with the bar and subscripts means that after differentiation we etc., and if hÁ ∂y ¯ Ë ∂x y =b are to replace x by a and y by b, n

Ê ∂ ∂ˆ 1Ê ∂ ∂ˆ f (a + h, b + k ) = f (a, b ) + Á h + k ˜ f ( x , y ) x =a + L + Á h + k ˜ f ( x , y ) x =a + L ∂y ¯ n! Ë ∂x ∂y ¯ Ë ∂x y =b y =b Maclaurin f ( x ) = f (0) + xf ¢(0) +

f ( ) (0) x2 x3 f ¢¢(0) + f ¢¢¢(0) + L + x n-1 +R 2! 3! (n - 1)! n n-1

where Rn =

n x n f ( ) (qx )

n!

, 0 < q <1

Exponential e =1+

1 1 1 1 + + + +L 1! 2! 3! 4!

ex = 1+ x +

© 2004 by CRC Press LLC

x 2 x3 x 4 + + +L 2! 3! 4!

(all real values of x )

1587_Book.fm Page 92 Monday, September 1, 2003 7:17 PM

5-92

CRC Handbook of Engineering Tables

Series (continued)

(x log a) + (x log a) 2

a x = 1 + x log e a +

3

e

e

2!

3!

+L

2 3 È (x - a) + (x - a) + Lùú e x = e a Í1 + ( x - a) + 2! 3! Í ú Î û

Logarithmic 2

log e x =

3

x - 1 1 Ê x - 1ˆ 1 Ê x - 1ˆ + Á ˜ + Á ˜ +L 2Ë x ¯ 3Ë x ¯ x

log e x = ( x - 1) -

1ˆ Ê Áx > ˜ Ë 2¯

2 3 1 (x - 1) + 13 (x - 1) - L 2

(2 ≥ x > 0)

È x - 1 1 Ê x - 1ˆ 3 1 Ê x - 1ˆ 5 ù log e x = 2 Í + Á ˜ + Á ˜ + Lú Ë ¯ Ë ¯ 5 x +1 ÍÎ x + 1 3 x + 1 úû 1 1 1 log e (1 + x ) = x - x 2 + x 3 - x 4 + L 2 3 4

( x > 0)

(-1 < x < 1)

1 1 È1 ù log e (n + 1) - log e (n - 1) = 2 Í + 3 + 5 + Lú 5n Î n 3n û 3 5 È x ù 1Ê x ˆ 1Ê x ˆ log e (a + x ) = log e a + 2 Í + Á ˜ + Á ˜ + Lú ÍÎ 2a + x 3 Ë 2a + x ¯ 5 Ë 2a + x ¯ úû

log e

( a > 0, - a < x < + • )

È ù 1+ x x3 x 5 x 2n-1 = 2Íx + + +L+ + Lú , - 1 < x < 1 1- x 3 5 2n - 1 Î û

log e x = log e a +

( x - a) - ( x - a) a

2a 2

2

+

( x - a)

2

3a3

- + L , 0 < x 2a Trigonometric

sin x = x -

x3 x 5 x 7 + +L 3! 5! 7!

(all real values of x )

cos x = 1 -

x2 x 4 x6 + +L 2! 4! 6!

(all real values of x )

tan x = x +

2 x 3 2 x 5 17 x 7 62x 9 + + + +L 3 15 315 2835

2n

(2

2n

)

- 1 B2n

(2n)!

x 2n-1 + L ,

È 2 p2 ù , and Bn represents the n'th Bernoulli number.ú Íx < 4 Î û cot x =

22n B2n 2n-1 x7 1 x x3 2x 5 - -Lx -L, x 3 45 945 4725 (2n)!

[x

sec x = 1 +

2

2

2n

E x x 5 61 6 277 8 + x4 + x + x + L + 2n +L, 2 24 720 8064 (2n)!

È 2 p2 ù , and Bn represents the n'th Euler number.ú Íx < 4 Î û

© 2004 by CRC Press LLC

]

< p 2 , and Bn represents the n'th Bernoulli number.

1587_Book.fm Page 93 Monday, September 1, 2003 7:17 PM

5-93

General Engineering and Mathematics

Series (continued) csc x =

(

)

2 22n-1 - 1 1 x 7 3 31 127 - + x + x5 + x7 + L + B x 2n-1 + L , x 6 360 15,120 604, 800 (2n)! 2n

[x

]

< p 2 , and Bn represents the n'th Bernoulli number.

2

Ê x ˆÊ x ˆÊ x ˆ sin x = x Á1 - 2 ˜ Á1 - 2 2 ˜ Á1 - 2 2 ˜ L Ë p ¯Ë 2 p ¯Ë 3 p ¯

(x

2

<•

Ê 4x 2 ˆ Ê 4x 2 ˆ Ê 4x 2 ˆ cos x = Á1 - 2 ˜ Á1 - 2 2 ˜ Á1 - 2 2 ˜ L 3 5 p p p ¯ Ë ¯Ë ¯Ë

(x

2

<•

2

ˆ p Ê x 3 1 ◊ 3x 5 1 ◊ 3 ◊ 5x 7 - Áx + + + + L˜ 2 Ë 2 ◊3 2 ◊ 4 ◊ 5 2 ◊ 4 ◊6 ◊7 ¯

tan -1 x = x tan -1 x =

(x

2

< 1, 0 < cos -1 x < p

) )

) (x < 1)

x3 x 5 x 7 + +L 3 5 7

2

p 1 1 1 1 - + + -L 2 x 3x 2 5x 5 7 x 7

tan -1 x = cot -1 x =

2

x3 1◊ 3 5 1◊ 3 ◊ 5 7 p pˆ Ê + x + x + L Á x 2 < 1, - < sin -1 x < ˜ Ë 2 ◊3 2 ◊ 4 ◊ 5 2 ◊ 4 ◊6 ◊7 2 2¯

sin -1 x = x + cos -1 x =

2

(x > 1)

p 1 1 1 1 - + + -L 2 x 3x 2 5x 5 7 x 7

(x < -1)

(x < 1)

p x3 x 5 x 7 -x+ + -L 2 3 5 7

log e sin x = log e x log e cos x = -

(x

x2 x 4 x6 -L 6 180 2835

< p2

2

)

Ê 2 p2 ˆ Áx < 4 ˜ Ë ¯

x 2 x 4 x 6 17 x 8 -L 2 12 45 2520

log e tan x = log e x + e sin x = 1 + x +

2

Ê 2 p2 ˆ Áx < 4 ˜ Ë ¯

x 2 7 x 4 62x 6 + + +L 3 90 2835

x 2 3x 4 8 x 5 3x 6 56x 7 + +L 2! 4! 5! 6! 7!

Ê x 2 4 x 4 31x 6 ˆ e cos x = eÁ1 + + L˜ 2! 4! 6! Ë ¯ e tan x = 1 + x +

Ê 2 p2 ˆ Áx < 4 ˜ Ë ¯

x 2 3x 3 9 x 4 37 x 5 + + + +L 2! 3! 4! 5!

sin x = sin a + ( x - a) cos a -

( x - a) 2!

2

( x - a)

3

sin a -

3!

cos a +

( x - a) 4!

4

sin a + L

Hyperbolic and Inverse Hyperbolic Table of expansion of certain functions into power series sinh x = x +

x3 x 5 x 7 x 2n+1 + + +L+ +L 3! 5! 7! (2n + 1)!

x <•

cosh x = 1 +

x2 x 4 x6 x 2n + + +L+ +L 2! 4! 6! 2 ( n)!

x <•

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Series (continued)

(

)

(-1) 22n 22n - 1 2n-1 (1) 1 2 17 7 62 9 tanh x = x - x 3 + x 5 x + x -L+ B2n x ±L 3 15 315 2835 (2n)! n+1

(-1) 22n B x 2n-1 ± L(1) x7 1 x x3 2x 5 + + +L+ x 3 45 945 4725 (2n)! 2n

x<

p 2

n+1

coth x =

0< x
(-1) E x 2n ± L(2) 1 2 5 4 61 6 1385 8 x + x - x + x -L+ 2! 4! 6! 8! (2n)! 2n n

sech x == 1 -

(

)

2( -1) 22n-1 - 1 1 x 7 x3 31x 5 1 - + +L+ B2n x 2n-1 + L( ) x 6 360 15,120 (2n)! n

cosech x =

argsinh x = x -

argcoth x = (1) (2)

x3 x 5 x 7 x 2n+1 + + +L+ +L 3 5 7 2n + 1

p 2

0< x
1 ◊ 3 ◊ 5(2n - 1) n 1 3 1◊ 3 5 1◊ 3 ◊ 5 7 x + x x + L + ( -1) ◊ x 2n+1 ± L 2 ◊3 2◊4◊5 2 ◊ 4 ◊6 ◊7 2 ◊ 4 ◊ 6K2n(2n + 1)

1 1◊ 3 1◊ 3 ◊ 5 È ù argcosh x = ± Íln(2 x ) - Lú 2 ◊ 2x 2 2 ◊ 4 ◊ 4x 4 2 ◊ 4 ◊ 6 ◊ 6x 6 Î û arg tanh x = x +

x<

x <1

x >1

x <1

1 1 1 1 1 + + + +L+ +L x 3x 3 5x 5 7 x 7 (2n + 1)x 2n+1

x >1

Bn denotes Bernoull’s numbers. En denotes Euler’s numbers Fourier

1. If f(x) is a bounded periodic function of period 2L (i.e., f(x + 2L) = f(x)), and satisfies the Dirichlet conditions: a) In any period f(x) is continuous, except possibly for a finite number of jump discontinuities. b) In any period f(x) has only a finie number of maxima and minima. Then f(x) may be represented by the Fourier series a0 + 2

•

Â ÊÁË a cos n

n-1

npx npx ˆ + bn sin ˜ L L ¯

where an and bn are as determined below. This series will converge to f(x) at every point where f(x) is continuous, and to

( ) ( )

f x+ + f x2

(i.e., the average of the left-hand and right-hand limits) at every point where f(x) has a jump discontinuity.

© 2004 by CRC Press LLC

an =

1 L

Ú

L

bn =

1 L

Ú

L

-L

-L

f ( x ) cos

npx dx , n = 0,1, 2, 3,K; L

f ( x ) sin

npx dx , n = 1, 2, 3,K L

1587_Book.fm Page 95 Monday, September 1, 2003 7:17 PM

5-95

General Engineering and Mathematics

Series (continued) We may also write an =

1 L

Ú

a +2L

a

npx 1 dx and bn = L L

f ( x ) cos

Ú

a +2L

a

f ( x ) sin

npx dx L

where a is any real number. Thus if a = 0, an =

1 L

Ú

2L

bn =

1 L

Ú

2L

f ( x ) cos

npx dx , n = 0,1, 2, 3,K; L

f ( x ) sin

npx dx , n = 1, 2, 3,K L

0

0

2. If in addition to the above restrictions, f(x) is even (i.e., f(–x) = f(x)), the Fourier series reduces to a0 + 2

•

Â a cos n

n=1

npx L

That is, bn = 0. In this case, a simpler formula for an is an =

2 L

Ú

L

f ( x ) cos

0

npx dx , n = 0,1, 2, 3,K L

3. If in addition to the restrictions in (1), f(x) is an odd function (i.e., f(–x) = –f(x)), then the Fourier series reduces to •

Âb sin n

n=1

npx L

That is, an = 0. In this case, a simpler formula for the bn is bn =

2 L

Ú

L

0

f ( x ) sin

npx dx , n = 1, 2, 3,K L

4. If in addition to the restrictions in (2) above, f(x) = –f(L – x), then an will be 0 for all even values of n, including n = 0. Thus in this case, the expansion reduces to •

Âa

2m-1

m=1

cos

(2m - 1)px L

5. If in addition to the restrictions in (3) above, f(x) = f(L – x), then bn will be 0 for all even values of n. Thus in this case, the expansion reduces to •

Âb m=1

2m-1

sin

(2m - 1)px L

(The series in (4) and (5) are known as odd-harmonic series, since only the odd hormonics appear. Similar rules may be stated for even-harmonic series, but when a series appears in the even-harmonic form, it means that 2L has not been taken as the smallest period of f(x). Since any integral multiple of a period is also a period, series obtained in this way will also work, but in general computation is simplified if 2L is taken to be the smallest period.) 6. If we write the Euler definitions for cos q and sin q, we obtain the complex form of the Fourier Series known either as the “Complex Fourier Series” or the “Exponential Fourier Series” of f(x). It is represented as f (x ) =

n=+•

Â

1 c e iwn x 2 n=-• n

where cn =

© 2004 by CRC Press LLC

1 L

Ú

L

-L

f ( x )e - iwn xdx , n = 0, ± 1, ± 2, ± 3,K

1587_Book.fm Page 96 Tuesday, September 2, 2003 3:25 PM

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CRC Handbook of Engineering Tables

Series (continued) np , n = 0, ± 1, ± 2,K L The set of coefficients {cn} is often referred to as the Fourier spectrum. 7. If both sine and cosine terms are present and if f(x) is of period 2L and expandable by a Fourier series, it can be represented as with w n =

f (x ) =

a0 + 2

•

Âc sinÊÁË n

n=1

npx ˆ + fn ˜ , where an = c n sin fn , ¯ L

Êa ˆ bn = c n cos fn , c n = an2 + bn2 , fn = arc tanÁ n ˜ Ë bn ¯ It can also be represented as f (x ) =

a0 + 2

•

Âc cosÊÁË n

n=1

npx ˆ + fn ˜ , where an = c n cos f n , ¯ L

Ê b ˆ bn = -c n sin f n , c n = an2 + bn2 , fn = arc tanÁ - n ˜ Ë an ¯ where fn is chosen so as to make an, bn, and cn hold. 8. The following table of trigonometric identities should be helpful for developing Fourier Series. n sin np cos np

–0 (–1)n

n even

n odd

n/2 odd

n/2 even

0 +1

0 –1

0 +1

0 +1

*sin

np 2

0

(–1)(n-1)/2

0

0

*cos

np 2

(–1)n/2

0

–1

+1

(–1)(n–2)/4

0

sin

n 2 + 4n+11) 2 (-1)( 2

np 4

* A useful formula for sin np (i) = 2 2

n+1

sin

8

np np and cos is given by 2 2

[(1 - 1) - 1] and cos n2p = (i2) [(-1) + 1] , where i = -1 n

n

n

2

Auxiliary Formulas for Fourier Series 1=

4 È px 1 3px 1 5px ù + sin + sin + Lú sin 5 p ÍÎ k 3 k k û

x=

2k È px 1 2px 1 3px ù - sin + sin - Lú sin k 2 k k p ÍÎ 3 û

x=

k 4k È px 1 3px 1 5px ù + cos + 2 cos + Lú cos k 32 k k 2 p 2 ÍÎ 5 û

© 2004 by CRC Press LLC

[0 < x < k] [-k < x < k] [0 < x < k]

1587_Book.fm Page 97 Monday, September 1, 2003 7:17 PM

5-97

General Engineering and Mathematics

Series (continued) x2 =

2k 2 p3 -

x2 =

ÈÊ p 2 4 ˆ 2px Ê p 2 4 ˆ 3px px p 2 - ˜ sin - sin +Á - 3 ˜ sin ÍÁ k k k 1 1 2 3 3 Ë ¯ Ë ¯ ÍÎ

ù 4px Ê p 2 4 ˆ 5px p2 +Á - 3 ˜ sin + Lú sin k k 4 Ë 5 5 ¯ úû

k 2 4k 2 - 2 3 p

2px 1 3px 1 4px È px 1 ù Ícos k - 22 cos k + 32 cos k - 42 cos k + Lú Î û

1-

1 1 1 p + - +L = 3 5 7 4

1+

1 1 1 p2 + 2 + 2 +L = 2 6 2 3 4

1-

1 1 1 p2 + - +L = 12 22 32 42

1+

1 1 1 p2 + 2 + 2 +L = 2 8 3 5 7

[0 < x < k] [-k < x < k]

1 1 1 1 p2 + + + +L = 24 22 42 62 82 From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 890–897.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Tables of Statistical Probability Mathematical probability deals with the random or chance variation of numerical data. When the probability or statistical chance is expressed numerically (percentage or decimal), it is a specific likelihood representing the ratio of chances in favor to total chances available. In the usual probability-distribution graphs probability is represented by an area under the frequency curve. Measures of central tendency are the mean (m) or arithmetical average, the median or middle value, and the mode or most frequent value. Measures of dispersion are the individual deviation (x), which is the difference between the mean and the specific value under consideration; the standard deviation (s), which is the square root of the mean of the squares of the deviations (rms†); and the variance, which is the square of the standard deviation (s2). The range is the spread between the smallest and the largest items of data. Frequency (y) is a measure of the importance of a given value in terms of the frequency of its occurrence. It is commonly expressed as the frequency of occurrence of stated values of the deviation from yo, the mean, but it also refers to the frequency of occurrence of a given magnitude in original data. Frequency distribution describes the frequency of occurrence of the various numerical values, or the frequency of occurrence of stated deviations from the mean. A frequency distribution is represented mathematically, by equations, curves, or tables. The distributions covered by the following tables include he normal, the binomial, the Poisson, the t, the F, and the chi-square distributions. Statistical sample is a random sample representative of all the original data. The data being sampled are referred to collectively as the population or the universe. Statistical significance is a general term for the assumed importance of the probability. The range of probabilities used to describe a very likely occurrence is often expressed as a percentage between 90 and 99.9. For very unlikely occurrences the probabilities between 0.1 percent and 10 percent are examined. The arbitrarily selected percentages are often called confidence limits, implying that there is a 100 percent probability, representing full or complete certainty. The borderline between a “significant” probability and one that is not significant must be arbitrarily selected. (See Student’s t-Distribution.) Degrees of freedom (N) refer to the number of independent properties of a sample. It is usually n-1, where n is the number of data items. Table 1. Normal or Gaussian Probability Distribution.‡ This “continuous” distribution is applicable to a population or universe for which the number of items of data is infinitely large and in which the deviations from the mean are random and unrelated. It applies also to a large representative sample of such data, such as 50 or 100 items; the larger the sample, the closer the approximation. For this symmetrical distribution the mean, the median, and the mode all coincide and are represented by the maximum ordinate yo. The table gives normalized values, in which the maximum probability area under 1 the curve is unity; the deviations are measured in units of s, the mean deviation, and the maximum ordinate is ---------= 0.39894. 2p

Table 2. Student’s t-Distribution. The t-test is widely used to evaluate the significance of differences, such as the difference between the means of two samples and the difference between a sample mean and the population mean. At the top of each column in the table is that probability that the difference would exist by chance alone. The probability of a match or a fit decreases as t increases. Two common borderline values are p = 0.01 and p = 0.05. For example, if the computed value of t is larger than the one given in the column headed 0.05, the interpretation might be as follows: the probability that this difference is due to chance alone is less than one in twenty; hence the difference is significant and is due to factors other than pure chance. The ratio t must be correctly computed.** For comparing a sample with a known parent population, it is the ratio of the difference between the sample mean and the population mean to the standard deviation of the mean of the parent population (corrected for sample size): t=

mean1 – mean2 s

N

The t-distribution approaches the normal distribution as the number of degrees of freedom approaches infinity, but in any case the means themselves are assumed to be normally distributed. Table 3. Chi-Square Distribution. This is another test for the significance of differences by evaluation of the spread of the data. There are several ways to apply the chi-square test. One involves the ratio of the squares of the two standard deviations: chi-square = N (s1 s 2 )

2

† For linear correlation by a line of regression, using least squares, the standard deviation of the points from the line is called the “standard error of estimate.” ‡ Also called the normal error function and the normal frequency curve. ** Consult a textbook on statistics; see References.

© 2004 by CRC Press LLC

1587_Book.fm Page 99 Friday, September 26, 2003 12:10 PM

5-99

General Engineering and Mathematics

Tables of Statistical Probability (continued) For example, if it is desired to test the variability or dispersion for a sample when that of a parent population is known, a value of chi-square (= N times the ratio of variances) larger than the one in the 0.10 column would mean that there are fewer than ten chances in one hundred that the sample represented the parent population, and that its larger variability occurred purely by chance. As the chi-square increases, the probability of matching or agreement decreases. Another application of the chi-square table uses the summation of the squares of frequency differences for goodness of fit with the parent distribution: chi-square =

S( y - y c )

2

yc

where the values of yc are those of the comparison standard. A very useful application of the chi-square test is in the evaluation of attribute data where there are a number of classes and the expectations in the different classes are unequal. Table 4. F-Distribution. This distribution is used for testing dispersion in terms of variance. One use for the F-test is to determine whether two samples, possibly of different sizes, drawn independently from two normal populations, actually represent populations with identical standard deviations. Here F is the ratio of the variance of the samples: F = s12 s 22 In the tables, since the two sample sizes and degrees of freedom may be unequal, the additional variable is accommodated by setting up a separate table for each probability value, the p values used here being in the range 0.001 to 0.10. The borderline between a significant difference and one that is not significant must be selected, and the table with that probability value is used. If the value of F is larger than the corresponding one in that table, the probability that the two samples came from like populations is even less than that selected as a borderline. Table 5. Binomial Distribution. This is a “discrete” distribution representing the probabilities of “success” in N trials for a population or sample in which only two outcomes are possible, but for which the eventual outcome is fixed and known if an infinite number of trials are made.† This eventual outcome is fixed by the conditions, such as 0.5 for one face of a coin or 0.1667 for one face of a six-sided die. Values in the body of the table represent the cumulative probability of X or more successes in N trials. In applications to acceptance or attribute sampling, the table gives the probability of X or more acceptances (or rejections) in a single sample of N items. In either case the known or fixed probability of the result (success or failure) for the entire population is represented by p. Table 6. Poisson Distribution. This is a discrete distribution approximating the binomial when the total number of items of data (the populations) is very large, but the probability (p) is very small and the sample is small compared with the population The Poisson cumulative probability, i.e., the probability that X is greater than or equal to X¢, is expressed as P=

•

Â

X =X¢

e

-N p

(Np)

x

X¢

for specified values of X¢ and Np. The table is arranged in terms of the product, Np, where N is the sample size and p is the fixed probability for the entire population. For this distribution Np = m = s2, i.e., both the mean and the variance are equal to Np. The standard deviation is s = Np . Values in the body of the table represent the cumulative probability of X or more successes in N trials (the same as for the binomial table); or in sampling, the values represent the probability of X or more acceptances in sample of N items. In either case the fixed probability for the whole population is p. †Outcomes might be expressed as successes or failure, yes or no, hit or miss, accept or reject, heads or talk, plus or minus, one or zero. References “Applied General Statistics,” 3rd ed., F.E. Croxton, D.J. Cowden and S. Klein, Eds., Prentice-Hall, Inc., 1967. “Biometrika Tables for Statisticians,” E.S. Pearson and H.O. Hartley, Eds., Vol. 1, Cambridge University Press, 1962. “CRC Handbook of Chemistry and Physics,” 50th ed., R.C. Weast, Ed., The Chemical Rubber Co., 1969. “CRC Handbook of Probability and Statistics,” 2nd ed., W.H. Beyer, Ed., The Chemical Rubber Co., 1968. “CRC Handbook of Tables for Mathematics,” 4th ed., S.M. Selby, Ed., The Chemical Rubber Co., 1970. “CRC Standard Mathematical Tables,” 17th ed., S.M. Selby, Ed., The Chemical Rubber Co., 1969. “Geigy Scientific Tables,” 6th ed., Geigy Chemical Corporation, 1962. “Navord Report,” No. 3369, Ordinance Test Station, 1955. “Quality Control Handbook,” J.M. Juran, Ed., McGraw-Hill Book Company, 1962. “Statistics,” A.D. Rickmers and H.N. Todd, Eds., McGraw-Hill Book Company, 1967. From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL. 1973, pp. 921–934.

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Table 1. Ordinates and Areas for Normal or Gaussian Probability Distribution

x

x Aox = Ax - 0.5

Ax

yo -x

x -x Att = 1 - Axx

x Axx = 2Aox

y

y/yo

SYMBOLS: x = deviation from the mean (or from zero error). One unit of x equals one standard deviation. y = frequency of occurrence of the deviation (“probability density”) 1 -x2 2 = f (x ) = e 2p Sx 2 s = standard deviation or error (rms) = n yo = frequency of occurrence of mean value y/yo = relative frequency in terms of mean frequency Ax = area under curve from –a to x =

Ú

+x

-•

1 2p

2

e - x 2dx

Aox = area under curve from zero to x Axx = area under curve from –x to +x = probability of occurrence of values deviating from mean value in range from –x to +x Att = residual area, in the two “tails” = 1 – Axx +• Note: All areas in the table are based on a transformation of the variable such that A-• = 1, with decimal values shown in the table.

Independent Variable = Deviation = x/s

© 2004 by CRC Press LLC

x/s

Axx

Aox

Ax

Att

y

y/yo

.00 .05 .10 .15 .20

.0000 .0398 .0797 .1192 .1585

.0000 .0199 .0398 .0596 .0793

.5000 .5199 .5398 .5595 .5793

1.0000 .9602 .9203 .8808 .8415

.3989 .3984 .3971 .3945 .3910

1.0000 .9986 .9950 .9888 .9802

.25 .30 .35 .40 .45

.1774 .2358 .2736 .3108 .3472

.0987 .1179 .1368 .1554 .1736

.5987 .6179 .6368 .6554 .6736

.8026 .7642 .7263 .6892 .6527

.3867 .3814 .3752 .3683 .3605

.9692 .9560 .9405 .9231 .9037

.50 .55 .60 .65 .70

.3829 .4176 .4515 .4844 .5161

.1915 .2088 .2257 .2422 .2580

.6915 .7088 .7257 .7422 .7580

.6171 .5823 .5485 .5157 .4839

.3521 .3429 .3332 .3230 .3123

.8825 .8596 .8353 .8096 .7827

.75 .80 .85 .90 .95

.5468 .5763 .6046 .6319 .6578

.2734 .2881 .3023 .3159 .3289

.7734 .7881 .8023 .8159 .8289

.4533 .4237 .3953 .3681 .3421

.3011 .2897 .2780 .2661 .2541

.7548 .7262 .6968 .6670 .6368

1587_Book.fm Page 101 Monday, September 1, 2003 7:17 PM

5-101

General Engineering and Mathematics

Table 1. Ordinates and Areas for Normal or Gaussian Probability Distribution (continued) x/s

Axx

Aox

Ax

Att

y

y/yo

1.00 1.05 1.10 1.15 1.20

.6827 .7062 .7286 .7498 .7698

.3413 .3531 .3643 .3749 .3849

.8413 .8531 .8643 .8749 .8849

.3173 .2938 .2714 .2502 .2302

.2420 .2299 .2179 .2059 .1942

.6065 .5762 .5461 .5162 .4868

1.25 1.30 1.35 1.40 1.45

.7887 .8064 .8229 .8384 .8530

.3944 .4032 .4115 .4192 .4265

.8944 .9032 .9115 .9192 .9265

.2113 .1936 .1771 .1616 .1470

.1826 .1714 .1604 .1497 .1394

.4578 .4296 .4020 .3753 .3495

1.50 1.55 1.60 1.65 1.70

.8664 .8788 .8904 .9010 .9108

.4332 .4394 .4452 .4505 .4554

.9332 .9394 .9452 .9505 .9554

.1336 .1212 .1096 .0990 .0892

.1295 .1200 .1109 .1023 .0940

.3247 .3008 .2780 .2563 .2376

1.75 1.80 1.85 1.90 1.95

.9198 .9281 .9356 .9426 .9488

.4599 .4641 .4678 .4713 .4744

.9599 .9641 .9678 .9713 .9744

.0802 .0720 .0644 .0574 .0512

.0863 .0790 .0721 .0656 .0596

.2163 .1979 .1806 .1645 .1494

2.00 2.05 2.10 2.15 2.20

.9545 .9596 .9642 .9684 .9722

.4772 .4798 .4821 .4842 .4861

.9772 .9798 .9821 .9842 .9861

.0455 .0404 .0358 .0316 .0278

.0540 .0488 .0440 .0396 .0355

.1353 .1223 .1040 .0992 .0890

2.25 2.30 2.35 2.40 2.45

.9756 .9786 .9812 .9836 .9858

.4878 .4893 .4906 .4918 .4929

.9878 .9893 .9906 .9918 .9929

.0244 .0214 .0188 .0164 .0143

.0317 .0283 .0252 .0224 .0198

.0796 .0709 .0632 .0561 .0497

2.50 2.55 2.60 2.65 2.70

.9876 .9892 .9907 .9920 .9930

.4938 .4946 .4953 .4960 .4965

.9938 .9946 .9953 .9960 .9965

.0124 .0108 .0093 .0080 .0070

.0175 .0155 .0136 .0119 .0104

.0439 .0387 .0341 .0299 .0261

2.75 2.80 2.85 2.90 2.95 3.00

.9940 .9948 .9956 .9962 .9968 .9973

.4970 .4974 .4978 .4981 .4984 .4987

.9970 .9974 .9978 .9981 .9984 .9987

.0060 .0051 .0044 .0037 .0032 .0027

.0091 .0079 .0069 .0060 .0051 .0044

.0228 .0198 .0172 .0150 .0129 .0111

x/s

Axx

Aox

Ax

Att

y

y/yo

.005 .013 .063 .126 .189

.005 .010 .050 .100 .150

.002 .005 .025 .050 .075

.502 .505 .525 .550 .575

.995 .990 .950 .900 .850

.399 .399 .398 .396 .392

.999 .999 .998 .990 .982

.253 .319

.200 .250

.100 .125

.600 .625

.800 .750

.386 .379

.965 .950

Independent Variable = Probability = Axx

© 2004 by CRC Press LLC

1587_Book.fm Page 102 Monday, September 1, 2003 7:17 PM

5-102

CRC Handbook of Engineering Tables

Table 1. Ordinates and Areas for Normal or Gaussian Probability Distribution (continued)

© 2004 by CRC Press LLC

x/s

Axx

Aox

Ax

Att

y

y/yo

.385 .454 .524

.300 .350 .400

.150 .175 .200

.650 .675 .700

.700 .650 .600

.370 .360 .348

.925 .900 .870

.598 .674 .755 .842 .935

.450 .500 .550 .600 .650

.225 .250 .275 .300 .325

.725 .750 .775 .800 .825

.550 .500 .450 .400 .350

.334 .318 .300 .280 .258

.835 .795 .749 .702 .643

1.036 1.150 1.282 1.440 1.645

.700 .750 .800 .850 .900

.350 .375 .400 .425 .450

.850 .875 .900 .925 .950

.300 .250 .200 .150 .100

.233 .206 .176 .142 .103

.583 .516 .440 .355 .257

1.960 2.054 2.170 2.326 2.576

.950 .960 .970 .980 .990

.475 .480 .485 .490 .495

.975 .980 .985 .990 .995

.050 .040 .030 .020 .010

.058 .048 .038 .027 .014

.146 .121 .095 .066 .036

2.748 3.090

.995 .999

.497 .499

.997 .999

.005 .001

.009 .003

.022 .008

1587_Book.fm Page 103 Monday, September 1, 2003 7:17 PM

5-103

General Engineering and Mathematics

Table 2. Student’s t-Distribution* Values of t at Specified Levels of Significance; Residual Area Att, Two Tails SYMBOLS: N = degrees of freedom P

P = probability of agreement

.50

.40

.30

.20

.10

.05

.02

.01

.005

.001

1 2 3 4 5

1.000 .816 .765 .741 .727

1.376 1.061 .978 .941 .920

1.963 1.386 1.250 1.190 1.156

3.078 1.886 1.638 1.533 1.476

6.314 2.920 2.353 2.132 2.015

12.706 4.303 3.182 2.776 2.571

31.821 6.965 4.541 3.747 3.365

63.657 9.925 5.841 4.604 4.032

127.32 14.089 7.453 5.598 4.773

636.619 31.598 12.924 8.610 6.869

6 7 8 9 10

.718 .711 .706 .703 .700

.906 .896 .889 .883 .879

1.134 1.119 1.108 1.100 1.093

1.440 1.415 1.397 1.383 1.372

1.943 1.895 1.860 1.833 1.812

2.447 2.365 2.306 2.262 2.228

3.143 2.998 2.896 2.821 2.764

3.707 3.499 3.355 3.250 3.169

4.317 4.029 3.832 3.690 3.581

5.959 5.408 5.041 4.781 4.587

11 12 13 14 15

.697 .695 .694 .692 .691

.876 .873 .870 .868 .866

1.088 1.083 1.079 1.076 1.074

1.363 1.356 1.350 1.345 1.341

1.796 1.782 1.771 1.761 1.753

2.201 2.179 2.160 2.145 2.131

2.718 2.681 2.650 2.624 2.602

3.106 3.055 3.012 2.977 2.947

3.497 3.428 3.372 3.326 3.286

4.437 4.318 4.221 4.140 4.073

16 17 18 19 20

.690 .689 .688 .688 .687

.865 .863 .862 .861 .860

1.071 1.069 1.067 1.066 1.064

1.337 1.333 1.330 1.328 1.325

1.746 1.740 1.734 1.729 1.725

2.120 2.110 2.101 2.093 2.086

2.583 2.567 2.552 2.539 2.528

2.921 2.898 2.878 2.861 2.845

3.252 3.222 3.197 3.174 3.153

4.015 3.965 3.922 3.883 3.850

21 22 23 24 25

.686 .686 .685 .685 .684

.859 .858 .858 .857 .856

1.063 1.061 1.060 1.059 1.058

1.323 1.321 1.319 1.318 1.316

1.721 1.717 1.714 1.711 1.708

1.080 2.074 2.069 2.064 2.060

2.518 2.508 2.500 2.492 2.485

2.831 2.819 2.807 2.797 2.787

3.135 3.119 3.104 3.090 3.078

3.819 3.792 3.767 3.745 3.725

26 27 28 29 30

.684 .684 .683 .683 .683

.856 .855 .855 .854 .854

1.058 1.057 1.056 1.055 1.055

1.315 1.314 1.313 1.311 1.310

1.706 1.703 1.701 1.699 1.697

2.056 2.052 2.048 2.045 2.042

2.479 2.473 2.467 2.462 2.457

2.779 2.771 2.763 2.756 2.750

3.067 3.056 3.047 3.038 3.030

3.707 3.690 3.674 3.659 3.646

40 60 120 •

.681 .679 .677 .674

.851 .848 .845 .842

1.050 1.046 1.041 1.036

1.303 1.296 1.289 1.282

1.684 1.671 1.658 1.645

2.021 2.000 1.980 1.960

2.423 2.390 2.358 2.326

2.704 2.660 2.617 2.576

2.971 2.915 2.860 2.807

3.551 3.460 3.373 3.291

N

* Abridged from Statistical Tables for Biological, Agricultural, and Medical Research, 6th ed., R.A. Fisher and F. Yates, published by Oliver and Boyd, by permission of the authors and publishers; and Biometrika Tables for Statisticians, E.S. Pearson and H.O. Hartley, Eds., Vol. 1, Cambridge University Press, 1962.

© 2004 by CRC Press LLC

1587_Book.fm Page 104 Monday, September 1, 2003 7:17 PM

5-104

CRC Handbook of Engineering Tables

Table 3. Chi-Square Distribution* Values of Chi Square at Specified Levels of Significance; Single Tail SYMBOLS: P N 1 2 3 4 5

N = degrees of freedom

P = probability of agreement

.995

.990

.975

.950

.900

.750

.500

.250

.100

.050

.025

.010

.005

.001

N

— .0100 .0717 .207 .412

.0002 .0201 .115 .297 .554

.001 .0506 .216 .484 .831

.0039 .103 .352 .711 1.15

.0158 .211 .584 1.06 1.61

.102 .575 1.21 1.92 2.67

.455 1.39 2.37 3.36 4.35

1.32 2.77 4.11 5.39 6.63

2.71 3.84 5.02 6.63 4.61 5.99 7.38 9.21 6.25 7.81 9.35 11.3 7.78 9.49 11.1 13.3 9.24 11.1 12.8 15.1

7.88 10.6 12.8 14.9 16.7

10.83 13.82 16.27 18.47 20.52

1 2 3 4 5

5.35 6.35 7.34 8.34 9.34

7.84 9.04 10.2 11.4 12.5

10.6 12.0 13.4 14.7 16.0

12.6 14.1 15.5 16.9 18.3

14.4 16.0 17.5 19.0 20.5

16.8 18.5 20.1 21.7 23.2

18.5 20.3 22.0 23.6 25.2

22.46 6 24.32 7 26.13 8 27.88 9 29.59 10

6 7 8 9 10

.676 .989 1.34 1.73 2.16

.872 1.24 1.65 2.09 2.56

1.24 1.69 2.18 2.70 3.25

1.64 2.17 2.73 3.33 3.94

2.20 2.83 3.49 4.17 4.87

3.45 4.25 5.07 5.90 6.74

11 12 13 14 15

2.60 3.07 3.57 4.07 4.60

3.05 3.57 4.11 4.66 5.23

3.82 4.40 5.01 5.63 6.26

4.57 5.23 5.89 6.57 7.26

5.58 6.30 7.04 7.79 8.55

7.58 8.44 9.30 10.2 11.0

10.3 11.3 12.3 13.3 14.3

13.7 14.8 16.0 17.1 18.2

17.3 18.5 19.8 21.1 22.3

19.7 21.0 22.4 23.7 25.0

21.9 21.3 24.7 26.1 27.5

24.7 26.2 27.7 29.1 30.6

26.8 28.3 29.8 31.3 32.8

31.26 32.91 34.53 36.12 37.70

11 12 13 14 15

16 17 18 19 20

5.14 5.70 6.26 6.84 7.43

5.81 6.41 7.01 7.63 8.26

6.91 7.56 8.23 8.91 9.59

7.96 8.67 9.39 10.1 10.9

9.31 10.1 10.9 11.7 12.4

11.9 12.8 13.7 14.6 15.5

15.3 16.3 17.3 18.3 19.3

19.4 20.5 21.6 22.7 23.8

23.5 24.8 26.0 27.2 28.4

26.3 27.6 28.9 30.1 31.4

28.8 30.2 31.5 32.9 34.2

32.0 33.4 34.8 36.2 37.6

34.3 35.7 37.2 38.6 40.0

39.25 40.79 42.31 43.82 45.32

16 17 18 19 20

21 22 23 24 25

8.03 8.64 9.26 9.89 10.5

8.90 9.54 10.2 10.9 11.5

10.3 11.0 11.7 12.4 13.1

11.6 12.3 13.1 13.8 14.6

13.2 14.0 14.8 15.7 16.5

16.3 17.2 18.1 19.0 19.9

20.3 21.3 22.3 23.3 24.3

24.9 26.0 27.1 28.2 29.3

29.6 30.8 32.0 33.2 34.4

32.7 33.9 35.2 36.4 37.7

35.5 36.8 38.1 39.4 40.6

38.9 40.3 41.6 43.0 44.3

41.4 42.8 44.2 45.6 46.9

46.80 48.27 49.73 51.18 52.62

21 22 23 24 25

26 27 28 29 30

11.2 11.8 12.5 13.1 13.8

12.2 12.9 13.6 14.3 15.0

13.8 14.6 15.3 16.0 16.8

15.4 16.2 16.9 17.7 18.5

17.3 18.1 18.9 19.8 20.6

20.8 21.7 22.7 23.6 24.5

25.3 26.3 27.3 28.3 29.3

30.4 31.5 32.6 33.7 34.8

35.6 36.7 37.9 39.1 40.3

38.9 40.1 41.3 42.6 43.8

41.9 43.2 44.5 45.7 47.0

45.6 47.0 48.3 49.6 50.9

48.3 49.6 51.0 52.3 53.7

54.05 55.48 56.89 58.30 59.70

26 27 28 29 30

*From: Biometrika Tables for Statisticians, E.S. Pearson and H.O. Hartley, Eds., Vol. 1, Cambridge University Press, 1962.

© 2004 by CRC Press LLC

Table A. p = .001 m n 1 2 3 4 5

1

2

3

4

4053† 5000† 5404† 5625† 998.5 999.0 999.2 999.2 167.0 148.5 141.1 137.1 74.14 61.25 56.18 53.44 47.18 37.12 33.20 31.09

5

6

7

5764† 5859† 5929† 999.3 999.3 999.4 134.6 132.8 131.6 51.71 50.53 49.66 29.75 28.84 28.16

8

9

10

15

30

60

•

5981† 6023† 6056† 6158† 6261† 6313† 6366† 999.4 999.4 999.4 999.4 999.5 999.5 999.5 130.6 129.9 129.2 127.4 125.4 124.5 123.5 49.00 48.47 48.05 46.76 45.43 44.75 44.05 27.64 27.24 26.92 25.91 24.87 24.33 23.79

6 7 8 9 10

35.51 29.25 25.42 22.86 21.04

27.00 21.69 18.49 16.39 14.91

23.70 18.77 15.83 13.90 12.55

21.92 17.19 14.39 12.56 11.28

20.81 16.21 13.49 11.71 10.48

20.03 15.52 12.86 11.13 9.92

19.46 15.02 12.40 10.70 9.52

19.03 14.63 12.04 10.37 9.20

18.69 14.33 11.77 10.11 8.96

18.41 14.08 11.54 9.89 8.75

17.56 13.32 10.84 9.24 8.13

16.67 12.53 10.11 8.55 7.47

16.21 12.12 9.73 8.19 7.12

15.75 11.70 9.33 7.81 6.76

12 15 30 60 •

18.64 16.59 13.29 11.97 10.83

12.97 11.34 8.77 7.76 6.91

10.80 9.34 7.05 6.17 5.42

9.63 8.25 6.12 5.31 4.62

8.89 7.57 5.53 4.76 4.10

8.38 7.09 5.12 4.37 3.74

8.00 6.74 4.82 4.09 3.47

7.71 6.47 4.58 3.87 3.27

7.48 6.26 4.39 3.69 3.10

7.29 6.08 4.24 3.54 2.96

6.71 5.54 3.75 3.08 2.51

6.09 4.95 3.22 2.55 1.99

5.76 4.64 2.92 2.25 1.66

5.42 4.31 2.59 1.89 1.00

†Multiply these entries by 100.

Table B. p = .005 m n 1 2 3 4 5

2

3

4

16211 20000 21615 22500 198.5 199.0 199.2 199.2 55.55 49.80 47.47 46.19 31.33 26.28 24.26 23.15 22.78 18.31 16.53 15.56 18.63 16.24 14.69 13.61 12.83

© 2004 by CRC Press LLC

14.54 12.40 11.04 10.11 9.43

12.92 10.88 9.60 8.72 8.08

12.03 10.05 8.81 7.96 7.34

5

6

7

23056 24437 23715 199.3 199.3 199.4 45.39 44.84 44.43 22.46 21.97 21.62 14.94 14.51 14.20 11.46 9.52 8.30 7.47 6.87

11.07 9.16 7.95 7.13 6.54

10.79 8.89 7.69 6.88 6.30

8

9

10

15

30

60

•

23925 24091 24630 24224 25044 25253 25465 199.4 199.4 199.4 199.4 199.5 199.5 199.5 44.13 43.88 43.69 43.08 42.47 42.15 41.83 21.35 21.14 20.97 20.44 19.89 19.61 19.32 13.96 13.77 13.62 13.15 12.66 12.40 12.14 10.57 8.68 7.50 6.69 6.12

10.39 8.51 7.34 6.54 5.97

10.25 8.38 7.21 6.42 5.85

9.81 7.97 6.81 6.03 5.47

9.36 7.53 6.40 5.62 5.07

9.12 7.31 6.18 5.41 4.86

8.88 7.08 5.95 5.19 4.64

5-105

6 7 8 9 10

1

1587_Book.fm Page 105 Tuesday, September 2, 2003 3:25 PM

For m and n Degrees of Freedom; p = .001 to .100; Single Tail

General Engineering and Mathematics

Table 4. F-Distribution*

m n 12 15 30 60 •

1 11.75 10.80 9.18 8.49 7.88

2 8.51 7.70 6.35 5.79 5.30

3 7.23 6.48 5.24 4.73 4.28

4 6.52 5.80 4.62 4.14 3.72

5 6.07 5.37 4.23 3.76 3.35

6

7

5.76 5.07 3.95 3.49 3.09

8

5.52 4.85 3.74 3.29 2.90

5.35 4.67 3.58 3.13 2.74

9 5.20 4.54 3.45 3.01 2.62

10 5.09 4.42 3.34 2.90 2.52

15 4.72 4.07 3.01 2.57 2.19

30 4.33 3.69 2.63 2.19 1.79

60 4.12 3.48 2.42 1.96 1.53

• 3.90 3.26 2.18 1.69 1.00

Table C. p = .010 m

2

3

4

5

6

7

8

9

10

15

30

60

•

4052 98.50 34.12 21.20 16.26

4999.5 99.00 30.82 18.00 13.27

5403 99.17 29.46 16.69 12.06

5625 99.25 28.71 15.98 11.39

5764 99.30 28.24 15.52 10.97

5859 99.33 27.91 15.21 10.67

5928 99.36 27.67 14.98 10.46

5982 99.37 27.49 14.80 10.29

6022 99.39 27.35 14.66 10.16

6056 99.40 27.23 14.55 10.05

6157 99.43 26.87 14.20 9.72

6261 99.47 26.50 13.84 9.38

6313 99.48 26.32 13.65 9.20

6366 99.50 26.13 13.46 9.02

6 7 8 9 10

13.75 12.25 11.26 10.56 10.04

10.92 9.55 8.65 8.02 7.56

9.78 8.45 7.59 6.99 6.55

9.15 7.85 7.01 6.42 5.99

8.75 7.46 6.63 6.06 5.64

8.47 7.19 6.37 5.80 5.39

8.26 6.99 6.18 5.61 5.20

8.10 6.84 6.03 5.47 5.06

7.98 6.72 5.91 5.35 4.94

7.87 6.62 5.81 5.26 4.85

7.56 6.31 5.52 5.96 4.56

7.23 5.99 5.20 4.65 4.25

7.06 5.82 5.03 4.48 4.08

6.88 5.65 4.86 4.31 3.91

12 15 30 60 •

9.33 8.68 7.56 7.08 6.63

6.93 6.36 5.39 4.98 4.61

5.95 5.42 4.51 4.13 3.78

5.41 4.89 4.02 3.65 3.32

5.06 4.56 3.70 3.34 3.02

4.82 4.32 3.47 3.12 2.80

4.64 4.14 3.30 2.95 2.64

4.50 4.00 3.17 2.82 2.51

4.39 3.89 3.07 2.72 2.41

4.30 3.80 2.98 2.63 2.32

4.01 3.52 2.70 2.35 2.04

3.70 3.21 2.39 2.03 1.70

3.54 3.05 2.21 1.84 1.47

3.36 2.87 2.01 1.60 1.00

1 2 3 4 5

Table D. p = .025 m n 1 2

1 647.8 38.51

© 2004 by CRC Press LLC

2 799.5 39.00

3 864.2 39.17

4 899.6 39.25

5 921.8 39.30

6 937.1 39.33

7 948.2 39.36

8 956.7 39.37

9 963.3 39.39

10 968.6 39.40

15 984.9 39.43

30

60

•

1001 39.46

1010 39.48

1018 39.50

CRC Handbook of Engineering Tables

1

n

1587_Book.fm Page 106 Monday, September 1, 2003 7:17 PM

5-106

Table 4. F-Distribution* (continued)

16.04 10.65 8.43

15.44 9.98 7.76

15.10 6.60 7.39

14.88 9.36 7.15

14.73 9.20 6.98

14.62 9.07 6.85

14.54 8.98 6.76

14.47 8.90 6.68

14.42 8.84 6.62

14.25 8.66 6.43

14.08 8.46 6.23

13.99 8.36 6.12

13.90 8.26 6.02

6 7 8 9 10

8.81 8.07 7.57 7.21 6.94

7.26 6.54 6.06 5.71 5.46

6.60 5.89 5.42 5.08 4.83

6.23 5.52 5.05 4.72 4.47

5.99 5.29 4.82 4.48 4.24

5.82 5.12 4.65 4.32 4.07

5.70 4.99 4.53 4.20 3.95

5.60 4.90 4.43 4.10 3.85

5.52 4.82 4.36 4.03 3.78

5.46 4.76 4.30 3.96 3.72

5.27 4.57 4.10 3.77 3.52

5.07 4.36 3.89 3.56 3.31

4.96 4.25 3.78 3.45 3.20

4.85 4.14 3.67 3.33 3.08

12 15 30 60 •

6.55 6.20 5.57 5.29 5.02

5.10 4.77 4.18 3.93 3.69

4.47 4.15 3.59 3.34 3.12

4.12 3.80 3.25 3.01 2.79

3.89 3.58 3.03 2.79 2.57

3.73 3.41 2.87 2.63 2.41

3.61 3.29 2.75 2.51 2.29

3.51 3.20 2.65 2.41 2.19

3.44 3.12 2.57 2.33 2.11

3.37 3.06 2.51 2.27 2.05

3.18 2.86 2.31 2.06 1.83

2.96 2.64 2.07 1.82 1.57

2.85 2.52 1.94 1.67 1.39

2.72 2.40 1.79 1.48 1.00

Table E. p = .050 m n 1 2 3 4 5

1

2

3

4

5

6

7

8

9

10

15

30

60

•

161.4 18.51 10.13 7.71 6.61

199.5 19.00 9.55 6.94 5.79

215.7 19.16 9.28 6.59 5.41

224.6 19.25 9.12 6.39 5.19

230.2 19.30 9.01 6.26 5.05

234.0 19.33 8.94 6.16 4.95

236.8 19.35 8.89 6.09 4.88

238.9 19.37 8.85 6.04 4.82

240.5 19.38 8.81 6.00 4.77

241.9 19.40 8.79 5.96 4.74

245.9 19.43 8.70 5.86 4.62

250.1 19.46 8.62 5.75 4.50

252.2 19.48 8.57 5.69 4.43

254.3 19.50 8.53 5.63 4.36

6 7 8 9 10

5.99 5.59 5.32 5.12 4.96

5.14 4.74 4.46 4.26 4.10

4.76 4.35 4.07 3.86 3.71

4.53 4.12 3.84 3.63 3.48

4.39 3.97 3.69 3.48 3.33

4.28 3.87 3.58 3.37 3.22

4.21 3.79 3.50 3.29 3.14

4.15 3.73 3.44 3.23 3.07

4.10 3.68 3.39 3.18 3.02

4.06 3.64 3.35 3.14 2.98

3.94 3.51 3.22 3.01 2.85

3.81 3.38 3.08 2.86 2.70

3.74 3.30 3.01 2.79 2.62

3.67 3.23 2.93 2.71 2.54

12 15 30 60 •

4.75 4.54 4.17 4.00 3.84

3.89 3.68 3.32 3.15 3.00

3.49 3.29 2.92 2.76 2.60

3.26 3.06 2.69 2.53 2.37

3.11 2.90 2.53 2.37 2.21

3.00 2.79 2.42 2.25 2.10

2.91 2.71 2.33 2.17 2.01

2.85 2.64 2.27 2.10 1.94

2.80 2.59 2.21 2.04 1.88

2.75 2.54 2.16 1.99 1.83

2.62 2.40 2.01 1.84 1.67

2.47 2.25 1.84 1.65 1.46

2.38 2.16 1.74 1.53 1.32

2.30 2.07 1.62 1.39 1.00

5-107

© 2004 by CRC Press LLC

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17.44 12.22 10.01

General Engineering and Mathematics

3 4 5

Table F. p = .100 m

2

3

1 2 3 4 5

39.86 8.53 5.54 4.54 4.06

49.50 9.00 5.46 4.32 3.78

53.59 9.16 5.39 4.19 3.62

6 7 8 9 10

3.78 3.59 3.46 3.36 3.29

3.46 3.26 3.11 3.01 2.92

12 15 30 60 •

3.18 3.07 2.88 2.79 2.71

2.81 2.70 2.49 2.39 2.30

4

8

9

10

15

30

60

•

58.91 9.35 5.27 3.98 3.37

59.44 9.37 5.25 3.95 3.34

59.86 9.38 5.24 3.94 3.32

60.19 9.39 5.23 3.92 3.30

61.22 9.42 5.20 3.87 3.24

62.26 9.46 5.17 3.82 3.17

62.79 9.47 5.15 3.79 3.14

63.33 9.49 5.13 3.76 3.10

3.05 2.83 2.67 2.55 2.46

3.01 2.78 2.62 2.51 2.41

2.98 2.75 2.59 2.47 2.38

2.96 2.72 2.56 2.44 2.35

2.94 2.70 2.54 2.42 2.32

2.87 2.63 2.46 2.34 2.24

2.80 2.56 2.38 2.25 2.16

2.76 2.51 2.34 2.21 2.11

2.72 2.47 2.29 2.16 2.06

2.33 2.21 1.98 1.87 1.77

2.28 2.16 1.93 1.82 1.72

2.24 2.12 1.88 1.77 1.67

2.21 2.09 1.85 1.74 1.63

2.19 2.06 1.82 1.71 1.60

2.10 1.97 1.72 1.60 1.49

2.01 1.87 1.61 1.48 1.34

1.96 1.82 1.54 1.40 1.24

1.90 1.76 1.46 1.29 1.00

5

6

55.83 9.24 5.34 4.11 3.52

57.24 9.29 5.31 4.05 3.45

58.20 9.33 5.28 4.01 3.40

3.29 3.07 2.92 2.81 2.73

3.18 2.96 2.81 2.69 2.61

3.11 2.88 2.73 2.61 2.52

2.61 2.49 2.28 2.18 2.08

2.48 2.36 2.14 2.04 1.94

2.39 2.27 2.05 1.95 1.85

7

*From Biometrika Tables for Statisticians, E.S. Pearson and H.O. Hartley, Eds., Vol. 1, Cambridge University Press, 1962.

© 2004 by CRC Press LLC

CRC Handbook of Engineering Tables

1

n

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5-108

Table 4. F-Distribution* (continued)

1587_Book.fm Page 109 Monday, September 1, 2003 7:17 PM

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General Engineering and Mathematics

Table 5. Binomial Distribution—Cumulative Probabilities: P* SYMBOLS: N = number of trials or size of a sample p = probability of the outcome for the entire population (success or failure, whichever is less) P = cumulative probability of observing X or more successes within N X N

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

2

1 2

.0975 .0025

.1900 .0100

.2775 .0225

.3600 .0400

.4375 .0625

.5100 .0900

.5775 .1225

.6400 .1600

.6975 .2025

.7500 .2500

3

1 2 3

.1426 .0072 .0001

.2710 .0280 .0010

.3859 .0608 .0034

.4880 .1040 .0080

.5781 .1562 .0156

.6570 .2160 .0270

.7254 .2818 .0429

.7840 .3520 .0640

.8336 .4252 .0911

.8750 .5000 .1250

4

1 2 3 4

.1855 .0140 .0005 .0000

.3439 .0523 .0037 .0001

.4780 .1095 .0120 .0005

.5904 .1808 .0272 .0016

.6836 .2617 .0508 .0039

.7599 .3483 .0837 .0081

.8215 .4370 .1265 .0150

.8704 .5248 .1792 .0256

.9085 .6090 .2415 .0410

.9375 .6875 .3125 .0625

5

1 2 3 4 5

.2262 .0226 .0012 .0000 .0000

.4095 .0815 .0086 .0005 .0000

.5563 .1648 .0266 .0022 .0001

.6723 .2627 .0579 .0067 .0003

.7627 .3672 .1035 .0156 .0010

.8319 .4718 .1631 .0308 .0024

.8840 .5716 .2352 .0540 .0053

.9222 .6630 .3174 .0870 .0102

.9497 .7438 .4069 .1312 .0185

.9688 .8125 .5000 .1875 .0312

6

1 2 3 4 5

.2649 .0328 .0022 .0001 .0000

.4686 .1143 .0158 .0013 .0001

.6229 .2235 .0473 .0059 .0004

.7379 .3447 .0989 .0170 .0016

.8220 .4661 .1694 .0376 .0046

.8824 .5798 .2557 .0705 .0109

.9246 .6809 .3529 .1174 .0223

.9533 .7667 .4557 .1792 .0410

.9723 .8364 .5585 .2553 .0692

.9844 .8906 .6562 .3438 .1094

6

.0000

.0000

.0000

.0001

.0002

.0007

.0018

.0041

.0083

.0156

1 2 3 4 5

.3017 .0444 .0038 .0002 .0000

.5217 .1497 .0257 .0027 .0002

.6794 .2834 .0738 .0121 .0012

.7903 .4233 .1480 .0333 .0047

.8665 .5551 .2436 .0706 .0129

.9176 .6706 .3529 .1260 .0288

.9510 .7662 .4677 .1998 .0556

.9720 .8414 .5801 .2898 .0963

.9848 .8976 .6836 .3917 .1529

.9922 .9375 .7734 .5000 .2266

6

.0000

.0000

.0001

.0004

.0013

.0038

.0090

.0188

.0357

.0625

1 2 3 4 5

.3366 .0572 .0058 .0004 .0000

.5695 .1869 .0381 .0050 .0004

.7275 .3428 .1052 .0214 .0029

.8322 .4967 .2031 .0563 .0104

.8999 .6329 .3215 .1138 .0273

.9424 .7447 .4482 .1941 .0580

.9681 .8309 .5722 .2936 .1061

.9832 .8936 .6846 .4059 .1737

.9916 .9368 .7799 .5230 .2604

.9961 .9648 .8555 .6367 .3633

6 7

.0000 .0000

.0000 .0000

.0002 .0000

.0012 .0001

.0042 .0004

.0113 .0013

.0253 .0036

.0498 .0085

.0885 .0181

.1445 .0352

1 2 3 4 5

.3698 .0712 .0084 .0006 .0000

.6126 .2252 .0530 .0083 .0009

.7684 .4005 .1409 .0339 .0056

.8658 .5638 .2618 .0856 .0196

.9249 .6997 .3993 .1657 .0489

.9596 .8040 .5372 .2703 .0988

.9793 .8789 .6627 .3911 .1717

.9899 .9295 .7682 .5174 .2666

.9954 .9615 .8505 .6386 .3786

.9980 .9805 .9102 .7461 .5000

6 7 8

.0000 .0000 .0000

.0001 .0000 .0000

.0006 .0000 .0000

.0031 .0003 .0000

.0100 .0013 .0001

.0253 .0043 .0004

.0536 .0112 .0014

.0994 .0250 .0038

.1658 .0498 .0091

.2539 .0898 .0195

1 2 3

.4013 .0861 .0115

.6513 .2639 .0702

.8031 .4557 .1798

.8926 .6242 .3222

.9437 .7560 .4744

.9718 .8507 .6172

.9865 .9140 .7384

.9940 .9536 .8327

.9975 .9767 .9004

.9990 .9893 .9453

7

8

9

10

© 2004 by CRC Press LLC

1587_Book.fm Page 110 Monday, September 1, 2003 7:17 PM

5-110

CRC Handbook of Engineering Tables

Table 5. Binomial Distribution—Cumulative Probabilities: P* (continued) X

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

4 5

.0010 .0001

.0128 .0016

.0500 .0099

.1209 .0328

.2241 .0781

.3504 .1503

.4862 .2485

.6177 .3669

.7340 .4956

.8281 .6230

6 7 8 9

.0000 .0000 .0000 .0000

.0001 .0000 .0000 .0000

.0014 .0001 .0000 .0000

.0064 .0009 .0001 .0000

.0197 .0035 .0094 .0000

.0473 .0106 .0016 .0001

.0949 .0260 .0048 .0005

.1662 .0548 .0123 .0017

.2616 .1020 .0274 .0045

.3770 .1719 .0547 .0107

1 2 3 4 5

.4596 .1184 .0196 .0022 .0002

.7176 .3410 .1109 .0256 .0043

.8578 .5565 .2642 .0922 .0239

.9313 .7251 .4417 .2054 .0726

.9683 .8416 .6093 .3512 .1576

.9862 .9150 .7472 .5075 .2763

.9943 .9576 .8487 .6533 .4167

.9978 .9804 .9166 .7747 .5618

.9992 .9917 .9579 .8655 .6956

.9998 .9968 .9807 .9270 .8062

6 7 8 9 10

.0000 .0000 .0000 .0000 .0000

.0005 .0001 .0000 .0000 .0000

.0046 .0007 .0001 .0000 .0000

.0194 .0039 .0006 .0001 .0000

.0544 .0143 .0028 .0004 .0000

.1178 .0386 .0095 .0017 .0002

.2127 .0846 .0255 .0056 .0008

.3348 .1582 .0573 .0153 .0028

.4731 .2607 .1117 .0356 .0079

.6128 .3872 .1938 .0730 .0193

1 2 3 4 5

.5367 .1710 .0362 .0055 .0006

.7941 .4510 .1841 .0556 .0127

.9126 .6814 .3958 .1773 .0617

.9648 .8329 .6020 .3518 .1642

.9866 .9198 .7639 .5387 .3135

.9953 .9647 .8732 .7031 .4845

.9984 .9858 .9383 .8273 .6481

.9995 .9948 .9729 .9095 .7827

.9999 .9983 .9893 .9576 .8796

1.0000 .9995 .9963 .9824 .9408

6 7 8 9 10

.0001 .0000 .0000 .0000 .0000

.0022 .0003 .0000 .0000 .0000

.0168 .0036 .0006 .0001 .0000

.0611 .0181 .0042 .0008 .0001

.1484 .0566 .0173 .0042 .0008

.2784 .1311 .0500 .0152 .0037

.4357 .2452 .1132 .0422 .0124

.5968 .3902 .2131 .0950 .0338

.7392 .5478 .3465 .1818 .0769

.8491 .6964 .5000 .3036 .1509

11 12

.0000 .0000

.0000 .0000

.0000 .0000

.0000 .0000

.0001 .0000

.0007 .0001

.0028 .0005

.0093 .0019

.0255 .0063

.0592 .0176

1 2 3 4 5

.6415 .2642 .0755 .0159 .0026

.8784 .6083 .3231 .1330 .0432

.9612 .8244 .5951 .3523 .1702

.9885 .9308 .7939 .5886 .3704

.9968 .9757 .9087 .7748 .5852

.9992 .9924 .9645 .8929 .7625

.9998 .9979 .9879 .9556 .8818

1.0000 .9995 .9964 .9840 .9490

1.0000 .9999 .9991 .9951 .9811

1.0000 1.0000 .9998 .9987 .9941

6 7 8 9 10

.0003 .0000 .0000 .0000 .0000

.0113 .0024 .0004 .0001 .0000

.0673 .0219 .0059 .0013 .0002

.1958 .0867 .0321 .0100 .0026

.3828 .2142 .1018 .0409 .0139

.5836 .3920 .2277 .1133 .0480

.7546 .5834 .3990 .2376 .1218

.8744 .7500 .5841 .4044 .2447

.9447 .8701 .7480 .5857 .4086

.9793 .9423 .8684 .7483 .5881

11 12 13 14 15

.0000 .0000 .0000 .0000 .0000

.0000 .0000 .0000 .0000 .0000

.0000 .0000 .0000 .0000 .0000

.0006 .0001 .0000 .0000 .0000

.0039 .0009 .0002 .0000 .0000

.0171 .0051 .0013 .0003 .0000

.0532 .0196 .0060 .0015 .0003

.1275 .0565 .0210 .0065 .0016

.2493 .1308 .0580 .0214 .0064

.4119 .2517 .1316 .0577 .0207

N

12

15

20

Note: Individual binomial probability terms can be obtained by subtraction, i.e., px =

Â

N x

(p ) - Â (p ) N

x

x +1

x

* Condensed from: CRC Handbook of Tables for Mathematics, 4th ed., S.M. Selby, Ed., The Chemical Rubber Co., 1970.

© 2004 by CRC Press LLC

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General Engineering and Mathematics

Table 6. Poisson Distribution—Cumulative Probabilities: P* SYMBOLS: N = number of trials or size of the sample p = fixed probability of the outcome for entire population (success or failure, whichever is less) P = cumulaive probability of X or more successes (or failures) within N Np X¢

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1 2 3 4

.095 .005 .000 .000

.181 .018 .001 .000

.259 .037 .004 .000

.330 .062 .008 .001

.394 .090 .014 .002

.451 .122 .023 .003

.503 .156 .034 .006

.551 .191 .047 .0009

.593 .228 .063 .014

.632 .264 .080 .019

.667 .301 .100 .026

.699 .337 .121 .034

Np X¢

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

1 2 3 4 5

.728 .373 .143 .043 .011

.753 .408 .167 .054 .014

.777 .442 .191 .066 .019

.798 .475 .217 .079 .024

.817 .507 .243 .093 .030

.835 .537 .269 .109 .036

.850 .566 .296 .125 .044

.865 .594 .323 .143 .053

.878 .620 .350 .161 .062

.889 .645 .377 .181 .073

.900 .669 .404 .201 .084

.909 .692 .430 .221 .096

6

.002

.003

.005

.006

.008

.010

.013

.017

.020

.025

.030

.036

Np X¢

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

1 2 3 4 5

.918 .713 .456 .242 .109

.926 .733 .482 .264 .123

.933 .751 .506 .286 .137

.939 .769 .531 .308 .152

.945 .785 .554 .330 .168

.950 .801 .577 .353 .185

.955 .815 .599 .375 .202

.959 .829 .620 .398 .219

.963 .841 .641 .420 .237

.967 .853 .660 .442 .256

.970 .864 .679 .463 .275

.973 .874 .697 .485 .294

6 7 8

.042 .014 .004

.049 .017 .005

.057 .021 .007

.065 .024 .008

.074 .029 .010

.084 .034 .012

.094 .039 .014

.105 .045 .017

.117 .051 .020

.130 .058 .023

.142 .065 .027

.156 .073 .031

Np X¢

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

1 2 3 4 5

.975 .884 .715 .506 .313

.978 .893 .731 .527 .332

.980 .901 .747 .547 .352

.982 .908 .762 .567 .371

.983 .916 .776 .586 .391

.985 .922 .790 .605 .410

.986 .928 .803 .623 .430

.988 .934 .815 .641 .449

.989 .939 .826 .658 .468

.990 .944 .837 .674 .487

.991 .948 .848 .690 .505

.992 .952 .858 .706 .524

6 7 8 9 10

.170 .082 .035 .014 .005

.184 .091 .040 .016 .006

.199 .101 .045 .019 .007

.215 .111 .051 .021 .008

.231 .121 .057 .025 .010

.247 .133 .064 .028 .011

.263 .144 .071 .032 .013

.280 .156 .079 .036 .015

.297 .169 .087 .040 .017

.314 .182 .095 .045 .020

.332 .195 .104 .050 .022

.349 .209 .113 .056 .025

Np X¢

4.9

5.0

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6.0

1 2 3 4 5

.993 .956 .867 .721 .542

.993 .960 .875 .735 .560

.994 .963 .884 .749 .577

.995 .966 .891 .762 .594

.995 .969 .898 .775 .611

.996 .971 .905 .787 .627

.996 .973 .912 .798 .643

.996 .976 .918 .809 .658

.997 .978 .923 .820 .673

.997 .979 .929 .830 .687

.997 .981 .933 .840 .701

.998 .983 .938 .849 .715

6 7 8

.367 .223 .123

.384 .238 .133

.402 .253 .144

.419 .268 .155

.437 .283 .167

.454 .298 .178

.471 .314 .191

.488 .330 .203

.505 .346 .216

.522 .362 .229

.538 .378 .242

.554 .394 .256

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Table 6. Poisson Distribution—Cumulative Probabilities: P* (continued) Np X¢

4.9

5.0

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6.0

9 10

.062 .028

.068 .032

.075 .036

.082 .040

.089 .044

.097 .049

.106 .054

.114 .059

.123 .065

.133 .071

.143 .077

.153 .084

11 12

.012 .005

.014 .006

.016 .006

.018 .007

.020 .008

.023 .010

.025 .011

.028 .013

.031 .014

.035 .016

.039 .018

.043 .020

Np X¢

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7.0

7.1

7.2

1 2 3 4 5

.998 .984 .942 .858 .728

.998 .985 .946 .866 .741

.998 .987 .950 .874 .753

.998 .988 .954 .881 .765

.999 .989 .957 .888 .776

.999 .990 .960 .895 .787

.999 .991 .963 .901 .798

.999 .991 .966 .907 .808

.999 .992 .968 .913 .818

.999 .993 .970 .918 .827

.999 .993 .973 .923 .836

.999 .994 .975 .928 .845

6 7 8 9 10

.570 .410 .270 .163 .091

.586 .426 .284 .174 .098

.601 .442 .298 .185 .106

.616 .458 .313 .197 .114

.631 .474 .327 .208 .123

.645 .489 .342 .220 .131

.659 .505 .357 .233 .140

.673 .520 .372 .245 .150

.686 .535 .386 .258 .151

.699 .550 .401 .271 .170

.712 .565 .416 .284 .180

.724 .580 .431 .297 .190

11 12

.047 .022

.051 .025

.056 .028

.061 .031

.067 .034

.073 .037

.079 .041

.085 .045

.092 .049

.099 .053

.106 .058

.113 .063

Np X¢

7.3

7.4

7.5

7.6

7.7

7.8

7.9

8.0

8.2

8.4

8.6

8.8

1 2 3 4 5 6 7 8 9 10

.999 .994 .976 .933 .853 .736 .594 .446 .311 .201

.999 .995 .978 .937 .861 .747 .608 .461 .324 .212

.999 .995 .980 .941 .868 .759 .622 .475 .338 .224

1.000 .996 .981 .945 .875 .769 .635 .490 .352 .235

1.000 .996 .983 .948 .882 .780 .649 .504 .366 .247

1.000 .996 .984 .952 .888 .790 .662 .519 .380 .259

1.000 .997 .985 .955 .895 .799 .674 .533 .394 .271

1.000 .997 .986 .958 .900 .809 .687 .547 .408 .283

1.000 .998 .988 .963 .911 .826 .710 .575 .435 .309

1.000 .998 .990 .968 .921 .843 .733 .601 .463 .334

1.000 .998 .991 .972 .930 .858 .754 .627 .491 .360

1.000 .999 .993 .976 .938 .872 .774 .652 .518 .386

11 12 13 14

.121 .068 .036 .018

.129 .074 .039 .020

.138 .079 .043 .022

.147 .085 .046 .024

.156 .092 .050 .026

.165 .098 .055 .029

.174 .105 .059 .031

.184 .112 .064 .034

.205 .127 .074 .041

.226 .143 .085 .048

.248 .160 .097 .056

.271 .178 .110 .064

Np X¢

9.0

10

11

12

13

14

15

16

17

18

19

20

1 3 4 5

.999 .994 .979 .945

1.000 .997 .990 .971

1.000 .999 .995 .985

1.000 1.000 .998 .992

1.000 1.000 .999 .996

1.000 1.000 1.000 .998

1.000 1.000 1.000 .999

1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000

.1.000 .1.000 .1.000 .1.000

6 7 8 9 10

.884 .793 .676 .544 .413

.933 .870 .780 .667 .542

.963 .921 .857 .768 .660

.980 .954 .911 .845 .758

.989 .974 .946 .900 .834

.995 .986 .968 .938 .891

.997 .992 .982 .963 .930

.999 .996 .990 .978 .957

.999 .998 .995 .987 .974

1.000 .999 .997 .993 .985

1.000 1.000 .999 .996 .991

.1.000 1.000 .999 .998 .995

11 12

.294 .197

.417 .303

.540 .421

.653 .538

.748 .647

.824 .740

.882 .815

.923 .873

.951 .915

.970 .945

.982 .965

.989 .979

© 2004 by CRC Press LLC

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General Engineering and Mathematics

Table 6. Poisson Distribution—Cumulative Probabilities: P* (continued) Np X¢

9.0

10

11

12

13

14

15

16

17

18

19

20

13 14 15

.124 .074 .042

.208 .136 .084

.311 .219 .146

.424 .319 .228

.537 .427 .325

.642 .536 .430

.732 .637 .534

.807 .726 .633

.865 .799 .719

.908 .857 .792

.939 .902 .850

.961 .934 .895

16 17 18 19 20

.022 .011 .005 .002 .001

.049 .027 .014 .007 .004

.093 .056 .032 .018 .009

.156 .101 .063 .037 .021

.236 .165 .110 .070 .043

.331 .244 .173 .117 .077

.432 .336 .251 .181 .125

.533 .434 .341 .258 .188

.629 .532 .436 .345 .264

.713 .625 .531 .438 .349

.785 .708 .622 .531 .439

.844 .779 .703 .619 .530

21 22 23 24 25

.000 .000 .000 .000 .000

.002 .001 .000 .000 .000

.005 .002 .001 .001 .000

.012 .006 .003 .002 .001

.025 .014 .008 .004 .002

.048 .029 .017 .009 .005

.083 .053 .033 .020 .011

.132 .089 .058 .037 .022

.195 .139 .095 .063 .041

.269 .201 .145 .101 .068

.353 .275 .207 .151 .107

.441 .356 .279 .213 .157

26

.000

.000

.000

.000

.001

.003

.006

.013

.025

.045

.073

.112

Note: Individual Poisson-probability terms can be obtained by subtraction, i.e., px =

Â

N x

(p ) - Â (p ) N

x

x +1

x

* Condensed from CRC Handbook of Tables for Mathematics, 4th ed., S.M. Selby, Ed., The Chemical Rubber Co., 1970.

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Critical Values for the Sign Test Two-tail Percentage Points for the Binomial for p = .5 The observations in a random sample of size n from X and those of the same size from Y are paired according to the order of observation: (Xi, Yi), i = 1, 2,…, n. The differences di = Xi – Yi are calculated for each of the n pairs. the null hypothesis is that the difference di has a distribution with median zero, i.e., the true proportion of positive (negative) signs is equal to p = 1-- . Thus the test is whether X and Y have 2 the same median. The probability of x positive (negative) signs is given by the binomial probability function n 1 ˆ Ê nˆ Ê 1 ˆ Ê f ( x ) = f Á x ; n, p = ˜ = Á ˜ Á ˜ Ë 2 ¯ Ë x¯ Ë 2 ¯

This table gives the critical value k such that P(x £ k) =

Ê nˆ Ê 1 ˆ n a Á ˜Á ˜ < Ë 2¯ 2 x =0 Ë x ¯ k

Â

n

1%

5%

1 2 3 4 5

10%

25%

n

1%

5%

10%

25%

0

0 0 0

46 47 48 49 50

13 14 14 15 15

15 16 16 17 17

16 17 17 18 18

18 19 19 19 20

0 0 1 1 1

1 1 1 2 2

51 52 53 54 55

15 16 16 17 17

18 18 18 19 19

19 19 20 20 20

20 21 21 22 22

6 7 8 9 10

0 0 0

0 0 0 1 1

11 12 13 14 15

0 1 1 1 2

1 2 2 2 3

2 2 3 3 3

3 3 3 4 4

56 57 58 59 60

17 18 18 19 19

20 20 21 21 21

21 21 22 22 23

23 23 24 24 25

16 17 18 19 20

2 2 3 3 3

3 4 4 4 5

4 4 5 5 5

5 5 6 6 6

61 62 63 64 65

20 20 20 21 21

22 22 23 23 24

23 24 24 24 25

25 25 26 26 27

21 22 23 24 25

4 4 4 5 5

5 5 6 6 7

6 6 7 7 7

7 7 8 8 9

66 67 68 69 70

22 22 22 23 23

24 25 25 25 26

25 26 26 27 27

27 28 28 29 29

26 27 28 29 30

6 6 6 7 7

7 7 8 8 8

8 8 9 9 10

9 10 10 10 11

71 72 73 74 75

24 24 25 25 25

26 27 27 28 28

28 28 28 29 29

30 30 31 31 32

31 32 33 34 35

7 8 8 9 9

9 9 10 10 11

10 10 11 11 12

11 12 12 13 13

76 77 78 79 80

26 26 27 27 28

28 29 29 30 30

30 30 31 31 32

32 32 33 33 34

36 37 38 39 40

9 10 10 11 11

11 12 12 12 13

12 13 13 13 14

14 14 14 15 15

81 82 83 84 85

28 28 29 29 30

31 31 32 32 32

32 33 33 33 34

34 35 35 36 36

41 42 43 44 45

11 12 12 13 13

13 14 14 15 15

14 15 15 16 16

16 16 17 17 18

86 87 88 89 90

30 31 31 31 32

33 33 34 34 35

34 35 35 36 36

37 37 38 38 39

For values of n larger than 90, approximate values of r may be found by taking the nearest integer less than (n – 1)/2 – k n + 1, where k is 1.2879, 0.9800, 0.8224, 0.5752 for the 1, 5, 10, 25% values, respectively. From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 935.

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General Engineering and Mathematics

Factors for Computing Control Limits A. Control Charts for Measurement If the process mean and standard deviation, m and s, are known, and it is assumed that the underlying distribution is

s normal, it is possible to assert with probability 1 – a that the mean of a random sample of size n will fall between x– – za/2 -----n

s - . These two limits on x– provide upper and lower control limits. In actual practice m and s are usually unknown, and x– + za/2 -----n

and it is necessary to estimate their values from a large sample taken while the process is “in control.” The central line of an x– chart is given by m, and the lower and upper three-sigma control limits are given by m – As and m + As, respectively, where 3- and n is the sample size. Where the population parameters are unknown, it is necessary to estimate these parameters A = -----n

on the basis of preliminary samples. If k samples are used, each of size n, denote the mean of the ith sample by x– i and the –

grand mean of the k sample means by x , i.e., x=

1 k

k

Âx

i

i =1

Denote the range of the ith sample by Ri and by R the mean of the k sample ranges, i.e., R=

1 k

k

ÂR

i

i =1

Since x– is an unbiased estimate of the population mean m, the central line for the x– chart is given by x . The statistic R does ------- . The constant multiplier A depends on the not provide an unbiased estimate of s, but A R is an unbiased estimate of 3s –

2

n

2

assumption of normality. Thus, the central line and the lower and upper three-sigma limits, LCL and UCL, for an x chart (with m and s estimated from past data) are given by central line = x LCL = x - A2R UCL = x + A2R The central line and control limits of an R chart are based on the distribution of the range of samples of size n from a normal population. The mean and standard deviation of the sampling distribution of R are given by d2s and d3s, respectively, when s is known. Here d2 and d3 are constants that depend on the size of the sample. The set of control-chart values for an R chart (with s known) is given by central line = d2s LCL = D1s UCL = D2s where D1 = d2 – 3d3 and D2 = d2 + 3d3. If s unknown, the control chart values for an R chart are given by central line = R LCL = D3R UCL = D4R D D where D3 = ------1- and D4 = ------2- . d2 d2 The central line and control limits of an s chart are based on estimates obtained from the samples. A pooled estimate of the population variance is obtained from the k samples, i.e.,

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Factors for Computing Control Limits (continued)

Â (n - 1)s = , Â (n - 1) 2 i

i

s 2p

i

i = 1, 2, K, k

i

i

If the sample sizes are all equal, the pooled estimate is s 2p =

1 k

Âs

2 i

i

The control chart values for an s chart are given by central line = C2¢s p LCL = B2¢s p UCL = B4¢ s p If one uses the biased estimator of the variance s¢p , as is often done in quality control work, the control chart values are given by central line = c 2 s ¢p LCL = B2 s ¢p UCL = B4 s ¢p B. Control Charts for Attributes Control limits for a fraction-defective chart are based on the sampling theory for proportions, using the normal curve approximation to the binomial. If k samples are taken, the estimator of p is given by

Âx , Ân i

p=

i

i = 1, 2, K, k

i

i

where xi is the number of defectives in the ith sample of size ni . The cenral line and control limits of a fraction-defective chart based on analysis of past data are given by central line = p LCL = p - 3

p(1 - p )

UCL = p + 3

p(1 - p )

ni

ni

Â

1 n. k i i Equivalent to the p chart for the fraction defective is the control chart for the number of defective. Here, if p is estimated – by p, the control-chart values for a number-of-defectives chart are given by When the sample sizes are approximately equal, ni is replaced by n =

central line = n p LCL = n p - 3 n p(1 - p ) UCL = n p + 3 n p(1 - p )

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General Engineering and Mathematics

Factors for Computing Control Limits (continued) In many cases it is necessary to control the number of defects per unit C, where C is taken to be a value of a random variable having a Poisson distribution. If k is the number of units available for estimating l, the parameter of the Poisson distribution, and if Ci is the number of defects in the ith unit, than l is estimated by C=

1 k

k

ÂC

i

i =1

and the control-chart values for the C chart are central line = C LCL = C - 3 C UCL = C + 3 C This table presents values of the factors for computing control limis for various sample sizes n. X Chart Number of Observations in Sample, n

R Chart

s Chart (biased)

s Chart

Factor for Factors for Factor for Factors for Factor for Factors for Factors for Control Limits Central Line Control Limits Central Line Control Limits Central Line Control Limits A

A2

d2

2 3 4 5

2.121 1.732 1.500 1.342

1.880 1.023 0.729 0.577

1.128 1.693 2.059 2.326

6 7 8 9 10

1.225 1.134 1.061 1.000 0.949

0.483 0.419 0.373 0.337 0.308

11 12 13 14 15

0.905 0.866 0.832 0.802 0.775

16 17 18 19 20 21 22 23 24 25

D3

D4

c¢2

0 0 0 0

3.267 2.575 2.282 2.115

0.798 0.886 0.921 0.940

2.534 2.704 2.847 2.970 3.078

0 0.076 0.136 0.184 0.223

2.004 1.924 1.864 1.816 1.777

0.285 0.266 0.249 0.235 0.223

3.173 3.258 3.336 3.407 3.472

0.256 0.284 0.308 0.329 0.348

0.750 0.728 0.707 0.688 0.671

0.212 0.203 0.194 0.187 0.180

3.532 3.588 3.640 3.689 3.735

0.655 0.640 0.626 0.612 0.600

0.173 0.167 0.162 0.157 0.153

3.778 3.819 3.858 3.895 3.931

B¢2

B¢4

c2

B2

B4

0 0 0 0

2.298 2.111 1.982 1.889

0.5642 0.7236 0.7979 0.8407

0 0 0 0

3.267 2.568 2.266 2.089

0.951 0.960 0.965 0.969 0.973

0.085 0.158 0.215 0.262 0.302

1.817 1.762 1.715 1.676 1.644

0.8686 0.8882 0.9027 0.9139 0.9227

0.030 0.118 0.185 0.239 0.284

1.970 1.882 1.815 1.761 1.716

1.744 1.716 1.692 1.671 1.652

0.976 0.977 0.980 0.981 0.982

0.336 0.365 0.392 0.414 0.434

1.616 1.589 1.568 1.548 1.530

0.9300 0.9359 0.9410 0.9453 0.9490

0.321 0.354 0.382 0.406 0.428

1.679 1.646 1.618 1.594 1.572

0.364 0.379 0.392 0.404 0.414

1.636 1.621 1.608 1.596 1.586

0.984 0.984 0.986 0.986 0.987

0.454 0.469 0.486 0.500 0.513

1.514 1.499 1.486 1.472 1.461

0.9523 0.9551 0.9576 0.9599 0.9619

0.448 0.466 0.482 0.497 0.510

1.552 1.534 1.518 1.503 1.490

0.425 0.434 0.443 0.452 0.459

1.575 1.566 1.557 1.548 1.541

0.988 0.988 0.989 0.989 0.990

0.525 0.536 0.546 0.556 0.566

1.451 1.440 1.432 1.422 1.414

0.9638 0.9655 0.9670 0.9864 0.9696

0.523 0.534 0.545 0.555 0.565

1.477 1.466 1.455 1.445 1.435

From Bolz, R.E. and Tuve, G.L., Mathematical and statistical tables, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 935.

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Number Systems and Change of Base Positional Notation In our ordinary system of writing numbers, the value of any digit depends on its position in the number. The value of a digit in any position is ten times the value of the same digit one position to the right, or one-tenth the value of the same digit one position to the left. For example, 173.246 = 1 ¥ 102 + 7 ¥ 101 + 3 + 2 ¥

1 1 1 +4¥ 2 +6¥ 3 10 10 10

There is no reason that a number other than 10 cannot be used as the base, or radix, of the number system. In fact, bases of 2, 8, and 16 are commonly used in working with digital computers. When the base used is not clear from the context, it is usually indicated as a parenthesized subscript or merely as a subscript. Thus 743(8) = 7 ¥ 82 + 4 ¥ 8 + 3 = 7 ¥ 64 + 4 ¥ 8 + 3 = 448 + 32 + 3 = 483(10) 1011.101(2) = 1 ¥ 23 + 0 ¥ 22 + 1 ¥ 2 + 1 + 1 ¥

1 1 1 + 0 ¥ + 1 ¥ = 11.625(10) 2 4 8

Change of Base In this section it is assumed that all calculations will be performed in base 10, since this is the only base in which most people can easily compute. However, there is no logical reason that some other base could not be used for the computations. To convert a number from another base into base 10: Simply write down the digits of the number, with each one multiplied by its appropriate positional value. Then perform the indicated computations in base 10, and write down the answer. To convert a number from base 10 into another base: The part of the number to the left of the point and the part to the right must be operated on separately. For the integer part (the part to the left of the point): a. Divide the number by the new base, getting an integer quotient and remainder. b. Write the remainder as the last digit of the number in the new base. c. Using the quotient from the last division in place of the original number, repeat the above two steps until the quotient becomes zero. For the fractional part (the part to the right of the point): a. Multiply the number by the new base. b. Write down the integral part of the product as the first digit of the fractional part in the new base. c. Using the fractional part of the last product in place of the original number, repeat the above two steps until the product becomes an integer, or until the desired number of places have been computed. Examples: These examples show a convenient method of arranging the computations. 1. Convert 103.118(10) to base 8. 8 8

103 12 1

7 4

147.074324… The calculation of the fractional part could be carried out as far as desired. It is a non-terminating fraction that will eventually repeat itself.

.118 8 .944 8 7.552 8 4.416 8 3.328 8 2.624 8 4.992

103.118(10) = 147.074324…(8) The calculations may be further shortened by not writing the multiplier and divisor at each step of the algorithm, as shown in the next example.

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General Engineering and Mathematics

Number Systems and Change of Base (continued) 2.

Convert 275.824(10) to base 5. 5

275 55 11 2

0 0 1

.824 4.120 0.600 3.000

275.824(10) = 2100.403(5) To convert from one base to another (neither of which is 10): The easiest procedure is usually to convert first to base 10, and then to the desired base. However, there are two exceptions to this: 1. If computational facility is possessed in either of the bases, it may be used instead of base 10, and the appropriate one of the above methods applied. 2. If the two bases are different powers of the same number, the conversion may be done digit-by-digit to the base that is the common root of both bases, and then digit-by-digit back to the other base. Example: Convert 127.653(8) to base 16. (For base 16, the letters A–F are used for the digits 10(10)–15(10).) The first step is to convert the number to base 2, simply by converting each digit to its binary equivalent: 127.653(8) = 001 010 111 · 110 101 011(2) Now by simply regrouping the binary number into groups of four binary digits, starting at the point, we convert to base 16: 127.653(16) = 101 0111 · 1101 0101 1(2) = 57.D58(16) From Bolz, R.E. and Tuve, G.L., Number systems and logic, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 949–950.

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CRC Handbook of Engineering Tables

Binary, Octal, and Decimal Numbers 10±n IN OCTAL SCALE 10n 1 12 144 1 750 23 420 3 46 575 7 346

10–n

n

303 641 113 360 545

240 100 200 400 000

10n

0 1 2 3 4

1.000 0.063 0.005 0.000 0.000

000 146 075 406 032

000 314 341 111 155

000 631 217 564 613

000 463 270 570 530

5 6 7 8 9

0.000 0.000 0.000 0.000 0.000

002 000 000 000 000

476 206 015 001 000

132 157 327 257 104

610 364 745 143 560

1 16 221 2 657 34 434 5 432 67 405

327 157 127 553

10–n

n

112 351 432 441 142

402 035 451 634 036

762 564 210 520 440

000 000 000 000 000

10 11 12 13 14

0.000 0.000 0.000 0.000 0.000

000 000 000 000 000

000 000 000 000 000

006 000 000 000 000

676 537 043 003 000

724 115 413 164

461 760 542 731

500 200 400 000

000 000 000 000

15 16 17 18

0.000 0.000 0.000 0.000

000 000 000 000

000 000 000 000

000 000 000 000

000 000 000 000

2n IN DECIMAL SCALE 2n

n 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

1.00069 1.00138 1.00208 1.00277 1.00347 1.00416 1.00486 1.00556 1.00625

2n

n

33874 72557 16050 64359 17485 75432 38204 05803 78234

62581 11335 79633 01078 09503 38973 23785 98468 97782

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

1.00695 1.01395 1.02101 1.02811 1.03526 1.04246 1.04971 1.05701 1.06437

2n

n

55500 94797 21257 38266 49238 57608 66836 80405 01824

56719 90029 07193 56067 41377 41121 23067 61380 53360

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.07177 1.14869 1.23114 1.31950 1.41421 1.51571 1.62450 1.74110 1.86606

34625 83549 44133 79107 35623 65665 47927 11265 59830

n log10 2, n log2 10 IN DECIMAL SCALE n 1 2 3 4 5

n log10 2 0.30102 0.60205 0.90308 1.20411 1.50514

n log2 10

99957 99913 99870 99827 99783

3.32192 6.64385 9.96578 13.28771 16.60964

n

80949 61898 42847 23795 04744

n log10 2

6 7 8 9 10

1.80617 2.10720 2.40823 2.70926 3.01029

n log2 10

99740 99696 99653 99610 99566

19.93156 23.25349 26.57542 29.89735 33.21928

ADDITION AND MULTIPLICATION TABLES Addition

Multiplication Binary Scale 0¥0=0 0¥1=1¥0=0 1¥1=1

0+0= 0 0+1=1+0= 1 1 + 1 = 10 Octal Scale Addition

© 2004 by CRC Press LLC

Multiplication

0

01 02 03 04 05 06 07

1

02 03 04 05 06 07

1 2 3 4 5 6 7

02 03 04 05 06 07 10

2 3 4 5 6 7

04 06 10 12 14 16

03 04 05 06 07 10 11

04 05 06 07 10 11 12

05 06 07 10 11 12 13

06 07 10 11 12 13 14

07 10 11 12 13 14 15

10 11 12 13 14 15 16

06 11 14 17 22 25

10 14 20 24 30 34

12 17 24 31 36 43

14 22 30 36 44 52

16 25 34 43 52 61

85693 66642 47591 28540 09489

36293 97035 44916 72894 73095 10398 12471 92248 73615

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General Engineering and Mathematics

Binary, Octal, and Decimal Numbers (continued) MATHEMATICAL CONSTANTS IN OCTAL SCALE p= p–1 = p= loge p = log2 p = 10 =

(3.11037 555421)(8) (0.24276 301556)(8) (1.61337 611067)(8) (1.11206 404435)(8) (1.51544 163223)(8) (3.12305 407267)(8)

e= e–1 = e= log10 e = log2 e = log2 10 =

(2.55760 521305)(8) (0.27426 530661)(8) (1.511411 230704)(8) (0.33626 754251)(8) (1.34252 166245)(8) (3.24464 741136)(8)

g= loge g = log2 g = 2= loge 2 = loge 10 =

(0.44742 147707)(8) –(0.43127 233602)(8) –(0.62573 030645)(8) (1.32404 746320)(8) (0.54271 027760)(8) (2.23273 067355)(8)

From Bolz, R.E. and Tuve, G.L., Number systems and logic, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 951.

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Octal-Decimal Integer Conversion 0

1

2

3

4

5

6

7

0000 0010 0020 0030 0040 0050 0060 0070

0000 0008 0016 0024 0032 0040 0048 0056

0001 0009 0017 0025 0033 0041 0049 0057

0002 0010 0018 0026 0034 0042 0050 0058

0003 0011 0019 0027 0035 0043 0051 0059

0004 0012 0020 0028 0036 0044 0052 0060

0005 0013 0021 0029 0037 0045 0053 0061

0006 0014 0022 0030 0038 0046 0054 0062

0007 0015 0023 0031 0039 0047 0055 0063

1100 0110 0120 0130 0140 0150 0160 0170

0064 0072 0080 0088 0096 0104 0112 0120

0065 0073 0081 0089 0097 0105 0113 0121

0066 0074 0082 0090 0098 0106 0114 0122

0067 0075 0083 0091 0099 0107 0115 0123

0068 0076 0084 0092 0100 0108 0116 0124

0069 0077 0085 0093 0101 0109 0117 0125

0070 0078 0086 0094 0102 0110 0118 0126

0200 0210 0220 0230 0240 0250 0260 0270

0128 0136 0144 0152 0160 0168 0176 0184

0129 0137 0145 0153 0161 0169 0177 0185

0130 0138 0146 0154 0162 0170 0178 0186

0131 0139 0147 0155 0163 0171 0179 0187

0132 0140 0148 0156 0164 0172 0180 0188

0133 0141 0149 0157 0165 0173 0181 0189

0300 0310 0320 0330 0340 0350 0360 0370

0192 0200 0208 0216 0224 0232 0240 0248

0193 0201 0209 0217 0225 0233 0241 0249

0194 0202 0210 0218 0226 0234 0242 0250

0195 0203 0211 0219 0227 0235 0243 0251

0196 0204 0212 0220 0228 0236 0244 0252

0197 0205 0213 0221 0229 0237 0245 0253

0

1

2

3

4

5

6

7

1000 1010 1020 1030 1040 1050 1060 1070

0512 0520 0528 0536 0544 0552 0560 0568

0513 0521 0529 0537 0545 0553 0561 0569

0514 0522 0530 0538 0546 0554 0562 0570

0515 0523 0531 0539 0547 0555 0563 0571

0516 0524 0532 0540 0548 0556 0564 0572

0517 0525 0533 0541 0549 0557 0565 0573

0518 0526 0534 0542 0550 0558 0566 0574

1100 1110 1120 1130 1140 1150 1160 1170

0576 0584 0592 0600 0608 0616 0624 0632

0577 0585 0593 0601 0609 0617 0625 0633

0578 0586 0594 0602 0610 0618 0626 0634

0579 0587 0595 0603 0611 0619 0627 0635

0580 0588 0596 0604 0612 0620 0628 0636

0581 0589 0597 0605 0613 0621 0629 0637

1200 1210 1220 1230 1240 1250 1260 1270

0640 0648 0656 0664 0672 0680 0688 0696

0641 0649 0657 0665 0673 0681 0689 0697

0642 0650 0658 0666 0674 0682 0690 0698

0643 0651 0659 0667 0675 0683 0691 0699

0644 0652 0660 0668 0676 0684 0692 0700

1300 1310 1320 1330

0704 0712 0720 0728

0705 0713 0721 0729

0706 0714 0722 0730

0707 0715 0723 0731

0708 0716 0724 0732

© 2004 by CRC Press LLC

0

1

2

3

4

5

6

7

0400 0410 0420 0430 0440 0450 0460 0470

0256 0264 0272 0280 0288 0296 0304 0312

0257 0265 0273 0281 0289 0297 0305 0313

0258 0266 0274 0282 0290 0298 0306 0314

0259 0267 0275 0283 0291 0299 0307 0315

0260 0268 0276 0284 0292 0300 0308 0316

0261 0269 0277 0285 0293 0301 0309 0317

0262 0270 0278 0286 0294 0302 0310 0318

0263 0271 0279 0287 0295 0303 0311 0319

0071 0079 0087 0095 0103 0111 0119 0127

0500 0510 0520 0530 0540 0550 0560 0570

0320 0328 0336 0344 0352 0360 0368 0376

0321 0329 0337 0345 0353 0361 0369 0377

0322 0330 0338 0346 0354 0362 0370 0378

0323 0331 0339 0347 0355 0363 0371 0379

0324 0332 0340 0348 0356 0364 0372 0380

0325 0333 0341 0349 0357 0365 0373 0381

0326 0334 0342 0350 0358 0366 0374 0382

0327 0335 0343 0351 0359 0367 0375 0383

0134 0142 0150 0158 0166 0174 0182 0190

0135 0143 0151 0159 0167 0175 0183 0191

0600 0610 0620 0630 0640 0650 0660 0670

0384 0392 0400 0408 0416 0424 0432 0440

0385 0393 0401 0409 0417 0425 0433 0441

0386 0394 0402 0410 0418 0426 0434 0442

0387 0395 0403 0411 0419 0427 0435 0443

0388 0396 0404 0412 0420 0428 0436 0444

0389 0397 0405 0413 0421 0429 0437 0445

0390 0398 0406 0414 0422 0430 0438 0446

0391 0399 0407 0415 0423 0431 0439 0447

0198 0206 0214 0222 0230 0238 0246 0254

0199 0207 0215 0223 0231 0239 0247 0255

0700 0710 0720 0730 0740 0750 0760 0770

0448 0456 0464 0472 0480 0488 0496 0504

0449 0457 0465 0473 0481 0489 0497 0505

0450 0458 0466 0474 0482 0490 0498 0506

0451 0459 0467 0475 0483 0491 0499 0507

0452 0460 0468 0476 0484 0492 0500 0508

0453 0461 0469 0477 0485 0493 0501 0509

0454 0462 0470 0478 0486 0494 0502 0510

0455 0463 0471 0479 0487 0495 0503 0511

0

1

2

3

4

5

6

7

0519 0527 0535 0543 0551 0559 0567 0575

1400 1410 1420 1430 1440 1450 1460 1470

0768 0776 0784 0792 0800 0808 0816 0824

0769 0777 0785 0793 0801 0809 0817 0825

0770 0778 0786 0794 0802 0810 0818 0826

0771 0779 0787 0795 0803 0811 0819 0827

0772 0780 0788 0796 0804 0812 0820 0828

0773 0781 0789 0797 0805 0813 0821 0829

0774 0782 0790 0798 0806 0814 0822 0830

0775 0783 0791 0799 0807 0815 0823 0831

0582 0590 0598 0606 0614 0622 0630 0638

0583 0591 0599 0607 0615 0623 0631 0639

1500 1510 1520 1530 1540 1550 1560 1570

0832 0840 0848 0856 0864 0872 0880 0888

0833 0841 0849 0857 0865 0873 0881 0889

0834 0842 0850 0858 0866 0874 0882 0890

0835 0843 0851 0859 0867 0875 0883 0891

0836 0844 0852 0860 0868 0876 0884 0892

0837 0845 0853 0861 0869 0877 0885 0893

0838 0846 0854 0862 0870 0878 0886 0894

0839 0847 0855 0863 0871 0879 0887 0895

0645 0653 0661 0669 0677 0685 0693 0701

0646 0654 0662 0670 0678 0686 0694 0702

0647 0655 0663 0671 0679 0687 0695 0703

1600 1610 1620 1630 1640 1650 1660 1670

0896 0904 0912 0920 0928 0936 0944 0952

0897 0905 0913 0921 0929 0937 0945 0953

0898 0906 0914 0922 0930 0938 0946 0954

0899 0907 0915 0923 0931 0939 0947 0955

0900 0908 0916 0924 0932 0940 0948 0956

0901 0909 0917 0925 0933 0941 0949 0957

0902 0910 0918 0926 0934 0942 0950 0958

0903 0911 0919 0927 0935 0943 0951 0959

0709 0717 0725 0733

0710 0718 0726 0734

0711 0719 0727 0735

1700 1710 1720 1730

0960 0968 0976 0984

0961 0969 0977 0985

0962 0970 0978 0986

0963 0971 0979 0987

0964 0972 0980 0988

0965 0973 0981 0989

0966 0974 0982 0990

0967 0975 0983 0991

0000 0000 to to 0777 0511 (Octal) (Decimal) Octal Decimal 10000- 4096 20000- 8192 30000-12288 40000-16384 50000-20480 60000-24576 70000-28672

1000 0512 to to 1777 1023 (Octal) (Decimal)

1587_Book.fm Page 123 Monday, September 1, 2003 7:17 PM

5-123

General Engineering and Mathematics

Octal-Decimal Integer Conversion (continued) 1340 1350 1360 1370

2000 to 2777 (Octal)

1024 to 1535 (Decimal)

Octal Decimal 10000- 4096 20000- 8192 30000-12288 40000-16384 50000-20480 60000-24576 70000-28672

3000 to 3777 (Octal)

1536 to 2047 (Decimal)

0736 0744 0752 0760

0737 0745 0753 0761

0738 0746 0754 0762

0739 0747 0755 0763

0740 0748 0756 0764

0741 0749 0757 0765

0742 0750 0758 0766

0743 0751 0759 0767

0

1

2

3

4

5

6

7

2000 2010 2020 2030 2040 2050 2060 2070

1024 1032 1040 1048 1056 1064 1072 1080

1025 1033 1041 1049 1057 1065 1073 1081

1026 1034 1042 1050 1058 1066 1074 1082

1027 1035 1043 1051 1059 1067 1075 1083

1028 1036 1044 1052 1060 1068 1076 1084

1029 1037 1045 1053 1061 1069 1077 1085

1030 1038 1046 1054 1062 1070 1078 1086

1031 1039 1047 1055 1063 1071 1079 1087

2100 2110 2120 2130 2140 2150 2160 2170

1088 1096 1104 1112 1120 1128 1136 1144

1089 1097 1105 1113 1121 1129 1137 1145

1090 1098 1106 1114 1122 1130 1138 1146

1091 1099 1107 1115 1123 1131 1139 1147

1092 1100 1108 1116 1124 1132 1140 1148

1093 1101 1109 1117 1125 1133 1141 1149

1094 1102 1110 1118 1126 1134 1142 1150

2200 2210 2220 2230 2240 2250 2260 2270

1152 1160 1168 1176 1184 1192 1200 1208

1153 1161 1169 1177 1185 1193 1201 1209

1154 1162 1170 1178 1186 1194 1202 1210

1155 1163 1171 1179 1187 1195 1203 1211

1156 1164 1172 1180 1188 1196 1204 1212

1157 1165 1173 1181 1189 1197 1205 1213

2300 2310 2320 2330 2340 2350 2360 2370

1216 1224 1232 1240 1248 1256 1264 1272

1217 1225 1233 1241 1249 1257 1265 1273

1218 1226 1234 1242 1250 1258 1266 1274

1219 1227 1235 1243 1251 1259 1267 1275

1220 1228 1236 1244 1252 1260 1268 1276

0

1

2

3

3000 3010 3020 3030 3040 3050 3060 3070

1536 1544 1552 1560 1568 1576 1584 1592

1537 1545 1553 1561 1569 1577 1585 1593

1538 1546 1554 1562 1570 1578 1586 1594

3100 3110 3120 3130 3140 3150 3160 3170

1600 1608 1616 1624 1632 1640 1648 1656

1601 1609 1617 1625 1633 1641 1649 1657

3200 3210 3220 3230 3240 3250 3260 3270 3300

1664 1672 1680 1688 1696 1704 1712 1720 1728

1665 1673 1681 1689 1697 1705 1713 1721 1729

© 2004 by CRC Press LLC

1740 1750 1760 1770

0992 1000 1008 1016

0993 1001 1009 1017

0994 1002 1010 1018

0995 1003 1011 1019

0996 1004 1012 1020

0997 1005 1013 1021

0998 1006 1014 1022

0999 1007 1015 1023

0

1

2

3

4

5

6

7

2400 2410 2420 2430 2440 2450 2460 2470

1280 1288 1296 1304 1312 1320 1328 1336

1281 1289 1297 1305 1313 1321 1329 1337

1282 1290 1298 1306 1314 1322 1330 1338

1283 1291 1299 1307 1315 1323 1331 1339

1284 1292 1300 1308 1316 1324 1332 1340

1285 1293 1301 1309 1317 1325 1333 1341

1286 1294 1302 1310 1318 1326 1334 1342

1287 1295 1303 1311 1319 1327 1335 1343

1095 1103 1111 1119 1127 1135 1143 1151

2500 2510 2520 2530 2540 2550 2560 2570

1344 1352 1360 1368 1376 1384 1392 1400

1345 1353 1361 1369 1377 1385 1393 1401

1346 1354 1362 1370 1378 1386 1394 1402

1347 1355 1363 1371 1379 1387 1395 1403

1348 1356 1364 1372 1380 1388 1396 1404

1349 1357 1365 1373 1381 1389 1397 1405

1350 1358 1366 1374 1382 1390 1398 1406

1351 1359 1367 1375 1383 1391 1399 1407

1158 1166 1174 1182 1190 1198 1206 1214

1159 1167 1175 1183 1191 1199 1207 1215

2600 2610 2620 2630 2640 2650 2660 2670

1408 1416 1424 1432 1440 1448 1456 1464

1409 1417 1425 1433 1441 1449 1457 1465

1410 1418 1426 1434 1442 1450 1458 1466

1411 1419 1427 1435 1443 1451 1459 1467

1412 1420 1428 1436 1444 1452 1460 1468

1413 1421 1429 1437 1445 1453 1461 1469

1414 1422 1430 1438 1446 1454 1462 1470

1415 1423 1431 1439 1447 1455 1463 1471

1221 1229 1237 1245 1253 1261 1269 1277

1222 1230 1238 1246 1254 1262 1270 1278

1223 1231 1239 1247 1255 1263 1271 1279

2700 2710 2720 2730 2740 2750 2760 2770

1472 1480 1488 1496 1504 1512 1520 1528

1473 1481 1489 1497 1505 1513 1521 1529

1474 1482 1490 1498 1506 1514 1522 1530

1475 1483 1491 1499 1507 1515 1523 1531

1476 1484 1492 1500 1508 1516 1524 1532

1477 1485 1493 1501 1509 1517 1525 1533

1478 1486 1494 1502 1510 1518 1526 1534

1479 1487 1495 1503 1511 1519 1527 1535

4

5

6

7

0

1

2

3

4

5

6

7

1539 1547 1555 1563 1571 1579 1587 1595

1540 1548 1556 1564 1572 1580 1588 1596

1541 1549 1557 1565 1573 1581 1589 1597

1542 1550 1558 1566 1574 1582 1590 1598

1543 1551 1559 1567 1575 1583 1591 1599

3400 3410 3420 3430 3440 3450 3460 3470

1792 1800 1808 1816 1824 1832 1840 1848

1793 1801 1809 1817 1825 1833 1841 1849

1794 1802 1810 1818 1826 1834 1842 1850

1795 1803 1811 1819 1827 1835 1843 1851

1796 1804 1812 1820 1828 1836 1844 1852

1797 1805 1813 1821 1829 1837 1845 1853

1798 1806 1814 1822 1830 1838 1846 1854

1799 1807 1815 1823 1831 1839 1847 1855

1602 1610 1618 1626 1634 1642 1650 1658

1603 1611 1619 1627 1635 1643 1651 1659

1604 1612 1620 1628 1636 1644 1652 1660

1605 1613 1621 1629 1637 1645 1653 1661

1606 1614 1622 1630 1638 1646 1654 1662

1607 1615 1623 1631 1639 1647 1655 1663

3500 3510 3520 3530 3540 3550 3560 3570

1856 1864 1872 1880 1888 1896 1904 1912

1857 1865 1873 1881 1889 1897 1905 1913

1858 1866 1874 1882 1890 1898 1906 1914

1859 1867 1875 1883 1891 1899 1907 1915

1860 1868 1876 1884 1892 1900 1908 1916

1861 1869 1877 1885 1893 1901 1909 1917

1862 1870 1878 1886 1894 1902 1910 1918

1863 1871 1879 1887 1895 1903 1911 1919

1666 1674 1682 1690 1698 1706 1714 1722 1730

1667 1675 1683 1691 1699 1707 1715 1723 1731

1668 1676 1684 1692 1700 1708 1716 1724 1732

1669 1677 1685 1693 1701 1709 1717 1725 1733

1670 1678 1686 1694 1702 1710 1718 1726 1734

1671 1679 1687 1695 1703 1711 1719 1727 1735

3600 3610 3620 3630 3640 3650 3660 3670 3700

1920 1928 1936 1944 1952 1960 1968 1976 1984

1921 1929 1937 1945 1953 1961 1969 1977 1985

1922 1930 1938 1946 1954 1962 1970 1978 1986

1923 1931 1939 1947 1955 1963 1971 1979 1987

1924 1932 1940 1948 1956 1964 1972 1980 1988

1925 1933 1941 1949 1957 1965 1973 1981 1989

1926 1934 1942 1950 1958 1966 1974 1982 1990

1927 1935 1943 1951 1959 1967 1975 1983 1991

1587_Book.fm Page 124 Monday, September 1, 2003 7:17 PM

5-124

CRC Handbook of Engineering Tables

Octal-Decimal Integer Conversion (continued) 3310 3320 3330 3340 3350 3360 3370

1736 1744 1752 1760 1768 1776 1784

1737 1745 1753 1761 1769 1777 1785

1738 1746 1754 1762 1770 1778 1786

1739 1747 1755 1763 1771 1779 1787

1740 1748 1756 1764 1772 1780 1788

1741 1749 1757 1765 1773 1781 1789

1742 1750 1758 1766 1774 1782 1790

1743 1751 1759 1767 1775 1783 1791

0

1

2

3

4

5

6

7

4000 4010 4020 4030 4040 4050 4060 4070

2048 2056 2064 2072 2080 2088 2096 2104

2049 2057 2065 2073 2081 2089 2097 2105

2050 2058 2066 2074 2082 2090 2098 2106

2051 2059 2067 2075 2083 2091 2099 2107

2052 2060 2068 2076 2084 2092 2100 2108

2053 2061 2069 2077 2085 2093 2101 2109

2054 2062 2070 2078 2086 2094 2102 2110

2055 2063 2071 2079 2087 2095 2103 2111

4100 4110 4120 4130 4140 4150 4160 4170

2112 2120 2128 2136 2144 2152 2160 2168

2113 2121 2129 2137 2145 2153 2161 2169

2114 2122 2130 2138 2146 2154 2162 2170

2115 2123 2131 2139 2147 2155 2163 2171

2116 2124 2132 2140 2148 2156 2164 2172

2117 2125 2133 2141 2149 2157 2165 2173

2118 2126 2134 2142 2150 2158 2166 2174

4200 4210 4220 4230 4240 4250 4260 4270

2176 2184 2192 2200 2208 2216 2224 2232

2177 2185 2193 2201 2209 2217 2225 2233

2178 2186 2194 2202 2210 2218 2226 2234

2179 2187 2195 2203 2211 2219 2227 2235

2180 2188 2196 2204 2212 2220 2228 2236

2181 2189 2197 2205 2213 2221 2229 2237

4300 4310 4320 4330 4340 4350 4360 4370

2240 2248 2256 2264 2272 2280 2288 2296

2241 2249 2257 2265 2273 2281 2289 2297

2242 2250 2258 2266 2274 2282 2290 2298

2243 2251 2259 2267 2275 2283 2291 2299

2244 2252 2260 2268 2276 2284 2292 2300

0

1

2

3

5000 5010 5020 5030 5040 5050 5060 5070

2560 2568 2576 2584 2592 2600 2608 2616

2561 2569 2577 2585 2593 2601 2609 2617

2562 2570 2578 2586 2594 2602 2610 2618

5100 5110 5120 5130 5140 5150 5160 5170

2624 2632 2640 2648 2656 2664 2672 2680

2625 2633 2641 2649 2657 2665 2673 2681

5200 5210 5220 5230 5240

2688 2696 2704 2712 2720

2689 2697 2705 2713 2721

1992 2000 2008 2016 2024 2032 2040

1993 2001 2009 2017 2025 2033 2041

1994 2002 2010 2018 2026 2034 2042

1995 2003 2011 2019 2027 2035 2043

1996 2004 2012 2020 2028 2036 2044

1997 2005 2013 2021 2029 2037 2045

1998 2006 2014 2022 2030 2038 2046

1999 2007 2015 2023 2031 2039 2047

0

1

2

3

4

5

6

7

4400 4410 4420 4430 4440 4450 4460 4470

2304 2312 2320 2328 2336 2344 2352 2360

2305 2313 2321 2329 2337 2345 2353 2361

2306 2314 2322 2330 2338 2346 2354 2362

2307 2315 2323 2331 2339 2347 2355 2363

2308 2316 2324 2332 2340 2348 2356 2364

2309 2317 2325 2333 2341 2349 2357 2365

2310 2318 2326 2334 2343 2350 2358 2366

2311 2319 2327 2335 2343 2351 2359 2367

2119 2127 2135 2143 2151 2159 2167 2175

4500 4510 4520 4530 4540 4550 4560 4570

2368 2376 2384 2392 2400 2408 2416 2424

2369 2377 2385 2393 2401 2409 2417 2425

2370 2378 2386 2394 2402 2410 2418 2426

2371 2379 2387 2395 2403 2411 2419 2427

2372 2380 2388 2396 2404 2412 2420 2428

2373 2381 2389 2397 2405 2413 2421 2429

2374 2382 2390 2398 2406 2414 2422 2430

2375 2383 2391 2399 2407 2415 2423 2431

2182 2190 2198 2206 2214 2222 2230 2238

2183 2191 2199 2207 2215 2223 2231 2239

4600 4610 4620 4630 4640 4650 4660 4670

2432 2440 2448 2456 2464 2472 2480 2488

2433 2441 2449 2457 2465 2473 2481 2489

2434 2442 2450 2458 2466 2474 2482 2490

2435 2443 2451 2459 2467 2475 2483 2491

2436 2444 2452 2460 2468 2476 2484 2492

2437 2445 2453 2461 2469 2477 2485 2493

2438 2446 2454 2462 2470 2478 2486 2494

2439 2447 2455 2463 2471 2479 2487 2495

2245 2253 2261 2269 2277 2285 2293 2301

2246 2254 2262 2270 2278 2286 2294 2302

2247 2255 2263 2271 2279 2287 2295 2303

4700 4710 4720 4730 4740 4750 4760 4770

2496 2504 2512 2520 2528 2536 2544 2552

2497 2505 2513 2521 2529 2537 2545 2553

2498 2506 2514 2522 2530 2538 2546 2554

2499 2507 2515 2523 2531 2539 2547 2555

2500 2508 2516 2524 2532 2540 2548 2556

2501 2509 2517 2525 2533 2541 2549 2557

2502 2510 2518 2526 2534 2542 2550 2558

2503 2511 2519 2527 2535 2543 2551 2559

4

5

6

7

0

1

2

3

4

5

6

7

2563 2571 2579 2587 2595 2603 2611 2619

2564 2572 2580 2588 2596 2604 2612 2620

2565 2572 2581 2589 2597 2605 2613 2621

2566 2574 2582 2590 2598 2606 2614 2622

2567 2575 2583 2591 2599 2607 2615 2623

5400 5410 5420 5430 5440 5450 5460 5470

2816 2824 2832 2840 2848 2856 2864 2872

2817 2825 2833 2841 2849 2857 2865 2873

2818 2826 2834 2842 2850 2858 2866 2874

2819 2827 2835 2843 2851 2859 2867 2875

2820 2828 2836 2844 2852 2860 2868 2876

2821 2829 2837 2845 2853 2861 2869 2877

2822 2830 2838 2846 2854 2862 2870 2878

2823 2831 2839 2847 2855 2863 2871 2879

2626 2634 2642 2650 2658 2666 2674 2682

2627 2635 2643 2651 2659 2667 2675 2683

2628 2636 2644 2652 2660 2668 2676 2684

2629 2637 2645 2653 2661 2669 2677 2685

2630 2638 2646 2654 2662 2670 2678 2686

2631 2639 2647 2655 2663 2671 2679 2687

5500 5510 5520 5530 5540 5550 5560 5570

2880 2888 2896 2904 2912 2920 2928 2936

2881 2889 2897 2905 2913 2921 2929 2937

2882 2890 2898 2906 2914 2922 2930 2938

2883 2891 2899 2907 2915 2923 2931 2939

2884 2892 2900 2908 296 2924 2932 2940

2885 2893 2901 2909 2917 2925 2933 2941

2886 2894 2902 2910 2918 2926 2934 2942

2887 2895 2903 2911 2919 2927 2935 2943

2690 2698 2706 2714 2722

2691 2699 2707 2715 2723

2692 2700 2708 2716 2724

2693 2701 2709 2717 2725

2694 2702 2710 2718 2726

2695 2703 2711 2719 2727

5600 5610 5620 5630 5640

2944 2952 2960 2968 2976

2945 2953 2961 2969 2977

2946 2954 2962 2970 2978

2947 2955 2963 2971 2979

2948 2956 2964 2972 2980

2949 2957 2965 2973 2981

2950 2958 2966 2974 2982

2951 2959 2967 2975 2983

© 2004 by CRC Press LLC

3710 3720 3730 3740 3750 3760 3770

4000 to 4777 (Octal)

2048 to 2559 (Decimal)

Octal Decimal 10000- 4096 20000- 8192 30000-12288 40000-16384 50000-20480 60000-24576 70000-28672

5000 to 5777 (Octal)

2560 to 3071 (Decimal)

1587_Book.fm Page 125 Monday, September 1, 2003 7:17 PM

5-125

General Engineering and Mathematics

Octal-Decimal Integer Conversion (continued)

6000 to 6777 (Octal)

3072 to 3583 (Decimal)

Octal Decimal 10000- 4096 20000- 8192 30000-12288 40000-16384 50000-20480 60000-24576 70000-28672

7000 to 7777 (Octal)

3584 to 4095 (Decimal)

5250 5260 5270

2728 2736 2744

2729 2737 2745

2730 2738 2746

2731 2739 2747

2732 2740 2748

2733 2741 2749

2734 2742 2750

2735 2743 2751

5650 5660 5670

2984 2992 3000

2985 2993 3001

2986 2994 3002

2987 2995 3003

2988 2996 3004

2989 2997 3005

2990 2998 3006

2991 2999 3007

5300 5310 5320 5330 5340 5350 5360 5370

2752 2760 2768 2776 2784 2792 2800 2808

2753 2761 2769 2777 2785 2793 2801 2809

2754 2762 2770 2778 2786 2794 2802 2810

2755 2763 2771 2779 2787 2795 2803 2811

2756 2764 2772 2780 2788 2796 2804 2812

2757 2765 2773 2781 2789 2797 2805 2813

2758 2766 2774 2782 2790 2798 2806 2814

2759 2767 2775 2783 2791 2799 2807 2815

5700 5710 5720 5730 5740 5750 5760 5770

3008 3016 3024 3032 3040 3048 3056 3064

3009 3017 3025 3033 3041 3049 3057 3065

3010 3018 3026 3034 3042 3050 3058 3066

3011 3019 3027 3035 3043 3051 3059 3067

3012 3020 3028 3036 3044 3052 3060 3068

3013 3021 3029 3037 3045 3053 3061 3069

3014 3022 3030 3038 3046 3054 3062 3070

3015 3023 3031 3039 3047 3055 3063 3071

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

6000 6010 6020 6030 6040 6050 6060 6070

3072 3080 3088 3096 3104 3112 3120 3128

3073 3081 3089 3097 3105 3113 3121 3129

3074 3082 3090 3098 3106 3114 3122 3139

3075 3083 3091 3099 3107 3115 3123 3131

3076 3084 3092 3100 3108 3116 3124 3132

3077 3085 3093 3101 3109 3117 3125 3133

3078 3086 3094 3102 3110 3118 3126 3134

3079 3087 3095 3103 3111 3119 3127 3135

6400 6410 6420 6430 6440 6450 6460 6470

3328 3336 3344 3352 3360 3368 3376 3384

3329 3337 3345 3353 3361 3369 3377 3385

3330 3338 3346 3354 3362 3370 3378 3386

3331 3339 3347 3355 3363 3371 3379 3387

3332 3340 3348 3356 3364 3372 3380 3388

3333 3341 3349 3357 3365 3373 3381 3389

3334 3342 3350 3358 3366 3374 3382 3390

3335 3343 3351 3359 3367 3375 3383 3391

6100 6110 6120 6130 6140 6150 6160 6170

3136 3144 3152 3160 3168 3176 3184 3192

3137 3145 3153 3161 3169 3177 3185 3193

3138 3146 3154 3162 3170 3178 3186 3194

3139 3147 3155 3163 3171 3179 3187 3195

3140 3148 3156 3164 3172 3180 3188 3196

3141 3149 3157 3165 3173 3181 3189 3197

3142 3150 3158 3166 3174 3182 3190 3198

3143 3151 3159 3167 3175 3183 3191 3199

6500 6510 6520 6530 6540 6550 6560 6570

3392 3400 3408 3416 3424 3432 3440 3448

3393 3401 3409 3417 3425 3433 3441 3449

3394 3402 3410 3418 3426 3434 3442 3450

3395 3403 3411 3419 3427 3435 3443 3451

3396 3404 3412 3420 3428 3436 3444 3452

3397 3405 3413 3421 3429 3437 3445 3453

3398 3406 3414 3422 3430 3438 3446 3454

3399 3407 3415 3423 3431 3439 3447 3455

6200 6210 6220 6230 6240 6250 6260 6270

3200 3208 3216 3224 3232 3240 3248 3256

3201 3209 3217 3225 3233 3241 3249 3267

3202 3210 3218 3226 3234 3242 3250 3258

3203 3211 3219 3227 3235 3243 3251 3259

3204 3212 3220 3228 3236 3244 3252 3260

3205 3213 3221 3229 3237 3245 3253 3261

3206 3214 3222 3230 3238 3246 3254 3262

3207 3215 3223 3231 3239 3247 3255 3263

6600 6610 6620 6630 6640 6650 6660 6670

3456 3464 3472 3480 3488 3496 3504 3512

3457 3465 3473 3481 3489 3497 3505 3513

3458 3466 3474 3482 3490 3498 3506 3514

3459 3467 3475 3483 3491 3499 3507 3515

3460 3468 3476 3484 3492 3500 3508 3516

3461 3469 3477 3485 3493 3501 3509 3517

3462 3470 3478 3486 3494 3502 3510 3518

3463 3471 3479 3487 3495 3503 3511 3519

6300 6310 6320 6330 6340 6350 6360 6370

3264 3272 3280 3288 3296 3304 3312 3320

3265 3273 3281 3289 3297 3305 3313 3321

3266 3274 3282 3290 3298 3306 3314 3322

3267 3275 3283 3291 3299 3307 3315 3323

3268 3276 3284 3292 3300 3308 3316 3324

3269 3277 3285 3293 3301 3309 3317 3325

3270 3278 3286 3294 3302 3310 3318 3326

3271 3279 3287 3295 3303 3311 3319 3327

6700 6710 6720 6730 6740 6750 6760 6770

3520 3528 3536 3544 3552 3560 3568 3576

3521 3529 3537 3545 3553 3561 3569 3577

3522 3530 3538 3546 3554 3562 3570 3578

3523 3531 3539 3547 3555 3563 3571 3579

3524 3532 3540 3548 3556 3564 3572 3580

3525 3533 3541 3549 3557 3565 3573 3581

3526 3534 3542 3550 3558 3566 3574 3582

3527 3535 3543 3551 3559 3567 3575 3583

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

7000 7010 7020 7030 7040 7050 7060 7070

3584 3592 3600 3608 3616 3624 3632 3640

3585 3593 3601 3609 3617 3625 3633 3641

3586 3594 3602 3610 3618 3626 3634 3642

3587 3595 3603 3611 3619 3627 3635 3643

3588 3596 3604 3612 3620 3628 3636 3644

3589 3597 3605 3613 3621 3629 3637 3645

3590 3598 3606 3614 3622 3630 3638 3646

3591 3599 3607 3615 3623 3631 3639 3647

7400 7410 7420 7430 7440 7450 7460 7470

3840 3848 3856 3864 3872 3880 3888 3896

3841 3849 3857 3865 3873 3881 3889 3897

3842 3850 3858 3866 3874 3882 3890 3898

3843 3851 3859 3867 3875 3883 3891 3899

3844 3852 3860 3868 3876 3884 3892 3900

3845 3853 3861 3869 3877 3885 3893 3901

3846 3854 3862 3870 3878 3886 3894 3902

3847 3855 3863 3871 3879 3887 3895 3903

7100 7110 7120 7130 7140 7150 7160 7170

3648 3656 3664 3672 3680 3688 3696 3704

3649 3657 3665 3673 3681 3689 3697 3705

3650 3658 3666 3674 3682 3690 3698 3706

3651 3659 3667 3675 3683 3691 3699 3707

3652 3660 3668 3676 3684 3692 3700 3708

3653 3661 3669 3677 3685 3693 3701 3709

3654 3662 3670 3678 3686 3694 3702 3710

3655 3663 3671 3679 3687 3695 3703 3711

7500 7510 7520 7530 7540 7550 7560 7570

3904 3912 3920 3928 3936 3944 3952 3960

3905 3913 3921 3929 3937 3945 3953 3961

3906 3914 3922 3930 3938 3946 3954 3962

3907 3915 3923 3931 3939 3947 3955 3963

3908 3916 3924 3932 3940 3948 3956 3964

3909 3917 3925 3933 3941 3949 3957 3965

3910 3918 3926 3934 3942 3950 3958 3966

3911 3919 3927 3935 3943 3951 3959 3967

© 2004 by CRC Press LLC

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CRC Handbook of Engineering Tables

Octal-Decimal Integer Conversion (continued) 7200 7210 7220 7230 7240 7250 7260 7270

3712 3720 3728 3736 3744 3752 3760 3768

3713 3721 3729 3737 3745 3753 3761 3769

3714 3722 3730 3738 3746 3754 3762 3770

3715 3723 3731 3739 3747 3755 3763 3771

3716 3724 3732 3740 3748 3756 3764 3772

3717 3725 3733 3741 3749 3757 3765 3773

3718 3726 3734 3742 3750 3758 3766 3774

3719 3727 3735 3743 3751 3759 3767 3775

7600 7610 7620 7630 7640 7650 7660 7670

3968 3976 3984 3992 4000 4008 4016 4024

3969 3977 3985 3993 4001 4009 4017 4025

3970 3978 3986 3994 4002 4010 4018 4026

3971 3979 3987 3995 4003 4011 4019 4027

3972 3980 3988 3996 4004 4012 4020 4028

3973 3981 3989 3997 4005 4013 4021 4029

3974 3982 3990 3998 4006 4014 4022 4030

3975 3983 3991 3999 4007 4015 4023 4031

7300 7310 7320 7330 7340 7350 7360 7360

3776 3784 3792 3800 3808 3816 3824 3832

3777 3785 3793 3801 3809 3817 3825 3833

3778 3786 3794 3802 3810 3818 3826 3834

3779 3787 3795 3803 3811 3819 3827 3835

3780 3788 3796 3804 3812 3820 3828 3836

3781 3789 3797 3805 3813 3821 3829 3837

3782 3790 3798 3806 3814 3822 3830 3838

3783 3791 3799 3807 3815 3823 3831 3839

7700 7710 7720 7730 7740 7750 7760 7770

4032 4040 4048 4056 4064 4072 4080 4088

4033 4041 4049 4057 4065 4073 4081 4089

4034 4042 4050 4058 4066 4074 4082 4090

4035 4043 4051 4059 4067 4075 4083 4091

4036 4044 4052 4060 4068 4076 4084 4092

4037 4045 4053 4061 4069 4077 4085 4093

4038 4046 4054 4062 4070 4078 4086 4094

4039 4047 4055 4063 4071 4079 4087 4095

From Bolz, R.E. and Tuve, G.L., Number systems and logic, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, pp. 952–955.

Boolean Theorems A+0=A A·1 = A A+A=A A·A = A A+1=1 A·0 = 0 A + AB = A A=A

AB = A + B (A + B) + C = A + (B + C) (AB)C = A(BC) A + AB = A + B

( ) ( A + B)( A + C ) = AC + AB A A + B = AB

( AC + BC) = AC + BC

( A + C )(B + C ) = ( A + C )(B + C )

A + B = AB EXPLANATION: These Boolean theorems (sometimes called switching theorems) are used in problems involving binary states. The two states may be considered as functional propositions, true or false (hence the alternate name “propositional calculus”). But in physical devices, such as switches, controls, or computers, the two states may be on or off, short circuit or open circuit, high voltage or low voltage, or presence or absence of a hole in a card or tape, and the digits 1 and 0 are arbitrarily used. In these theorems each of the variables can represent an arbitrary function. One method for manipulating forms in switching algebra is to use a map. Since the use of symbols in Boolean algebra has not yet been fully standardized, the following is a detailed explanation of the symbols used in the above table. SYMBOLS: A, B, and C are variables. The bar above the variable indicates the negation of the variable, e.g., A means “not A”. The plus sign, +, is used for the or function. This function does not obey the conventional arithmetical rules for sums. The multiplication sign, ·, is used for the and function, sometimes called conjunction. This function obeys the conventional arithmetical rules for products. Thus if the binary values are taken arithmetically as one and zero, 1·1 = 1, and 1·0 = 0. But, in Boolean notation, 1 + 1 = 1, which is not correct by arithmetical notation. – If a variable (e.g., a switch) can have only two sates, designated as 1 or 0, it follows that 1 is equivalent to 0, and 0 is equivalent to 1. From Bolz, R.E. and Tuve, G.L., Number systems and logic, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 967.

© 2004 by CRC Press LLC

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General Engineering and Mathematics

Applications and Functions of Two Variables Table of Combinations AND

OR

A

B

X

X

H H L L

H L H L

H L L L

X

H H L L

H L H L

L L H L

X

H H L L

H L H L

L H L L

X

H H L L

H L H L

L L L H

X

H H L L

H L H L

H H H L

X

H H L L

H L H L

H L H H

X

H H L L

H L H L

H H L H

X

H H L L

H L H L

L H H H

A X

B

B

A

A X

B

B

A X B

A B

A

A X

B

B

A

A X

B

B

A X

A

B

B

A

A X B

B

A

A X B

A

B

From Bolz, R.E. and Tuve, G.L., Number systems and logic, in CRC Handbook of Tables for Applied Engineering Science, CRC Press, Boca Raton, FL, 1973, p. 968, Originally from MIL-STD 806B, February 1962.

© 2004 by CRC Press LLC