TRANSPORT PHENOMENA DATA COMPANION L.P.B.M. Janssen M.M.C.G. Warmoeskerken
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TRANSPORT PHENOMENA DATA COMPANION
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TRANSPORT PHENOMENA DATA COMPANION L.P.B.M. Janssen professor at the Department of Chemical Engineering of Groningen University M.M.C.G. Warmoeskerken professor at the Faculty of Science and Technologyof the University of Twente
VSSD
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Transport Phenomena Data Companion
© VSSD First edition 1987 Third edition 1997, 2001, 2006 Published by: VSSD Leeghwaterstraat 42, 2628 CA Delft, The Netherlands tel. +31 15 27 82124, telefax +31 15 27 87585, e-mail:
[email protected] internet: http://www.vssd.nl/hlf URL on this and related books: http://www.vssd.nl/hlf/c017.htm All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher. Printed in The Netherlands ISBN 90-71301-59-1 NUR 952 Keywords: transport phenomena
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Preface Many of the data needed for calculations in chemical engineering are dispersed over the literature. Moreover, various systems of units are used, often forcing the user to perform tedious conversions before a ‘quick’ calculation can be started. In this companion the authors have compiled those data that, according to their experience, are used frequently in transport phenomena and related subjects and, since all data are in S.I. units, rapid access to various calculations is facilitated. This book is of course no substitute for a complete literature survey and no compendium on all data available in literature. On many occasions a selection had to be made from a multitude of expressions. For instance, for the mass transfer to bubbles, drops and particles, dozens of correlations are available. In those cases the most general correlation or the expression most commonly used has been chosen. This companion consists of four parts. The first part is general and gives information varying from the Greek alphabet to calibration curves for thermocouples and pH ranges of indicators. The second part consists of frequently used mathematics. In addition to general mathematical techniques, a selection of vectorial and tensorial calculus relevant to hydrodynamics and elementary rheology has been added. The third part is a compendium of the transport phenomena. A systematic arrangement facilitates its use. The figures are in such a form that easy reading and accuracy are combined. In the final part various material properties are given. Special attention has been paid to the most commonly used materials: air and water, but also frequently used materials like for instance hydrocarbons, foods and others are included. For easy access to the data an extensive index is very important, so, special attention has been given to make the index as complete as possible. We hope this book will be useful for all those involved in transport phenomena, students, scientists as well as engineers, and we are grateful to everybody who has contributed to improve this companion by suggestions and criticism. Any further suggestions and amendments will be gratefully received. Groningen and Delft, L.P.B.M. Janssen M.M.C.G. Warmoeskerken
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Contents MISCELLANEOUS Greek Alphabet S.I. Prefixes Periodic Table Mathematical Constants Standard S.I. Units Derived S.I. Units Physical Constants Conversion Factors Temperature Scales Approximations for Physical Properties Therrnocouples pH Range of Acid Base Indicators
11 12 12 13 14 14 14 15 16 18 19 20 24
MATHEMATICS Volume and Surface of Some Bodies Integrals Elementary Differential Equations Approximations for Bessel Functions The Error Function Laplace Transforms Properties Frequently used Laplace transforms Vectors and Tensors Differentiation in Vector and Tensor Notation Linear Regression
25 26 29 37 39 42 43 43 45 47 49 52
TRANSPORT PHENOMENA Concentration Notation Microscopic Balances in General Form Bernoulli Equations Balances for Idealised Materials Frequently Occurring Flow Fields in Tensor Notation Rheological Models
53 54 55 58 59 62 63
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Pressure – Throughput Characteristics for the Flow of Liquids Through a Straight Round Tube Residence Time Distribution Quantities and Their Dimensions Alphabetical List of Dimensionless Numbers Frequently Used Dimensionless Correlations Analogies between Heat Transfer and Mass Transfer Drag Coefficient C w for Flow around Obstacles Richardson-Zaki equation Friction coefficient Cw of packed beds as a function of Reh Drag coefficients for flow around spheres, cylinders and disks Friction Coefficient Kw for Flow through Tube Systems Friction factor for flow in tubes Hydraulic diameters The power number Po of impellers as a function of Re Humidity Diagrams for Air-Water Systems at Atmospheric Pressure Fourier Instationary Heat and Mass Transfer Shapes of Free Rising Bubbles or Drops in Newtonian Liquids Rising Velocity of Air Bubbles in Water Rising Velocity or Fall Velocity of Drops in Liquids of Low Viscosity Two Phase Gas-Liquid Flow in Horizontal Tubes Two Phase Cocurrent Flow of Gas-Liquid through Vertical Tubes Formation of Bubbles at a Nozzle Heat and Mass Transfer for Flow around Spheres MATERIAL PROPERTIES Water The Prandtl number Thermal diffusion coefficient Heat of vaporization Cubic expansion coefficient Dielectrical constant Surface tension Electrical conductivity Density
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Vapor pressure Thermal conductivity coefficient Dynamic viscosity Specific heat Compressibility Refractive index Velocity of sound Properties of water and steam above 100 °C Physical Properties of Ice Air Composition of air The Prandtl number Thermal diffusion coefficient Density Dynamic viscosity Thermal conductivity coefficient Specific heat Ratio of specific heats Sound velocity Physical Properties of Some Materials Density, specific heat and heat conductivity coefficient Heat of combustion of some fuels Properties of natural gas Melting point and heat of melting of some materials Properties of some liquids Properties of some gases Physical properties of some metals Absorption coefficient a of various surfaces for heat radiation Electrical conductivity of some aqueous solutions Cubic coefficient of expansion of some liquids Eutectic temperature of freezing mixtures with snow or ice Properties of some plastics Refractive index of aqueous solutions at 20 °C Properties of foods Viscosities of foods Compressibility of Gases
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107 107 108 109 110 110 111 111 112 113 113 113 114 114 115 115 116 116 116 117 117 117 118 118 119 120 121 121 122 123 123 124 126 127 128 129
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Transport Phenomena Data Companion Transport Phenomena Data Companion
Critical constants, boiling point and molecular weight of various substances Solubility Table Solubility Parameters Liquified gases at 90 K Liquid solvents at 25 °C Amorphous polymers near 25 °C Diffusion Coefficients Diffusion coefficients of gases in water Diffusion coefficients of gases and vapours in air Diffusion coefficients of ions in water at very low concentrations Henry's Law Henry's law constant for the solubility of gases in water Henry's law constant for the solubility of gases in ionic solutions Equilibrium Data for Hydrocarbons Dynamic Viscosity Dynamic viscosity of ethanol-water solutions Dynamic viscosity of glycerol-water solutions Dynamic viscosity of glycerol-water solutions as a function of temperature at different weight percentages of glycerol Dynamic viscosity of cane sugar dissolved in water as a function of temperature at different weight percentages of cane sugar Dynamic viscosity of PVP (type K.90) dissolved in tap water at 20 °C Dynamic viscosity of some gases as a function of temperature at atmospheric pressure Surface Tension Surface tension of some inorganic substances in water against air Surface tension against air and interfacial tension against water of some organic liquids Surface tension against air of some water-organic liquid solutions INDEX
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148 149 150 151 151 152 153 154
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Miscellaneous
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Greek Alphabet • S.I. Prexes
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Periodic Table
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Mathematical Constants • Standard S.I. Units • Derived S.I. Units
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Physical Constants
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Conversion Factors
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Conversion Factors (continued)
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Conversion Factors (continued) • Temperature Scales
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Approximations for Physical Constants of Water and Air
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Thermocouples
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Thermocouples (continued)
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Thermocouples (continued)
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Thermocouples (continued)
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pH Range of Acid Base Indicators
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Mathematics
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Volume and Surface of Some Bodies
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Volume and Surface of Some Bodies (continued)
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Volume and Surface of Some Bodies (cont.)
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Integrals
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Integrals (continued)
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Integrals (continued)
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Integrals (continued)
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Integrals (continued)
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Integrals (continued)
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Integrals (continued)
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Integrals (continued)
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Elementary Differential Equations
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Elementary Differential Equations
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Approximations for Bessel Functions
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Approximations for Bessel Functions
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Approximations for Bessel Functions
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The Error Function
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Laplace Transforms
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Laplace Transforms
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Laplace Transforms
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Laplace Transforms
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Vectors and Tensors
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Vectors and Tensors (continued)
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Vectors and Tensors (continued)
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Vectors and Tensors (continued)
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Vectors and Tensors (continued)
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Linear Regression
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Transport Phenomena
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Concentration Notation
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Microscopic Balances in General Form
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Microscopic Balances in General Form (cont.)
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Microscopic Balances in General Form (cont.)
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Bernoulli Equations
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Balances for Idealised Materials
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Balances for Idealised Materials (cont.)
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energy balance for Newtonian fluids with constant density and constant heat conductivity
Balances for Idealised Materials (cont.)
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Frequently Occurring Flow Fields in Tensor Notation
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Rheological Models
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Rheological Models (continued)
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Pressure-Throughput Characteristics for Laminar Flow of Liquids in a Straight Round Tube
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Residence Time Distribution
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Residence Time Distribution (continued)
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Quantities and their Dimensions
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Quantities and their Dimensions (continued)
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Dimensionless Numbers
Alphabetical List of Dimensionless Numbers
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Dimensionless Numbers (continued)
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Dimensionless Numbers (continued)
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Dimensionless Numbers (continued)
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Dimensionless Numbers (continued)
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Frequently Used Dimensionless Correlations
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Frequently Used Dimensionless Correlations (continued)
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Frequently Used Dimensionless Correlations (continued)
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Analogies between Heat Transfer and Mass Transfer
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Drag Coefcient Cw for Flow around Obstacles
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Drag Coefcient Cw for Flow around Obstacles (continued)
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Drag Coefcient Cw for Flow around Obstacles (continued)
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Friction Coefcient Kw for Flow through Tube Systems
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Friction Coefcient Kw for Flow through Tube Systems (continued)
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Friction Coefcient Kw for Flow through Tube Systems (continued)
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Friction Coefcient Kw for Flow through Tube Systems (continued)
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Friction Coefcient Kw for Flow through Tube Systems (continued)
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Friction Coefcient Kw for Flow through Tube Systems (continued)
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Humidity Diagram for Air-Water Systems at Atmospheric Pressure (I)
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Humidity Diagram for Air-Water Systems at Atmospheric Pressure (II)
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Fourier Instationary Heat and Mass Transfer
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Fourier Instationary Heat and Mass Transfer (continued)
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Fourier Instationary Heat and Mass Transfer (continued)
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Shapes and Free Rising Bubbles or Drops in Newtonian Liquids
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Rising Velocity of Air Bubbles in Water
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Rising Velocity or Fall Velocity of Drops in Liquids of Low Viscosity hc < 5 m Pa s
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Two Phase Gas-Liquid Flow in Horizontal Tubes
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Two Phase Gas-Liquid Flow in Horizontal Tubes (continued)
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Two Phase Cocurrent Flow of Gas-Liquid through Vertical Tubes
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Formation of Bubbles at a Nozzle
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Heat and Mass Transfer for Flow around Spheres
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Material Properties
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Transport Phenomena Data Companion
Water
Water – Prandtl – thermal diffusion coefficient – heat of vaporization – cubic expansion coefficient – dielectrical constant – surface tension – electrical conductivity – density – vapor pressure – thermal condutivity coefficient – dynamic viscosity – specific heat – compressibility – refractive index – velocity of sound – properties of water and steam above 100 °C
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Water (continued)
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Physical Properties of Ice
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Air
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Air (continued)
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Air (continued)
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Air (continued)
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Physical Properties of Some Materials
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Physical Properties of Some Materials (cotinued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Physical Properties of Some Materials (continued)
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Compressibility of Gases
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Compressibility of Gases (continued)
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Solubility Table
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Solubility Table
Solubility
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Table
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Solubility Parameters
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Diffusion Coefcients
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Diffusion Coefcients (continued)
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Henry’s Law
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Henry’s Law (continued)
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Equilibrium Data for Hydrocarbons
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Equilibrium Data for Hydrocarbons (continued)
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Equilibrium Data for Hydrocarbons (continued)
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Equilibrium Data for Hydrocarbons (continued)
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Equilibrium Data for Hydrocarbons (continued)
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Dynamic Viscosity
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Dynamic Viscosity (continued)
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Dynamic Viscosity (continued)
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Dynamic Viscosity (continued)
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Dynamic Viscosity (continued)
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Dynamic Viscosity (continued)
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Dynamic Viscosity (continued)
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Surface Tension
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Surface Tension (continued)
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Surface Tension (continued)
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Index 90° open channel, hydraulic diameters 86 A a naphtol benzeine 24 Abel’s theorem 44 absolute humidity 19, 88, 89 absorption coefficient 121 acetate 133 acetic acid 123, 153 acetone 119, 123, 126, 153 acetylene 117, 120, 130, 135 acid base indicators 24 actinide series 13 activation energy 68, 70 adiabatic cooling line 88, 89 adiabatic flow ideal gas 58 air 19, 113, 120, 130, 137 air-water system 88, 89 alcohol 117, 123 alizarine, yellow 24 alphabet, greek 12 aluminium 118, 121, 132 —, sulphate 151 ammonia 117, 120, 130, 135 ammonium 132, 150 —, chloride 123, 151 —, hydroxide 151 amyl alcohol 153 analogies between heat transfer and mass transfer 78 aniline 152, 153 annular 96 antimony 118, 133 sauce 127, 128 approximation formulae for thermocouples 20 aqueous solution 122, 126 Archimedes 75 —, number 70 argon 113, 134, 135 Arrhenius number 70 arsenate 132 arsenite 132 asbestos 117, 121 asphalt 117 atomic mass 13 atomic number 13 avogadro number 15 axial diffusion 70 azolithmine 24
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B balanced idealised materials 59 balances 55 barium 132 barium chloride 151 basic integrals 29–34 benzaldehyde 152 benzene 119, 123, 130, 134, 135, 152 benzyl alcohol 152 Bernoulli equations 58 Bernoulli, differential equations 37 Bessel functions 39–41 Bessel, differential equations 38 biaxial elongation 62 binary diffusion coefficient 19 binary vapour-liquid equilibrium 139 Bingham 64, 128 —, number 70 —, plastic 63, 65 Biot number 70 bismuth 133 black bodies 121 black lacques 121 Blake-Kozeny 80 Blasius flow 75 block 26 Bodenstein number 70 boiling point 130 Boltzman constant 15 Bond number 70 borate 132 brass 118, 121 brick 117, 121 brilliant cresyl blue 24 Brinkman number 70 bromide 132, 134, 136 bromo cresol blue 24 bromo cresol purple 24 bromo phenol blue 24 brown coal 117 bubble flow 98 bubble formation 99 bubble shape 93 bulk expansion coefficient 69 buoyancy force 72 Burke-Plummer 80 butane 117 butanol 153 butter 127 butyric acid 153
C cadmium 118, 133, 136 calcium 132, 136 —, chloride 123, 151 candela 14 cane sugar 148 caproic acid 153 carbon dioxide 120, 130, 135, 10 carbon disulfide 134 carbon monoxide 117, 130, 134 carbon tetrachloride 134, 152 carbon tetrafluoride 134 carbonate 132 carbondioxide 113 Casson 128 —, fluid 63 Cauchy number 70 Cauchy, differential equations 38 cellulose acetate 124 cellulose diacetate 134 Celsius 18 centrifugal force 71 cesium 136 characteristic length 68 characteristic process time 71 chemical reaction rate 71, 74 chemical resistance 125 Chilton-Colburn analogy 78 chlorate 132 chloric acid 122, 123 chloride 132, 136 chlorine 120, 135 chloro phenol red 24 chloroform 119, 123, 152 chocolate 128, 132 chromel/alumel thermocouple 20–23 chromium 118, 121, 132 classical Maxwell fluid 63 coal 117, 121 cobalt 118, 121, 133 codeformational derative 51 composition of air 113 composition of gas 118 compressibility 110 —, gas 129 concentration notation 54 concentric tube, hydraulic diameters 86 concrete 117 conduction of heat 70
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Index conductive heat transfer 72, 73 conductive transport of heat 71 cone 27 consistency 63, 65, 128 continuity equation 58, 59 contraction 82, 70 convective heat transfer 72, 73 convective mass transfer rate 71 convective transport of heat 71 conversion factor 16 copper 118, 121, 133 —, sulphate 123, 151 copper/constantan thermocouple 20–23 cork 117 corn oil 127 corn syrrup 148 cotton seed oil 128 cream 128 cresol red 24 critical constant 130 critical pressure 129 critical temperature 129 critical volume 129 crystallization temperature 125 cube 26 curl vector field 50 curve-fit 52 Cw coefficient 79 cyanide 132 cyclohexane 130, 134, 152 cyclohexanol 152 cyclopentane 130 cylinder 27 —, segment 27 D Damköhler number 71 Dean number 71 Deborah number 71 deformation tensor 62 density 19, 54, 69, 106, 114, 117–121, 124, 127 —, water 111 derived S.I. units 14 dielectrical constant 105 diethylketone 153 differential equations 37–38 differentiation in tensor notation 49 differentiation in vector notation 49 diffusion coefficient 68, 135, 136
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diffusive mass transfer 73, 74 diffusive mass transfer rate 74 dimensionless correlation 75– 77 dimensionless number 70–74 dimensions 67 dimethyl yellow 24 dirac puls 45 dispersed flow 98 divergence vector field 50 drag coefficient 79, 81 drop 93 —, shape 93 dynamic viscosity 69, 108, 115, 144–150 E effective diffusion time 72 effective time for heat conduction 72 elastic force 71, 72 elasticity number 71 electrical conductivity 105, 122 enamel 121 energy balance 57, 61 enlargement 82 enthalpy of water 111 entropy of water 111 Eötvös number 71, 93 equation of continuity 55 equation of motion 58, 60, 56 equilibrium constants hydrocarbons 140–143 equilibrium data 139 erfx 42 Ergun 80 error function 42 ethane 117, 130, 134 ethanol 119, 126, 135, 152, 153 ethanol-water solution 144, 145 ethyl benzene 134, 152 ethyl ether 119, 135, 152 ethyl propyl ketone 152 ethylbenzene 130 ethylene 130, 135 Euler, differential equations 38 eutectic temperature 123 exit age distribution 66 expansion coefficient 104, 123 external heat transfer resistance 70 external mass transfer resistance 70 Eyring fluid 63
F fahrenheit 18 fall velocity drops in liquid 95 Fanning friction factor 71 ferricyanide 132 ferrocyanide 132 ferrosulphate 151 film flow 98 fish 127 flour 127 flow around obstacles 79 flow around spheres 100 flow field tensor notation 62 flow resistance 79 flow, dimensionless correlation 75 fluidisation velocity 75 fluoride 132 food 127, 128 Fourier 90 —, number 72, 90–92, 100 free rising bubbles 93 freezing mixture 123 friction coefficient 80, 82 friction factor 75, 84, 85, see also Fanning friction factor frictionless flow 58 froth 96 Froude number 72 fuel 117 fuel oil 117 G Galileo number 72 gas constant 15, 68, 129 gas-liquid flow 96 glass 117, 121 glucose 126 glycerol 118, 119, 123, 126 glycerol-water solution 146, 147 gold 118, 121, 133 gradient scalar field 50 Graetz 75, 76 —, number 72 granite 117 Grashof 76, 77 —, number 72 gravitational acceleration 15, 68 gravitational force 70–72 greek alphabet 12 gypsum 121 H half filled pipe, hydraulic diameters 86 Hatta number 72 heat capacity of fluid 74 heat conductivity 19, 127
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—, coefficient 117, 119– 121 heat of combustion 117, 118 heat of melting 118 heat of reaction 69, 71 heat of vaporization 104 —, water 111 heat transfer 74, 100 —, coefficient 68 —, dimensionless correlation 75 —, number 78 Heaviside theorem 44 helium 113, 120, 135, 150 Henry’s law 137, 138 hertz 14 homogeneous, differential equations 37 honey 128 Hooke number 72 horizontal tubes 96 humidity diagram 88, 89 hydraulic diameters 86 hydrocarbon 139 hydrodynamic boundary layer 74 —, thickness 73 hydrogen 113, 117, 120, 130, 135, 137, 150 —, chloride 126, 151 —, nitrate 151 —, sulfide 120, 130, 135 —, sulphate 151 hydroxide 132 I ice 117, 118, 121, 127 ideally mixed tank 66, 67 ideally mixed tanks in serie 67 ignition temperature 118 impellers 87 incompressible medium 58 inertia force 70–74 instationery heat transfer 90 instationery mass transfer 90 integrals 29–36 interfacial tension 152 internal age distribution 66 internal heat transfer resistance 70 internal mass transfer resistance 70 invariant of tensor 48 iodide 132, 136 iron 118, 121, 133 iron/constantan thermocouple 20–23 isobutane 130 isopentane 130, 134 isothermal flow ideal gas 58
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J J-factor analogy 78 Jaumann derative 51 Jaumann Maxwell fluid 64 Joule 14 K Kelvin 14, 18 kilogram 14 kinematic viscosity 69 kinetic energy 71, 73 krypton 113 L l-hexane 134 lamb 127 laminar flow 65 —, round tube 67 lanthanide series 13 Laplace transforms 43–46 Laplacian scalar field 50 Laplacian vector field 50 lead 118, 121, 133 Lewis number 72 linear expansion coefficient 121 linear regression 52 linear thermal expansion 124 liquid film, hydraulic diameters 86 liquid solvent 134 liquids 119 liquified gas 134 lithium chloride 151 M m-xylene 130 maganese 132 —, sulphate 151 magnesium 121, 132 —, chloride 123, 151 —, sulphate 151 manganese 118, 121 marble 117 margarine 128 mass balance 55, 59 mass fraction 54 mass transfer 100 —, boundary layer 74 —, boundary layer thickness 72 —, coefficient 68 —, dimensionless correlation 75 —, number 78 —, with chemical reaction 72 —, without chemical reaction 72 mathematical constants 14
Maxwell fluid 63 mayonnaise 128 melting point 118, 121 melting temperature 112 mercury 118, 121, 133 metals 121 meter 14 methane 117, 120, 130, 134, 150 methanol 119, 126, 135, 152, 153 methyl butyl ketone 152 methyl ether 123 methyl ethyl ketone 153 methyl propyl ketone 152 methyl red 24 methylcyclohexane 130 methylcyclopentane 130 milk 127,128 mixing rule 129 modified Bessel functions 41 modified Bessel, differential equations 38 modulus of elasticity 69 molar concentration 54 molar mass 19, 54 mole fraction 19, 54 molecular weight 130 Morton number 73, 93 multicomponent system 129 mustard 128 N n-butane 130 n-butanol 152 n-decane 130 n-heptane 119, 130 n-hexadecane 134 n-hexane 119, 130, 134, 152 n-nonane 130 n-octane 119, 130, 134, 152 n-pentane 119, 130, 134 n-pentanol 152, 153 nabla identities 50 nabla operator 49 natural gas 118 Navier-Stokes equation 56, 60 neon 113, 135 neopentane 134 neutral red 24 Newton 64, 65, 128 — fluid 63 newton 14 newtonian liquids 93 nickel 118, 121, 132 nitramine 24 nitrate 132 nitric acid 119, 122, 123 nitro benzene 152 nitrogen 113, 120, 130, 134,
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Index 135, 137, 150 —, dioxide 135 nitrous oxide 135 nozzle 99 number averaged molar mass 54 Nusselt 75–78 Nusselt number 73, 100 nylon 6/6 124 O o-xylene 130, 152 oakwood 117 octahedron 26 oil 127, 128 Oldroyd derivative 51 Oldroyd Maxwell fluid 64 olive oil 127, 128 open channel, hydraulic diameters 86 oranges 127 organic liquid 152 organic solution 153 oxalate 132 oxide 132 oxygen 113, 120, 130, 134, 135, 137, 150 ozone 113 P p-xylene 130, 152 packed bed 80 paint 121 paraffin 118 —, oil 117 Pascal 14 peanut oil 128 Péclet number 66, 73 penetration of heat 90 penetration of mass 90 pentane 123 perfluoro-n-heptane 134 periodic table 13 perspex 124 petrol 117 petroleum 117, 123 pH range 24 phenol 123, 153 —, red 24 phenolphtalien 24 phenyl chloride 152 phosphate 132 physical constants 15 physical properties 19, 117 —, phases 73 pipe entrance 83 pipe exit 83 plaster 117 plastic 124–125 platinum 118, 121, 133
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platinum/platinum-rhodium thermocouple 20–23 plexiglass 124 plug flow 67 —, with axial dispersion 67 plugs 96 plutonium 121 Poisseulle flow 75 polished marble 121 polyacrylonitrile 134 polyamide 6/6 124 polybutadiene 134 polycarbonate 124 polydimethyl silicone 134 polyethylene 124, 134 polyisobutylene 134 polymer 134 polymethyl methacrylate 134 polymethylmethacrylate 124 polypropene 124 polystyrene 134 polytetrafluoro ethylene 124 polyurethane 124 polyvinyl chloride 124, 134 polyvinylidene chloride 134 pork 127 potassium 121, 132 —, bromide 151 —, carbonate 151 —, chloride 123, 151 —, hydroxide 123 —, nitrate 151 —, nitrite 151 —, sulphate 123, 151 potatoes 127 potential energy 73 poultry 127 Powell-Eyring fluid 63 power added 68, 73 power input 87 power law 63, 64, 65, 128 —, index 63, 65, 128 power number 73, 87 power transferred to kinetic energy 73 Prandtl 75–78 —, fluid 63 —, number 73, 100, 103, 113, 119, 120 Prandtl-Eyring fluid 63 precious metal 121 prefix 12 pressure 19, 68 —, throughput characteristics 65 process time 72 propane 117, 120, 130, 150 propanol 119 properties of ice 112
properties of steam 111 properties of water 111 propionic acid 153 propylene 130, 135 PVP 149 pyramid 26 Q quartz 117 R radiation 121 rankine 18 Rayleigh number 73 reaction constant 68 rectangular pip, hydraulic diameters 86 Redlich-Kwong 129 refractive index 110, 124, 126 relative humidity 19, 88, 89 relative roughness 84, 85 relaxation time 63, 69, 71 residence time 66 —, distribution 66 Reynolds 80, 82 —. number 73, 75–79, 93, 100 rheogram 64 rheological model 63, 64 Richardson number 73 rising velocity air bubbles in water 94 rising velocity drops in liquid 95 round tube, hydraulic diameters 86 rubber 121 S S.I. prefix 12 salicyl yellow 24 sauce 128 Schmidt 76–78 —, number 74, 100 second 14 second invariant deformation tensor 63 second order fluid 63 separation of variables 37 service temperature 125 shear stress 63 —, energy wall 65, 71 Sherwood 76–78 —, number 74, 100 silicate 132 silver 118, 121, 133 —, nitrate 151 simple elongation 62 simple shear 62 slug flow 98
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slugs 96 sodium 118, 121, 132, 136 —, bromide 151 —, carbonate 123 —, chloride 122, 123, 126, 151 —, hydroxide 122, 126, 151 —, nitrate 123, 151 —, sulphate 151 softening temperature 125 solubility 131–133 —, gas in ionic solution 138 —, gas in water 137 —, parameter 134 sound velocity 116 soup 128 soy bean oil 127, 128 specific heat 19, 68, 109, 112, 116, 117, 119, 120, 121, 124, 127 specific mass 69 specific volume dry air 88 specific volume saturated air 88 speed of light 15 sphere 28 —, sector 28 —, segment 28 spiral diameter 68 spray 96 standard pressure 15 standard S.I. units 14 standard temperature 15 Stanton number 74 steel 121 Stefan-Boltzman constant 15 straight round tube 65 stratified 96 strirrer diameter 68 strontium 132 styrene 134, 152 substantial derivative 51 sulfate 132, 136 sulfide 132 sulfur 118 —, dioxide 120, 130 sulfuric acid 119, 122 surface calculations 26–28 surface tension 69, 96, 105, 151–153 —, force 70, 71, 73, 74 T T-junction 83 tantalum 121 teflon 134 temperature 19 —, conversion 18 —, scale 18
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tensor 47–51 —, mathematics 47 —, operation 48 tetrachloroethylene 134 tetrahedron 26 thermal boundary layer thickness 72, 73 thermal conductivity 69, 121, 124 —, coefficient 107, 115 thermal diffusion 68 —, coefficient 103, 114, 119, 120 thermal energy 70 thermocouples 20 thermovoltage 21 —, high temperature 23 —, low temperature 22 Thiele modulus 74 thiocyanate 132 thymol blue 24 thymol phatalein 24 tin 118, 121, 133 titanium 121 toluene 119, 130, 134, 135, 152 tomato juice 128 total derivative 51 total heat transfer 73 total mass transfer 74 transcendental functions, integrals 34–36 transformed Bessel, differential equations 38 transparency 125 tropaelin 00 24 truncated cone 28 truncated cylinder 27 truncated pyramid 27 tube 27 tube system 82 turpentine 123 two phase flow 96, 98
visco-elastic force 74 viscosity 19, 63, 65, 118–120, 127, 128 viscous dissipation 70 viscous force 70–74 viscous stress 70 volume calculations 26–28 volume ideal gas 15 W water 19, 102, 119, 121, 130, 135 —, content 127 —, vapor 19 watt 14 wave 96 —, flow 98 Weber number 74 Weissenberg number 74 Wien’s displacement constant 15 Williamson fluid 63 wolfram 121 wood 117, 121 wool 117 X xenon 113 xylene 135 Y yield strength 124 yield stress 63, 65, 69, 70, 128 Z zinc 118, 121, 132 zinc sulphate 151
U uniaxial elongation 62 unit step 45 uranium 121 V valve 83 Van der Waals 129 vapor pressure 107, 112 vaporization entropy 111 veal 127 vector 47–51 —, mathematics 47 —, operations 48 velocity 69 —, of sound 111
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Transport Phenomena Data Companion Many of the data needed for calculations in chemical engineering are dispersed over the literature. Moreover, various systems of units are used, often forcing the user to perform tedious conversions before a 'quick' calculation can be started. In this companion the authors have compiled those data that, according to their experience, are used frequently in transport phenomena and related subjects. Since all data are in S.I. units, rapid access to various calculations is facilitated. This companion consists of four parts. The first part is general and gives information varying from the Greek alphabet to calibration curves for thermocouples and pH ranges of indicators. The second part consists of frequently used mathematics. In addition to general mathematical techniques, also a selection of vectorial and tensorial calculus, relevant to hydrodynamics and elementary rheology, has been included. The third part is a compendium of the transport phenomena. A systematic arrangement facilitates its use. The figures are in such a form that easy reading and accuracy are combined. In the final part various material properties are presented. Special attention has been given to the most common materials: air and water, but also frequently used materials like for instance hydrocarbons, foods and others. Published by VSSD URL on this book: http://www.vssd.nl/hlf/c017.htm ISBN-10 90-71301-59-1 ISBN-13 978-90-71301-59-9
c017
