Информационно-аналитические системы магистральных трубопроводов

UFA STATE PETROLEUM TECHNOLOGICAL UNIVERSITY Sergei Kutukov ANALYTICAL ENGINEERING FOR OIL PIPELINING INFORMATION & AN...

Author: Кутуков С.Е.

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UFA STATE PETROLEUM TECHNOLOGICAL UNIVERSITY

Sergei Kutukov

ANALYTICAL ENGINEERING FOR OIL PIPELINING INFORMATION & ANALYTICAL FACILITIES IN TRUNK PIPELINE CONTROL SYSTEMS

CHAPTER 1 : ANALYSIS OF PIPELINE ENERGY CONSUMPTION CHAPTER 2 : STATE OF THE ART ANALYTICAL AND INFORMATION FACILITIES FOR OIL PIPELINING CONTROL SYSTEM CHAPTER 3 : GEOGRAPHICAL INFORMATION TECHNOLOGY CHAPTER 4 : ADVANTAGES OF CONTROL SYSTEM INTEGRATION BASED ON GIS CHAPTER 5 : PATH OF ELABORATION FOR OIL PIPELINING CONTROL SYSTEM

Copyright  2002 Ufa State Petroleum Technological University. 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, photocopying, recording or otherwise without the prior permission of the publisher.

УФИМСКИЙ ГОСУДАРСТВЕННЫЙ НЕФТЯНОЙ ТЕХНИЧЕСКИЙ УНИВЕРСИТЕТ

Кутуков С.Е.

ИНФОРМАЦИОННО-АНАЛИТИЧЕСКИЕ СИСТЕМЫ МАГИСТРАЛЬНЫХ ТРУБОПРОВОДОВ

Издательство СИП РИА Москва, 2002

УДК 622.692.4.052 К-95

Кутуков С.Е. Информационно-аналитические системы магистральных трубопроводов. М.:СИП РИА, 2002.-324с. ISBN 5-89354-150-2 Рассмотрены современные программные и технические средства, применяемые в управлении магистральными нефте- и продуктопроводами. Особое внимание уделено методологическим основам, перспективам и возможностям, как традиционно используемым интеллектуальным продуктам, так и вновь создаваемым, прошедшим лишь апробацию на объектах магистрального транспорта нефти АК «Транснефть». На основе результатов энергоаудита объектов магистральных трубопроводов показаны возможности снижения энергопотребления процесса перекачки за счёт повышения эффективности управления транспортом нефти. Для инженерно-технических и научных работников, занятых вопросами проектирования и эксплуатации трубопроводов, а также может быть полезна студентам и аспирантам нефтяных специальностей. Табл. 28, ил. 58, список лит. - 143 назв. Рецензенты:

Институт проблем транспорта энергоресурсов (ИПТЭР) Институт по проектированию МНП «Гипротрубопровод»

© Уфимский государственный нефтяной технический университет, 2002

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>ey ^Zggh]h lbiZ ^\b]Zl_ey kbkl_fgZy khklZ\eyxsZy ihl_jv hij_^_e_gZ dZlZeh`ghc\_ebqbghcG:KHKGH=HH;HJM>H<:GBY < hlkmlkl\b_ nZdlbq_kdbo bg^b\b^mZevguo oZjZdl_jbklbd hp_gdm wnn_dlb\ghklb wdkiemZlZpbb gZkhkgh]h h[hjm^h\Zgby ij_^eh`_gh ijhba\h^blv \ khihklZ\e_gbb dZlZeh`guo agZq_gbc nZdlbq_kdhfm wg_j]hihlj_[e_gbx b ^bki_lq_jkdbf^Zggufihijhba\h^bl_evghklbb^Z\e_gbyfgZ\oh^_b\uoh^_GIK Ih dZlZeh`guf oZjZdl_jbklbdZf \dexq_gguo gZkhkh\ fZ]bkljZevguo b ih^ihjguo kljhblkyjZ[hqZyoZjZdl_jbklbdZGIK\p_ehf NZdlbq_kdb_^Zggu_ihgZihjmhp_gb\Zxlkyih^bki_lq_jkdbf^Zgguf G Jg –J1)/ρg, ]^_

(2)

Jg –^Z\e_gb_gZ]g_lZgbyGIKjbkmghd >IZ@ J1 –^Z\e_gb_gZ\kZku\ZgbbgZkhkh\>IZ@

Ihe_agZyjZ[hlZgZkhkguoZ]j_]Zlh\\uqbkey_lkyihnhjfme_ W]b^j= Σ(P2 – P1)⋅Qi⋅τ ,

(3)

]^_ Q –k_dmg^gZyijhba\h^bl_evghklvgZkhkh\>f3k@ NZdlbq_kdh_ihlj_[e_gb_we_dljhwg_j]bbWgik[_j_lkyihkmlhqgufagZq_gbyf ba `mjgZeZ mq_lZ GIK aZ \uq_lhf ihl_jv \ ih^\h^ys_c k_lb ljZgknhjfZlhjZo b we_dljh^\b]Zl_eyo Z lZd `_ ihlj_[e_gby gZ WOA b ijhqb_ j_`bfgu_ f_jhijbylby Dhwnnbpb_glihe_agh]h^_ckl\bygZkhkguoZ]j_]Zlh\bkqbkey_lkyhlghr_gb_f

ηgk = W]b^j/(Wgik- Wk_lv- W^\- WWOA)

(4)

]^_

Wk_lv -ihl_jb\ih^\h^ys_ck_lbbljZgknhjfZlhjZo W^\ -ihl_jb\^\b]Zl_eyo WWOA –jZkoh^wewg_j]bb\WOAb^jm]bol_ogheh]bq_kdbokbkl_fZoGIK KjZ\g_gb_jZkkqblZgguobdZlZeh`guoiZjZf_ljh\jZ[hqbooZjZdl_jbklbdGIK ihdZau\Z_l hlghkbl_evgh_ kgb`_gb_ ihdZaZl_e_c jZ[hlu gZkhkguo Z]j_]Zlh\ Kbkl_fgmxkhklZ\eyxsmxihl_jvgZgZkhkZohij_^_ey_f[_jyihdZaZl_evfhsghklbb DI>kdZlZeh`ghcoZjZdl_jbklbdb WΣsys = ΣNi⋅τ⋅(1-ηgkL),

(5)

25

]^_

Ni –dZlZeh`gh_agZq_gb_fhsghklbgZijhba\h^bl_evghklb4i. Dhfi_gkbjmy hlkmlkl\b_ ^Zgguo ihlj_[e_gby we_dljhwg_j]bb hl^_evgh fZ]bkljZevgufb b ih^ihjgufb gZkhkZfb h[sb_ wg_j]hihl_jb ^_ebf ijhihjpbhgZevgh hlghr_gbx jZa\b\Z_fh]h gZihjZ Gi gZ DI> gZkhkZ ηi ijb nZdlbq_kdhcijhba\h^bl_evghklb ïîä Hi ∑ ïîä ηi Σ , (6) W ïîä = W sys ⋅ ïîä   H iÍÌ H i ∑  ÍÌ + ïîä  ηi   ηi ÍÌ Hi ∑ ÍÌ ηi Σ (7) W ÍÌ = W sys ⋅ ïîä   H iÍÌ H i ∑  ÍÌ + ïîä  η η i  i  ]^_ GF –bg^_dkiZjZf_ljh\fZ]bkljZevguogZkhkh\ ih^ –bg^_dkiZjZf_ljh\ih^ihjguogZkhkh\ JZagbpZ nZdlbq_kdh]h wg_j]hihlj_[e_gby b dZlZeh`gh]h ^Z_l ^bgZfbq_kdmx khklZ\eyxsmx (8) ∆W^bg = Wgik – WΣsys :gZeba ijbqbg kgb`_gby DI> ih^jh[gh ijb\_^_g \ jZ[hlZo DheiZdh\Z E=>@=mf_jh\Z:=b;Z`ZcdbgZK=>@gh\uoh^ylaZjZfdb^Zgghcf_lh^bdb JZajZ[hldZ dhgdj_lguo f_jhijbylbc \ wlhf gZijZ\e_gbb lj_[m_l agZgby bg^b\b^mZevguo oZjZdl_jbklbd dZ`^h]h gZkhkgh]h Z]j_]ZlZ b ij_^iheZ]Z_l ijbf_g_gb_ijhp_^mjuiZjZf_ljbq_kdh]h^bZ]ghklbjh\Zgby < fbjh\hc ijZdlbd_ ijh[e_fZ hilbfbaZpbb jZ[hlu gZkhkguo klZgpbc b wdhghfbb we_dljhwg_j]bb lZd`_ kms_kl\m_l \ke_^kl\b_ bklhs_gby f_klhjh`^_gbc J:<EBQ?KD:YKHKL:<EYXS:YWG?J=?LBQ?KDH=H;:E:GK: :gZebabjm_fuf h[t_dlhf y\ey_lky mqZklhd ljm[hijh\h^Z f_`^m gZkhkgufb klZgpbyfbK[jhkuih^dZqdb \ih^dexq_ggu_j_a_j\mZjugZGIKjZkkfZljb\Zxlky dZdj_a_j\Zddmfmebjmxs_ckihkh[ghklbmqZkldZljm[hijh\h^Z >ey hij_^_e_gby jZ[hlu kbe lj_gby gZ ljZgkihjl g_nlb kbkl_fghc khklZ\eyxs_c jZkkqblZ_fihl_jbgZlj_gb_h1-2gZmqZkld_ljm[hijh\h^Zf_`^m^\mfy GIKihdeZkkbq_kdhcf_lh^bd_]b^jZ\ebq_kdh]hjZkq_lZljm[hijh\h^h\>@ l −l c ϑ 2 ϑ 2 + c sin (9) + ∑ζ h = ∑ λ⋅ n n ⋅ ∑l αk , D n 2g m 2g k k n ]^_

ln, Dn –^ebgZb^bZf_ljQ-h]hmqZkldZljm[hijh\h^Z>f@ lck –^ebgZkZfhl_qguomqZkldh\>f@ ζ -dhwnnbpb_gluf_klguokhijhlb\e_gbc

26

λ -dhwnnbpb_gl]b^jZ\ebq_kdbokhijhlb\e_gbc>Zjkb αk –mdehgkZfhl_qgh]hmqZkldZ n –dhebq_kl\hmqZkldh\ljm[hijh\h^ZkjZaebqghc]_hf_ljb_c m –dhebq_kl\hf_klguokhijhlb\e_gbc; k –qbkehkZfhl_qguomqZkldh\ Dhwnnbpb_gl]b^jZ\ebq_kdbokhijhlb\e_gbcλ\uqbkey_lkyihdeZkkbq_kdhc f_lh^bd_

λ=

]^_

, #0

^eyRe < 2320;

(10)

 1 2,51  = −2 ⋅ lg k ý + ^eyRe > 2320. , λ  3,7 D Re λ  kw –dhwnnbpb_glwd\b\Ze_glghcr_jhoh\Zlhklb\gmlj_gg_cih\_joghklbljm[u 4⋅Q -iZjZf_ljJ_cghev^kZ Re = π ⋅ D ⋅ν

KZfhl_qgu_ mqZkldb hij_^_eyxlky gZeh`_gb_f ebgbb iv_ahf_ljbq_kdbo mdehgh\bijhnbeyljZkkumqZkldZljm[hijh\h^Z>@ >ey hp_gdb Zfieblm^u ^bgZfbq_kdhc khklZ\eyxs_c ^Z\e_gby ih mijhs_gghc ko_f_ jZkkqblZ_f bg_jpbhgguc gZihj \hagbdZxsbc aZ kq_l baf_g_gby ijhba\h^bl_evghklbljm[hijh\h^ZaZnbdkbjh\Zgghc\^\moihke_^h\Zl_evguoaZibkyo ^bki_lq_jkdh]hebklZ hin = 4(Qi – Qi-1)⋅L/(π⋅g⋅D2⋅τ), (11) ]^_

i, i-1 –bg^_dkuaZibk_c\^bki_lq_jkdhfebkl_ τ = 2⋅L/a –nZaZ]b^jhm^ZjZ>F@ L –^ebgZwdkiemZlZpbhggh]hmqZkldZljm[hijh\h^Z>f@ Z fk–kdhjhklva\mdZ\g_nlb LZdbfh[jZahfjZkq_lgucihlj_[gucgZihje_`bl\^bZiZahg_agZq_gbc Hi = hi + hin,

(12)

Kbkl_fgZykhklZ\eyxsZyihl_jvgZmqZkld_ljm[hijh\h^Zf_`^mGIKjZ[hlZ kbelj_gbygZljZgkihjlg_nlb hp_gb\Z_lky\ujZ`_gb_f Wp =Σρ⋅g⋅Qi⋅Hi ,

(13)

]^_ Σ - kmffZ jZkq_lguo bgl_j\Zeh\ ih ebfblbjmxs_fm nhjfZlm \u[hjdb ^bki_lq_jkdbo^Zgguo–^\moqZkh\hcijhba\h^bl_evghklbmqZkldZFGI NZdlbq_kdb_ ihl_jb fh`gh hp_gblv ih ^bki_lq_jkdbf ^Zgguf JZkkfhljbf [ZeZgkwg_j]bbgZmqZkld_ljm[hijh\h^Zf_`^m^\mfyGIK 2 2 ϑk ϑk +1 P1,k + 1 P 2 ,k (14) +α = Z k +1 + +α + h k −k + 1 , Zk + 2g 2g ρg ρg ]^_

Z –\ukhlgu_hlf_ldbGIK>f@ P -iv_ahf_ljbq_kdb_gZihju>f@ ρg

27

ϑ -kdhjhklvijh^mdlZ\ljm[_>fk@ k –bg^_dkGIK KdhjhklghcgZihj\pbebg^jbq_kdhcljm[_hklZ_lkyg_baf_ggufZ\j_Zevghf ljm[hijh\h^_ g_ f_gy_lky k lhqghklvx ^h ijhp_glZ hl ]b^jh^bgZfbq_kdh]h gZihjZ ihwlhfm_]hfh`ghkhdjZlblv\h[_boqZklyomjZ\g_gby;_jgmeeb K N − N + = = N − = N + + ]^_

3 N − 3 N + , ρJ

(15)

J2,k –^Z\e_gb_gZ]g_lZgbyihke_j_]meylhjZ^Z\e_gbygZGIKk; J1,k+1 –^Z\e_gb_gZ\kZku\ZgbbGIKk+1.

Ij_^iheZ]Zy j_`bf wdkiemZlZpbb mqZkldZ FGI aZ jZkkfZljb\Z_fuc ^\moqZkh\hc i_jbh^ [ebadbf d mklZgh\b\r_fmky ih hkj_^g_gguf ^bki_lq_jkdbf ^Zggufhp_gb\Z_fwg_j]haZljZlugZ`b^dhklgh_lj_gb_ Wlj =Σρ⋅g⋅Qi⋅hi,(k-k+1) .

(16)

Hlghr_gb_ jZkq_lguo b nZdlbq_kdbo wg_j]haZljZl aZ\bkbl lhevdh hl khhlghr_gby khhl\_lkl\_gguo ]b^jZ\ebq_kdbo ihl_jv ld iehlghklv g_nlb b ijhba\h^bl_evghklvb\lhfb\^jm]hfkemqZ_[_jmlkyba^bki_lq_jkdbo^Zgguo

η ãèäð =

∑ ρ i ⋅ Qi ⋅ H i Wp = ⋅ 100% . ôàêò W òð ∑ ρ i ⋅ Q i ⋅ hi , ( k − k +1)

(17)

;ZeZgkh\h_agZq_gb_]b^jZ\ebq_kdhckhklZ\eyxs_chlebqZ_lkyhlnZdlbq_kdbo wg_j]haZljZl gZ \_ebqbgm h[mkeh\e_ggmx jZaghklvx ]b^jh^bgZfbq_kdbo gZihjh\ ihlhdZg_nlbgZ\kZku\ZxsboebgbcGIKkbGIKk+1:  P1,k + 1− P1,k   ⋅ Qi = , ∆W = ∑ ρ i ⋅ g ⋅  Z k +1− Z k +  i ρ g  

(

(18)

)

= (Z k +1 − Z k )⋅ ∑ ρ i ⋅ g ⋅ Qi + ∑ P1, k + 1 − P1, k ⋅ Qi i i Ihl_jbh[mkeh\e_ggu_^jhkk_ebjh\Zgb_fgZj_]meylhj_^Z\e_gbyhljZ`Zxlky \[ZeZgk_khklZ\eyxs_c

(

)

W äð = ∑ P í , k − P 2, k ⋅ Qi i

(19)

LZdbf h[jZahf ihlj_[e_gb_ we_dljhwg_j]bb gZ ljZgkihjl g_nlb ih ^bki_lq_jkdbf^Zgguf\uqbkey_lkydZdjZaghklv WnZdl= Wlj + W^j+ ∆W.

(20)

1.2.7. K?GB?;:E:GK:WG?J=HIHLJ?;E?GBYGIKIHN:DLM >ey ZgZebaZ wg_j]hihlj_[e_gby hl^_evguo GIK wdkiemZlZpbhgguo mqZkldh\ FGIJGMbJ_]bhgZevgh]hmijZ\e_gby\p_ehfaZaZ^Zgguci_jbh^\j_f_gbkmldbb [he__ dhlhjuc hij_^_ey_lky ihklZ\e_gghc aZ^Zq_c ij_^eh`_gh k\h^blv [ZeZgk h[t_dlZ ih \k_f khklZ\eyxsbf ihlj_[e_gby we_dljbq_kdhc b f_oZgbq_kdhc wg_j]bc
LZ[ebpZ ;ZeZgkwg_j]hihlj_[e_gbyGIKwdkiemZlZpbhggh]hmqZkldZFGI JGMbebJ_]bhgZevgh]hmijZ\e_gby

GZbf_gh\Zgb_ Kmlhqgh_ihlj_[e_gb_

[1] [2]

Klhjhggb_ihlj_[bl_eb

[3]

Kh[kl\_ggu_gm`^u Ihl_jb\ih^\h^ys_ck_lb

Bklhqgbd @mjgZeuwg_j]hihlj_[e_gby GIK @mjgZeuwg_j]hihlj_[e_gby GIK @mjgZeuwg_j]hihlj_[e_gby GIK

Kbkl_fgZykhklZ\eyxsZy [4]

-Zdlb\gh_ihlj_[e_gb_ -j_Zdlb\gh_ihlj_[e_gb_

F_lh^oZjZdl_jguokmlhd

>bgZfbq_kdZykhklZ\eyxsZy [5] [6] [7]

L_ogheh]bq_kdb_gm`^u LjZgkihjlg_nlb WOA Ihl_jb\we_dljh^\b]Zl_eyo FZ]bkljZevguogZkhkh\

[8]

-kbkl_fgZykhklZ\eyxsZy -^bgZfbq_kdZykhklZ\eyxsZy Ih^ihjguogZkhkh\

@mjgZeuwg_j]hihlj_[e_gby GIK KmffZ]jZn>7]+[8]+[9]+[10] @mjgZeuwg_j]hihlj_[e_gby GIK F_lh^bdZjZkq_lZihl_jv Zdlb\ghcfhsghklb\ kbgojhgghf^\b]Zl_e_ >Kfijbeh`_gb_@

-kbkl_fgZykhklZ\eyxsZy -^bgZfbq_kdZykhklZ\eyxsZy

[9]

Ihl_jb\gZkhkZo -kbkl_fgZykhklZ\eyxsZy -^bgZfbq_kdZykhklZ\eyxsZy

NhjfmeZ«

FZ]bkljZevgu_ Ih^ihjgu_ [10] [11] [12] [13]

AZljZlu\ebg_cghcqZklb

NhjfmeZ

Ihl_jbgZj_]meylhj_

NhjfmeZ

JZaghklv]b^jh^bgZfbq_kdbo gZihjh\ =b^jZ\ebq_kdb_ihl_jbNZdl

NhjfmeZ) NhjfmeZ

[14]

=b^jZ\ebq_kdb_ihl_jbjZkq_l

NhjfmeZ

[15]

K\_joghjfZlb\gu_ihl_jb

JZagbpZ]jZn>@- [14]

[16]

Ijhqb_ihl_jb

[1] – [2] - [3] - [6]]

29

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43

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{ }

=BF

{K i },

i = 1, n.

(21)

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j = 1, m;

i = 1, n.

(22)

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96

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(23)

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{; i },

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{ }

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q = 1, L i ,

i = 1, n,

(24)

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i = 1, n.

(25)

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(26)

{ } { }

I : E iq → Tqi ,

(27)

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97

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107

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108

ij_`^_\k_]h[hevrbfh[t_fhfh[jZ[Zlu\Z_fhcijhf_`mlhqghcbgnhjfZpbbZlZd`_ pbnjh\hcdZjluf_klghklb^hklZlhqghih^jh[gh]hfZkrlZ[Z @ IJH;E?FUJ:KQ?L:BKL?Q?GBYG?NLBBA:<:JBCGUOHL?GBBG?NL?IJH:. DeZkkbq_kdZy =b^jZ\ebdZ ij_^eZ]Z_l \_kvfZ g_aZfukeh\Zlmx aZ\bkbfhklv ^ey hij_^_e_gbyjZkoh^Z`b^dhklbq_j_ahl\_jklbybgZkZ^db>@ Q = µ⋅f⋅√2gH, ]^_

(28)

µ -dhwnnbpb_gljZkoh^Zhl\_jklbygZkZ^dZ f –iehsZ^v`b\h]hk_q_gbyhl\_jklbygZkZ^dZ g –mkdhj_gb_k\h[h^gh]hiZ^_gby G ∆Jρg -gZihjijbdhlhjhfijhbkoh^blbkl_q_gb_

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109

]^_

µ0 – dhwnnbpb_gl jZkoh^Z ijb bkl_q_gbb ba fZeh]h hl\_jklby \ lhgdhc

kl_gd_ Re

-qbkehJ_cghev^kZ

We

-<_[_jZ

Fr

-Njm^Z

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4   µ σ = µ 0 ⋅ 1 + .  We 

(29)

>ey fZeuo hl\_jklbc ∅ ≈ δlj ijhp_kk h[j_lZ_l ki_pbnbdm bkl_q_gby ba gZkZ^dh\ b \ wlhf kemqZ_ \ bgl_j\Ze_ qbk_e Re = 102…105 b δ⁄D « fh`gh bkihevah\ZlvaZ\bkbfhklv>@ −1

 48 δ lj   . µ G = 1,23+ ⋅  Re D  

(30)

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110

Re , 1,5 + 1,4 ⋅ Re 0,27 , ijbRe< 10000 µ 0 = 0,592 + 1/ 6 Re 5,5 . ijbRe µ 0 = 0,592 + Re

µ0 =

ijb25
(31)

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µ' =

2F

(

)

H gZq − H dhg , f ⋅τ ⋅ 2 g

(32)

]^_

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ijba⁄b = 0.077

C = 0.062, n = 0.6;

ijb a⁄b = 0.119

C = 0.094, n = 0.5;

ijb a⁄b = 0.15

C = 0.113, n = 0.45.

>eylmj[me_glgh]hj_`bfZfh`ghbkihevah\ZlvaZ\bkbfhklv>@

µ = 0,457 ⋅ Re

− 0 , 008

a   b

−0 , 24

.

(34)

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111

Dmax

α\o

α\uo Lpbe

Dmin

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− H = Pin Pout , ρg

(35)

]^_

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 1  µi =  +Z   µ2   

−1 / 2

,

(36)

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(37)

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112

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µ⋅f0 = π⋅d2⁄4.

(38)

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V1 = µ⋅f0⋅τ √(2gHH),

114

(39)

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V2 = µ⋅f0⋅τ (√(2gHH) + √(2gHK))/2,

(40)

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Gkl JZlf-Js)/ρg.

(41)

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H[tzfml_q_ddm[f

9 9 9

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9 9 9

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VΣ = V1 + V2 + V3 – V4– V5. Ij_^iheZ]Zy qlh \_ebqbgZ wdheh]bq_kdh]h ms_j[Z ijhihjpbhgZevgZ h[t_fZf Z\Zjbcguo ml_q_d aZ]jyagyxsbo \h^h_fu \\_^_f \ jZkkfhlj_gb_ iZjZf_lj µ1 dZd hlghkbl_evgmx\_ebqbgmihl_gpbZevgh]hms_j[Z

µ1i = VΣi⁄VΣ max,

(42)

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ρ g_nlb ]^_

∂V dh dx + n e ⋅ ρ ]j + q = 0 , ∂x dt

(43)

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V = C ⋅ Rh ⋅ i0 ,

(44)

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FbN –qbkeh\oh^h\b\uoh^h\ljm[hijh\h^ghck_lb ∆Fj(t) –baf_g_gb_dhebq_kl\Zijh^mdlZ\ljm[hijh\h^_aZ\j_fyt. Kms_kl\m_l ^\Z kihkh[Z j_r_gby mjZ\g_gby NbjfZ Shell UK ij_^eZ]Z_l klZlbklbq_kdbc f_lh^ >@ bkdexqZxsbc keh`gh_ fh^_ebjh\Zgb_ ljm[hijh\h^Z < kbkl_f_ ih ^Zgguf SCADA ijhba\h^blky g_ij_ju\guc jZkqzl klZlbklbq_kdbo \_jhylghkl_c \hagbdgh\_gby ml_q_d Dhebq_kl\h ijh^mdlZ \ ljm[hijh\h^_ ^ey \uqbke_gby ∆Fj(t) jZkkfZljb\Z_lky dZd Z^Zilb\gZy klZlbklbq_kdZy nmgdpby hl wdkiemZlZpbhgguo iZjZf_ljh\ mqZkldZ ljm[hijh\h^Z b kdhjhklb bo baf_g_gby GZb[hevr__ ij_bfms_kl\h klZlbklbq_kdh]h f_lh^Z aZdexqZ_lky \ iheghf hldZa_ hl keh`guofh^_e_cljm[hijh\h^h\qlhagZqbl_evghkhdjZsZ_lh[t_fih^]hlh\bl_evguo jZ[hlbjZkoh^h\Kms_kl\_ggufbg_^hklZldZfbkihkh[Zy\eyxlky_]hbg_jpbhgghklv \j_fyh[gZjm`_gbyml_qdb^hi_jbh^h\hijhkZ^Zlqbdh\ [hevrZyih]j_rghklv\ ehdZebaZpbb f_klZ ml_qdb b ^ebl_evguc i_jbh^ \j_f_gb h[mq_gby klZlbklbq_kdbc fh^_eb ijb kf_g_ dhgkljmdlb\guo iZjZf_ljh\ kbkl_fu k\hckl\ i_j_dZqb\Z_fh]h ijh^mdlZ beb \g_rgbo mkeh\bc wdkiemZlZpbb ]jmglh\uo ]b^jheh]bq_kdbo ih]h^ghdebfZlbq_kdbobij Ijbgpbiu ^_l_jfbgbjh\Zggh]h fh^_ebjh\Zgby j_`bfh\ wdkiemZlZpbb FGI gZrebk\h_hljZ`_gb_\jZ[hlZoki_pbZebklh\BILWJ>@bJMG=bf=m[dbgZ>@ dhlhju_[uebj_Zebah\Zgu\ijh]jZff_©BJWGª-³baf_g_gb_j_`bfh\wdkiemZlZpbb g_nl_ijh^mdlhijh\h^h\´ GZb[he__ i_jki_dlb\guf kihkh[hf j_r_gby mjZ\g_gby y\ey_lky fZl_fZlbq_kdh_ fh^_ebjh\Zgb_ \ jZfdZo kbkl_fu nmgdpbhgZevghc ^bZ]ghklbdb hkeh`g_gbcl_ogheh]bq_kdboj_`bfh\wdkiemZlZpbbljm[hijh\h^Z Baf_g_gby dhebq_kl\Z ijh^mdlZ\ljm[hijh\h^_ ∆Fj(t)fh`ghij_^klZ\blvdZd kmffm we_f_glZjguo ijbjZs_gbc deZkkbnbpbjh\Zgguo ih ijbqbgZf bo \hagbdgh\_gby (46) ∆ M p (t ) = ∆(ρ ⋅ V ) = ∆ρ ⋅ V 0 + ρ 0 ⋅ ∆V ]^_ V0 , ρ0 – h[t_f mqZkldZ ljm[hijh\h^Z b iehlghklv ijh^mdlZ ijb ba\_klguo l_fi_jZlmj_b^Z\e_gbb ∆P   ∆ρ = ρ 0  − ξ ⋅ ∆T +  - ijbjZs_gb_ iehlghklb aZ kqzl baf_g_gby K   l_fi_jZlmju gZ \_ebqbgm ∆L b ^Z\e_gby - ∆J ξ - dhwnnbpb_gl h[t_fgh]h jZkrbj_gbyD–fh^mevmijm]hklbijh^mdlZ ∆V = ∆VT + ∆VP - ∆Vω -ijbjZs_gb_h[t_fZmqZkldZljm[hijh\h^Z ∆ V T = α ⋅ ∆T , ]^_ α - dhwnnbpb_gl h[t_fgh]h jZkrbj_gby f_lZeeZ ^ey klZebα ≈ 3,3⋅10-5 1/0K D ∆ V P = V o ⋅ 0 ⋅ ∆P ]^_?–fh^mevXg]Z^eyklZeb?≈ 2⋅1011IZ E ⋅δ

125

k k −1 ∆V ϖ = ∑ (ϖ n − ϖ n )⋅ l n

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127

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G f Q = 68 dm[f\qZk DI> N = 42 d\l

G f Q = 68 dm[f\qZk DI> N = 39 d\l

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128

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F_klhiheh`_gb_kdj_[dZ Iheh`_gb_ ID >ZlZ 12.03.1998 èëèìîâî <j_fy 15:34:45

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Jbkmghd–
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20 =m`h\:BKh\f_klguck[hjbljZgkihjlg_nlbb]ZaZ–FG_^jZ– k 21 =mf_jh\ := DheiZdh\ E= ;Z`Zcdbg K= <_drl_cgF=P_gljh[_`gu_ gZkhku \ kbkl_fZo k[hjZ ih^]hlh\db b fZ]bkljZevgh]h ljZgkihjlZ g_nlbFG_^jZ-k 22 >hehlp_\ ;G Om^hrbg :: >Z\u^h\Z ?: :\lhfZlbabjh\ZggZy kbkl_fZ dhgljheyaZkhklhygb_fh[t_dlh\;_ahiZkghklvljm^Z\ijhfure_gghklb– 1997. - 23 >hiheg_gb_dJ>-39-030-©Ihjy^hdhij_^_e_gbyhq_j_^ghklbj_fhglZ ^_n_dlh\ fZ]bkljZevguo g_nl_ijh\h^h\ ih j_amevlZlZf \gmljbljm[ghc ^bZ]ghklbdbª–F:D©LjZgkg_nlvª–k 24 ?:KM F_lh^heh]by kha^Zgby _^bghc kbkl_fu dhgljhey b mijZ\e_gby l_ogbq_kdbfh[kem`b\Zgb_fbj_fhglhfKDMLHJ h[t_dlh\bkhhjm`_gbc g_nl_ijh\h^h\ :D ©LjZgkg_nlvª Ljm[hijh\h^guc ljZgkihjl g_nlb – 1996. -–k-12. 25 @_e_adh XK DML>I©MolZªLjm[hijh\h^gucljZgkihjlg_nlb– 1998. -–k12. 27 AZ\Z^kdbc:H:H©MjZeljZgkg_nl_ijh^mdlª-MnZBa^-\h©Keh\hª– k 28 AZj_pdbc K< Ijh[e_fu ihabpbhgbjh\Zgby \ g_nl_]Zah\hc hljZkeb G_nl_]Zah\u_l_ogheh]bb, 2000. -–k-13. 29 Dex_\ << G_jZajmrZxsbc dhgljhev b ^bZ]ghklbdZ [_ahiZkghklb AZ\h^kdZyeZ[hjZlhjby>bZ]ghklbdZfZl_jbZeh\–l- 30 DheiZdh\ E= P_gljh[_`gu_ gZkhku fZ]bkljZevguo g_nl_ijh\h^h\- F G_^jZ 31 DheiZdh\E=Gh\hk_eh\<<RfZldh\::JZkq_ldhwnnbpb_glZjZkoh^Z ijbbkl_q_gbbbahl\_jklbyh[jZah\Z\r_]hky\fZ]bkljZevghfg_nl_ijh\h^_ \]jmglK[gZmqklZl_cLjm[hijh\h^gucljZgkihjl-MnZM=GLM 32 DheiZdh\ E= JZofZlmeebg RB DZ\blZpby \ p_gljh[_`guo gZkhkZo ijb i_j_dZqd_g_nl_cbg_nl_ijh^mdlh\-FG_^jZ 33 Dhfie_dk ijh]jZff ©JZkqzl j_`bfh\ jZ[hlu g_nl_ijh\h^h\ª :FRZffZah\ G?Ibjh]h\ XIJ_lxgbg b ^j Ljm[hijh\h^guc ljZgkihjlg_nlbIjbeh`_gb_-–k-18. 34 Dhgp_ipby ?^bghc Z\lhfZlbabjh\Zgghc kbkl_fu mijZ\e_gby ?:KM :D ©LjZgkg_nlvªLjm[hijh\h^gucljZgkihjlg_nlb– 1995. -–k-17. 35 DhjihjZlb\gu_ bgnhjfZpbhggu_ kbkl_fu \ mijZ\e_gbb g_nl_ijh\h^guf ljZgkihjlhfLjm[hijh\h^gucljZgkihjlg_nlb– 1998. -–k-25. 36 DhjrZd :: RZffZah\ :F Hkgh\u g_nl_]Zah\h]h ^_eZ – MnZ HHH

158

©>baZcgIheb]jZnK_j\bkª–k 37 Dhlh\ << BgnhjfZpbhggh-ZgZeblbq_kdZy kbkl_fZ ©Wdki_jlª Ljm[hijh\h^gucljZgkihjlg_nlb– 1997. -–k-27. 38 Dhlh\<<H\g_^j_gbbbjZa\blbbbgnhjfZpbhggh-ZgZeblbq_kdhckbkl_fu ©Wdki_jlªLjm[hijh\h^gucljZgkihjlg_nlb– 1999. -–k-28. 39 Dmebdh\ : Mqzl wdkihjlZ g_nlb b g_nl_ijh^mdlh\ FQKJ;–k-156. 41 Dmlmdh\ K? ;Zolbabg JG IZ\eh\ K< Ijbf_g_gb_ =BK ^ey hp_gdb wdheh]bq_kdh]h jbkdZ Z\Zjbb gZ fZ]bkljZevghf ljm[hijh\h^_ ;Zrdbjkdbc wdheh]bq_kdbc\_klgbd- –k-47. 42 Dmlmdh\ K? ;Zolbabg JG IZ\eh\ K< Ki_pbnbdZ =BK ljm[hijh\h^gh]h ljZgkihjlZ FZl_jbZeu III dhg]j_kkZ g_nl_]Zahijhfure_ggbdh\ Jhkkbb GZmqgu_ljm^uK_dpbyG©Ijh[e_fug_nlbb]ZaZª-fZy]–MnZ Ba^-\h©J_Zdlb\ª-k-216. 43 Dmlmdh\ K? <eZkh\ <: Wdheh]bq_kdb_ Zki_dlu j_]bhgZevghc wdhghfbdb ljm[hijh\h^gh]h ljZgkihjlZ Lxf_gkdh]h K_\_jZ LjZgkihjl gZmdZ l_ogbdZmijZ\e_gb_-Fbkk_jlZpby dZg^l_oggZmdgZmqgucjmdJG;Zolbabg-MnZM=GLM– k 48 Ebkbg X< Kh\_jr_gkl\h\Zgb_ kbkl_fu mijZ\e_gby b dhgljhey l_ogbq_kdh]h h[kem`b\Zgby b j_fhglZ g_nl_ijh\h^h\ k p_evx ih\ur_gby gZ^_`ghklbbowdkiemZlZpbbLjm[hijh\h^gucljZgkihjlg_nlb– 1997. - 3. –k-17. 49 Ehdhldh\:<Qlh^he`gZmf_lvkbkl_fZSCADAKh\j_f_ggu_l_ogheh]bb Z\lhfZlbaZpbb-–k-46. 50 Wdki_jbf_glZevgZy ijh\_jdZ Ze]hjblfh\ ijbdeZ^gh]h ijh]jZffgh]h h[_ki_q_gbyih^bZ]ghklbd_ml_q_dg_nlbgZg_nl_ijh\h^ZoEhk_gdh\:K Lj_nbeh\:=GZjoh\<Ib^jLjm[hijh\h^gucljZgkihjlg_nlb 1996. –k-10. 51 Emjv_F<FZdZjh\IK=b^jZ\ebq_kdZyehdZpbyml_q_dg_nl_ijh^mdlZgZ mqZkld_ ljm[hijh\h^Z LjZgkihjl b ojZg_gb_ g_nl_ijh^mdlh\ GLK – F

159

PGBBLWg_nl_obf––k-18. 52 Emjv_ F< FZdZjh\ IK Q_jgbdbg <: Gh\uc Ze]hjblf hi_jZlb\gh]h h[gZjm`_gby ml_q_d `b^dhklb ba ljm[hijh\h^h\ LjZgkihjl b ojZg_gb_ g_nl_ijh^mdlh\GLK–FPGBBLWg_nl_obf––k-18. 53 FZeh\ ?: ;jhgnbg B; >he]hiylh\ <G b ^j
57 F_lh^bdZhij_^_e_gbyms_j[Zhdjm`Zxs_cijbjh^ghckj_^_ijb Z\ZjbyogZfZ]bkljZevguoljm[hijh\h^Zoml\Fbglhiwg_j]hJN ghy[jy] -MnZBILWJ 58 F_lh^bdZhij_^_e_gbyms_j[Zhdjm`Zxs_cijbjh^ghckj_^_ijb Z\ZjbyogZfZ]bkljZevguoljm[hijh\h^Zoml\Fbglhiwg_j]hJN ghy[jy] -MnZBILWJ 59 F_lh^bdZjZkq_lZ\u[jhkh\\j_^guo\_s_kl\\Zlfhkn_jmKZfZjZ 60 F_lh^bq_kdb_ j_dhf_g^Zpbb ih ijbf_g_gbx Zwjhdhkfbq_kdbo f_lh^h\ ^ey ^bZ]ghklbdb ljm[hijh\h^guo ]_hl_ogbq_kdbo kbkl_f b fhgblhjbg]Z hdjm`Zxs_ckj_^u–FMGP=Zaijhf–k 61 F_lh^bq_kdb_ hkgh\u jZajZ[hldb f_jhijbylbc ih ij_^mij_`^_gbx qj_a\uqZcguo kblmZpbc ijb wdkiemZlZpbb fZ]bkljZevguo g_nl_ijh\h^h\ / <B EZjbhgh\ KIKms_\ :==mf_jh\ b ^j \ FZl_jbZeZo III j_kim[ebdZgkdh]h GLK©H[_ki_q_gb_ijhfure_gghc[_ahiZkghklbhiZkguo ijhba\h^kl\_gguoh[t_dlh\LWDJ;ªhl–MnZBILWJM=GLM 2002. – 37-45. 62 F_lh^bq_kdb_ j_dhf_g^Zpbb ih ijh]ghabjh\Zgbx j_fhglZ b j_dhgkljmdpbb fZ]bkljZevguo ljm[hijh\h^h\ gZ hkgh\Zgbb fZl_jbZeh\ Zwjhdhkfbq_kdbo ktzfhdljZkk–F
160

66 Fbk_\bqmk ;B KZ_gdh <: ?^bgZy Z\lhfZlbabjh\ZggZy kbkl_fZ mijZ\e_gby:D©LjZgkg_nlvªLjm[hijh\h^gucljZgkihjlg_nlb– 1993. –k-44. 67 Fbk_\bqmk ;B KZ_gdh <: b ^j :\lhfZlbabjh\ZggZy kbkl_fZ dhgljhey bkiheg_gby ^h]h\hjh\ ijhba\h^kl\_ggh]h h[t_^bg_gby fZ]bkljZevguo g_nl_ijh\h^h\ :D ©LjZgkg_nlvª Ljm[hijh\h^guc ljZgkihjl g_nlb – 1994. -–k-20. 68 Fbk_\bqmk ;B KZ_gdh <: b ^j :\lhfZlbabjh\ZggZy kbkl_fZ dhgljhey bkiheg_gby ^h]h\hjh\ ijhba\h^kl\_ggh]h h[t_^bg_gby fZ]bkljZevguo g_nl_ijh\h^h\ :D ©LjZgkg_nlvª Ljm[hijh\h^guc ljZgkihjl g_nlb – 1994. -–k-14. 69 FboZceh\ K LZj]meyg H G_nlygu_ jZaeb\u – \b^ ba dhkfhkZ ARC REVIEW Kh\j_f_ggu_ ]_hbgnhjfZpbhggu_ l_ogheh]bb - – k 70 Fmabgh\ OG DZjZkbd <I L_ogbq_kdh_ i_j_\hhjm`_gb_ :KMLI Z H:H ©Kb[g_nl_ijh\h^ª Hiul kha^Zgby kbkl_f \lhjh]h ihdZe_gby Ljm[hijh\h^gucljZgkihjlg_nlb– 1997. -–k-40. 71 Fmexdh\ N= WdkiemZlZpby kbkl_f h[gZjm`_gby ml_q_d \ H:H ©JyaZgvljZgkg_nl_ijh^mdlªLjZgkihjlbojZg_gb_g_nl_ijh^mdlh\GLK– FPGBBLWg_nl_obf--10. –k-33. 72 GZ[b_\ JJ b ^j :\lhfZlbabjh\ZggZy bgnhjfZpbhggZy kbkl_fZ h[t_dlh\ fZ]bkljZevguo g_nl_ijh\h^h\ H:H ©MjZekb[g_nl_ijh\h^ bf >:Q_jgy_\ZªLjm[hijh\h^gucljZgkihjlg_nlb– 1997. -–k-30. 73 Hk[hjg N =hllnjb^ I ;jbllhg ; Kha^Zgb_ ]hkm^Zjkl\_gghc dZjlh]jZnbq_kdhckbkl_fuljm[hijh\h^h\G_nl_]Zah\u_l_ogheh]bb -–k-89. 74 Hlq_l h GBJ -2- ©F_lh^bdZ hp_gdb wnn_dlb\ghklb bkihevah\Zgby we_dljhwg_j]bb gZ i_j_dZqdm g_nlb ih ljm[hijh\h^Zf \ mkeh\byo kgb`_gby h[t_fh\i_j_dZqdbª–MnZBgklblmlF_oZgbdbJ:G] 75 Hlq_l h GBJ ©:gZeba wg_j]hihlj_[e_gby b jZajZ[hldZ f_jhijbylbc ih kgb`_gbx wg_j]haZljZl \ kbkl_f_ H:H ©Ijb\he`kdb_ fZ]bkljZevgu_ g_nl_ijh\h^uª–MnZM=GLM 76 Hlq_l h GBJ -2-01- ©JZajZ[hldZ b \g_^j_gb_ \ H:H IFG dhfie_dkZ ih hij_^_e_gbx DI> gZkhkguo Z]j_]Zlh\ b \u^ZqZ ij_^eh`_gbc ih ih\ur_gbxwnn_dlb\ghklbjZ[hlugZkhkh\ª-MnZBILWJ 77 IZ\eh\K<=BK–hkgh\Zkh\j_f_ggh]hbgnhjfZpbhggh]hh[_ki_q_gbyijb mijZ\e_gbb l_jjblhjbZevgh-jZkij_^_e_ggufb kbkl_fZfb GLK ©GZmqghl_ogbq_kdb_ijh[e_fuLWDJ;ª–MnZBa^-\hNKJGL– 63-k 78 IZ\eh\ K< ;Z]fZgh\ <O =\ha^_\ <? ?^bgZy ]hkm^Zjkl\_ggZy kbkl_fZ wdheh]bq_kdh]h fhgblhjbg]Z J; < dg Wdheh]bq_kdb_ ijh[e_fu j_]bhgh\ Jhkkbb–J;
ljm^Z\ijhfure_gghklb– 1996. - 81 IhlZih\G:Fbjdbg:AMkbgvr<<Dhfie_dkgZykbkl_fZh[_ki_q_gby gZ^_`ghklb b [_ahiZkghklb ijhba\h^kl\ ;_ahiZkghklv ljm^Z \ ijhfure_gghklb– 1995. - 82 IjbdeZ^gu_g_qzldb_kbkl_fuI_jkyihgkdh]hIh^j_^LLwjZghD:kZb FKm]wgh–FFbj–k 83 Ijhfukeh\u_ ljm[hijh\h^u Dmebdh\ <> Rblg_\ :< Ydh\e_\ :? :glbiv_\<G–FG_^jZ1994. –k 84 IZjZf_ljbq_kdZy kbkl_fZ h[gZjm`_gby ml_q_d ^ey g_nl_ijh\h^h\ k kZfhl_qgufb mqZkldZfb JAGZ]Z_\ <;Iehlgbdh\ :KEhk_gdh\ X<Njheh\Ljm[hijh\h^gucljZgkihjlg_nlb– 2002. -Ijbe–k13. 85 JZkqzl fZ]bkljZevguo ]Zahijh\h^h\ \ dZjkljh\hc ahg_ :FRZffZah\ <:Qbq_eh\JFAZjbih\b^j–MnZ=be_f–k 86 JZofZlmeebgRB=mf_jh\:= -375- F_lh^bq_kdb_ j_dhf_g^Zpbb ih khklZ\e_gbx ^_deZjZpbb ijhfure_gghc [_ahiZkghklb hiZkgh]h ijhba\h^kl\_ggh]h h[t_dlZ ml\_j`^_guihklZgh\e_gb_f=hk]hjl_ogZ^ahjZJhkkbbhl3). 88 J>-120-F_lh^bq_kdb_mdZaZgbyihijh\_^_gbxZgZebaZjbkdZhiZkguo ijhfure_gguoh[t_dlh\ 89 J> -39-030- ©F_lh^bdZ j_fhglZ ^_n_dlguo mqZkldh\ fZ]bkljZevguo g_nl_ijh\h^h\ ih j_amevlZlZf \gmljbljm[ghc ^bZ]ghklbdbª – F :D ©LjZgkg_nlvª98. –k 90 J> -9147103-372- ©Bgkljmdpby ih h[ke_^h\Zgbx dhjjhabhggh]h khklhygbyfZ]bkljZevgh]hg_nl_ijh\h^Zª-MnZ
162

97 KZfb]meebg =O Dhfivxl_jgu_ ijh]jZffgu_ kj_^kl\Z ^ey dhgljhey [_ahiZkghklb \aju\h- b ih`ZjhhiZkgh]h h[hjm^h\Zgby hiZkguo ijhba\h^kl\_gguoh[t_dlh\FZl-euIIIGIK©H[_ki_q_gb_ijhfure_gghc [_ahiZkghklb hiZkguo ijhba\h^kl\_gguo h[t_dlh\ LWD J; – MnZ M=GLM 2002. –k.133-145. 98 Kbkl_fu ^bki_lq_jkdh]h mijZ\e_gby b k[hjZ ^Zgguo SCADA – kbkl_fu H[ahjdhfiZgbb©:gd_cªFbjdhfivxl_jghcZ\lhfZlbaZpbb-k-9. 99 Kdjbigbdh\ X< KZahgh\ H< Kdh\hjh^gbdh\ X: Gh\uc kihkh[ ijbf_g_gby ^_ij_kkhjguo ijbkZ^hd ijb i_j_dZqd_ \ukhdhiZjZnbgbkluo g_nl_cLjZgkihjlbojZg_gb_g_nlbbg_nl_ijh^mdlh\– 1975. -–k 100 Kh[he_\ <K Ijh]jZffgh_ h[_ki_q_gb_ kh\j_f_gguo kbkl_f k[hjZ b h[jZ[hldb baf_jbl_evghc bgnhjfZpbb Ijb[hju b kbkl_fu mijZ\e_gby – 1998. - 101 Kha^Zgb_ _^bghc bgnhjfZpbhgghc kbkl_fu h[t_dlh\ ljm[hijh\h^ghc k_lb J_kim[ebdb ;ZrdhjlhklZg :FRZffZah\ JG;Zolbabg K?Dmlmdh\ <:;mj_gbg IG=jb]hj_gdh K<IZ\eh\ FZl_jbZeu dhgn ´Kbkl_fguc ZgZebaijhp_kkh\jZajZ[hldbg_nlyguof_klhjh`^_gbcbljZgkihjlZg_nlbb g_nl_ijh^mdlh\´-MnZ:GD´;Zrg_nlv´-k-50. 102 Kl_iZgygp <K ;_eZrh\ << :\lhfZlbabjh\ZggZy kbkl_fZ h[_ki_q_gby [_ahiZkghcwdkiemZlZpbbg_nl_obfbq_kdboh[t_dlh\;_ahiZkghklvljm^Z\ ijhfure_gghklb– 1996. - 103 Kujhfylgbdh\ B: J_`bfu jZ[hlu Zkbgojhgguo b kbgojhgguo we_dljh^\b]Zl_e_c-F-E=hkwg_j]hba^Zl 104 L_ogbq_kdb_ kj_^kl\Z ^bZ]ghklbjh\Zgby KijZ\hqgbd <<Dex_\ IIIZjohf_gdh <?:[jZfqmd b ^j ih^ h[s j_^ <<Dex_\Z – F: FZrbghkljh_gb_–k 105 LdZq_\ H: Lm]mgh\ IB KhdjZs_gb_ ihl_jv g_nlb ijb ljZgkihjl_ b ojZg_gbb-FG_^jZ-k 106 Ljm[hijh\h^guc ljZgkihjl g_nl_ijh^mdlh\ BLBrfmoZf_lh\ KEBkZ_\ F<Emjv_KIFZdZjh\–FG_nlvb]Za–k 107 Lm]mgh\IBG_klZpbhgZjgu_j_`bfui_j_dZqdbg_nl_cbg_nl_ijh^mdlh\FG_^jZ-k 108 Lm]mgh\ IB Dmlmdh\ K? <eZkh\ <: Ijbjh^hhojZggu_ j_r_gby ljm[hijh\h^gh]h ljZgkihjlZ m]e_\h^hjh^gh]h kujvy \ \_qghf_jaeuo ]jmglZoFZl_jbZeuhljZke_\h]hkh\_sZgbyFbgg_nl_]ZaijhfZIjh[e_fu hojZgu hdjm`Zxs_c kj_^u \ g_nlyghc ijhfure_gghklb – MnZ
163

111 Lm]mgh\IBY[ehgkdbc<KIjh]j_\]jmglZebg_cgufbpbebg^jbq_kdbf bklhqgbdhfijb]jZgbqguomkeh\byoIIIjh^ZBa\<MAh\G_nlvb]Za # 9,-k-86. 112 Lmlgh\ B: ;ZaZjh\Z ?: >mrd_\bq <F MijZ\ey_fu_ [Zau ^Zgguo ^ey hilbfbaZpbb kjhdh\ \hkklZgh\bl_evgh]h j_fhglZ fZ]bkljZevguo ljm[hijh\h^h\;_ahiZkghklvljm^Z\ijhfure_gghklb– 1994. - 113 NZjf_j W>` BkiulZgb_ gh\hc kbkl_fu h[gZjm`_gby ml_q_d ba ljm[hijh\h^ZG_nlv]Zabg_nl_obfbyaZjm[_`hf– 1993. -–k-53. 114 N_^_jZevguc aZdhg ©H ijhfure_gghc [_ahiZkghklb ijhba\h^kl\_gguoh[t_dlh\ªhl-NA

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115 N_^hjh\ <L Hiul jZajZ[hldb b wdkiemZlZpbb J:BK \ H:H ©K_\_jgu_ fZ]bkljZevgu_ g_nl_ijh\h^uª Ljm[hijh\h^guc ljZgkihjl g_nlb Ijbe 2000. -–k-9. 116 OZjbhgh\kdbc << LjZgkihjl ]ZaZ \ Jhkkbb gZ^_`ghklv b Z\Zjbcghklv Ijbjh^guc ]Za \ [u\r_f Kh\_lkdhf Khxa_ ki_p ijbeh`_gb_ d `mjgZem ©=Zah\Zyijhfure_gghklvª– 1995. – b ^j BgnhjfZpbhggh_ h[_ki_q_gb_ kbkl_fu l_ogbq_kdh]h h[kem`b\Zgby b j_fhglZ ih^\h^guo ljm[hijh\h^h\ \ :D ©LjZgkg_nlvª Ljm[hijh\h^gucljZgkihjlg_nlb– 1996. -–k-6. 121 Q_jgy_\<>b^jHiulkha^ZgbybgnhjfZpbhgguol_ogheh]bc\mijZ\e_gbb h[kem`b\Zgb_f b j_fhglhf fZ]bkljZevguo g_nl_ijh\h^h\ Ljm[hijh\h^gucljZgkihjlg_nlb– 1998. -–k-7. 122 Qbjbdh\ K<Fbk_\bqmk;BKZ_gdh<:Dhgp_ipbyihkljh_gbykbkl_fu ^bki_lq_jkdh]h dhgljhey b mijZ\e_gby KD>M :D ©LjZgkg_nlvª Ljm[hijh\h^gucljZgkihjlg_nlb– 1996. -–k-21. 123 RfZldh\ :: b ^j GLK
164

126 $UF9LHZ<_jkbyJmdh\h^kl\hihevah\Zl_ey–k 127 Bose J.R., Olson M.R. TAPS’s leak detection seeks greater precision // Oil & Gas J. – 1993. – Vol. 91.14. – P. 43,44,46-48. 128 Brauner N. Role of Interfacial Shear Modeling in Predicting Stability of Stratified Two-Phase Flow. INVITED Chapter / Encyclopedia of Fluid Mechanics, edited by N.P.Cheremisinoff, Vol. 5, “Advances in Engineering Fluid Mechanics: Boundary Conditions Required for CFD Simulation”, 1996. – p. 317-378. 129 Clarke S.L. Centralized control improves operating efficiency. // Oil & Gas J., 2002. – Vol. 100.7. – p. 50-55. 130 Council T.L., Honey D.J., Cox M.L. Environmental Solutions – Key Successful South Texas Line Installation. /Oil & Gas J. – 2000. –Vol. 98.30. - July 24. – p. 7072. 131 Don M. Scott // Oil&Gas J. 1999. # 11. – p.51-57. 132 ERDAS Field Guide (4th edition). Revised and Expanded ERDAS(Atlanta, Georgia 30329 - 2137 USA), 2000. – 686 p. 133 ERDAS Imagine 8.2 Manual - ERDAS(Atlanta, Georgia USA), 2001. – 713 j. 134 Feizlmayer A.H., Weil F. Economic analysis of crude oil pipelines. //Oil&Gas J., Vol. 98.47, Nov. 20, 2000. – pp.70-77. 135 Furukawa H., Ihara M., Takao S., Kohda K. Design of Large-Scale Experimental Facilities for Multiphase Production Systems. //BHRG 6-th International Conference on Multiphase Production. (Cannes, France), 1993. 136 Hewitt G.F. Annular Two Phase Flow. – London: Pergamon Press, 1970. 137 Information System for Optimization of Trunk Pipelines Operation Modes /S.E.Kutukov , A.N. Vasiliev, S.V. Pavlov, R.N. Bakhtizin, R.R. Nabiev / European, Middle Eastern and Africa User Conference “GIS for the New Millennium” (18-20 Oct. 2000). - Istanbul, Turkey: ESRI EMEA, 2000. – p. 13. 138 Jackson L. High-resolution on-line inspection. //Hydrocarbon Technol. Internat. The international review for the refining? petrochemical and gas processing industries. – N.Y.: Perkin Elmer, 1994. 139 Samoilov B., Truskov P. Transneft holds onto key transportation role, tries to ensure reliability. //Oil *DV-RXUQDO9RO1RY– p.41-46. 140 Simulation Method of Pipeline Sections Ranking by Environmental Hazard due to Oil Damage Spill / R. Bakhtizin, S. Kutukov, R. Nabiev, S. Pavlov, A.Vasiliev / Proceedings "Intellectual Service for Oil and Gas Industry: Analysis, Solutions, Perspectives" / edit.A. Shammazov, L. Besenyei et. all. - Ufa: Publ. USPTU, 2000.P. 163-171. 141 Scott Don M. CPM offers an additional leak detection capability //Pipe Line & Gas Ind. - 2001. – Vol.84. -- p.43-46,48. 142 Teitel Y., Dukler A.E., Barnea D. Modelling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes. //AIChE J., Vol. 26,1980. – pp.345354. 143 Zadeh L.A. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. – IEEE Trans.Syst., Man, Cybern.,Vol. SMC-3, 1973, Jan., p.28-44. 165

Ijbeh`_gb_

IJBEH@?GB?1.

F?LH>BD:J:KQ,L:IHL?JVWE?DLJHWG?J=BB
KH>?J@:GB? :

HIJ?>?E?GB?IHL?JVWE?DLJHWG?J=BB
k 166

J:AEBQGUOJ?@BF:O?=HJ:;HLUBA:=JMADHCIH:DLB
:

J?@BFIJB&26ϕ = 1

168

: J?@BFIJBGHFBG:EVGHFLHD??GBY(I< = I<.G, K< = 1)

169

:

J?@BFJ:;HLUK>K&26ϕ = COSϕG

169

:

J?@BFKGHFBG:EVGUFAG:Q?GB?FJ?:DLB
169

:

KHKL:<EYXSB?IHL?JV< K>

170

:

IHL?JBIJBJ?@BF?J:;HLUKCOSϕ = 1

171

:

IHL?JBIJBGHFBG:EVGHFLHD??GBY

172

:

IHL?JBIJB&26ϕ = COSϕG

172

:

IHL?JBIJBGHFBG:EVGHCJ?:DLB
172

: J:KQ?LIHL?JV<>–8000–2
172

J:;HLU

:
174

<

IMKDH
176

<

HIJ?>?E?GB?I:J:F?LJH
176

<

HIJ?>?E?GB?IHL?JVFHSGHKLBQ?J?AWD
177

KHIJHLB<E?GB?

<

IHKLJH?GB?IMKDH

178

<

IHKLJH?GB?DJB
182

<

J:KQ?LIMKDH
184

166

Ijbeh`_gb_

Ihl_jbwe_dljhwg_j]bb\kbgojhgguo^\b]Zl_eyofh`ghjZa^_eblvgZg_kdhevdh khklZ\eyxsboKbkl_fgZykhklZ\eyxsZyihl_jv^ey^\b]Zl_e_cgZijbf_jKL>-6300-2 b KL>-8000- Eukv\_gkdh]h lmj[h]_g_jZlhjgh]h aZ\h^Z hij_^_ey_lky ih dZlZeh]Zf «:hkgh\gZyqZklv^bgZfbq_kdhckhklZ\eyxs_ch[mkeh\e_gZg_^h]jmadZfb\ nZdlbq_kdhf j_`bf_ wdkiemZlZpbb Djhf_ lh]h g_ihkj_^kl\_ggh ijb imkd_ kbgojhggh]h ^\b]Zl_e_c KL>-6300- b KL>-8000- l_jy_lky « d@ Mlhqg_gb_ \_ebqbgu ihl_jv we_dljhwg_j]bb ijb imkdZo \hafh`gh ijb kgylbb bg^b\b^mZevghc oZjZdl_jbklbdb Z]j_]Zlh\ Wlhl \b^ ihl_jv \ [ZeZgk_ wg_j]hihlj_[e_gby[m^_lhlg_k_g\klZlvx©WOAbijhqb_ª >ey kbgojhggh]h ^\b]Zl_ey aZ^Zgghc y\ey_lky gZ]jmadZ gZ \Zem hij_^_ey_fZy f_oZgbafhfIml_fj_]mebjh\ZgbylhdZ\ha[m`^_gbyfh`ghmklZgZ\eb\ZlvjZaebqgu_ j_`bfujZ[hluFRVϕ FRQVWdZdqZklguckemqZcFRVϕ ijbihklhygguoagZq_gbyo lhdZ \ha[m`^_gby b j_Zdlb\ghc fhsghklb ijbf_gy_fuc ijb fZ]bkljZevghf ljZgkihjl_ g_nlb >ey lh]h qlh[u j_rblv \hijhk h[ wdhghfbqghklb lh]h beb bgh]h j_`bfZg_h[oh^bfhhij_^_eblvihl_jb\wlhfj_`bf_ IjbghfbgZevghfj_`bf_Zdlb\gZyfhsghklvihlj_[ey_fZybak_lb P1g = Pg + ∆Pihkl. + ∆Pkl.g + ∆P\.g , ]^_

Pg –ihe_agZyfhsghklvgZ\Zem ∆Pihkl –ihklhyggu_ihl_jbihl_jb\klZebbf_oZgbq_kdb_ihl_jb

∆Pklg –ihl_jb\h[fhld_klZlhjZijbghfbgZevghflhd_klZlhjZ,g\dexqZy ^h[Z\hqgu_ihl_jb ∆P\g –ihl_jbgZ\ha[m`^_gb_ijbghfbgZevghflhd_\ha[m`^_gby,\g. H[sb_ ihl_jb \ kbgojhgghf ^\b]Zl_e_ \ ghfbgZevghf j_`bf_ hij_^_eyxlky kmffhc

∑ ∆P

g

= P1g − Pg = ∆Pihkl. + ∆Pkl.g + ∆P\.g ,

Ijb gZ]jmad_ gZ \Zem J lhd_ klZlhjZ , b lhd_ \ha[m`^_gby ,\ hlebqguo hl ghfbgZevguoagZq_gbcihlj_[ey_fZybak_lbZdlb\gZyfhsghklv 2

2

 I  I P1 = P + ∆Pihkl. + ∆Pkl.g ⋅   + ∆P\.g ⋅  \  .  Ig   I \ .g  H[sb_ihl_jbijbgZ]jmad_3 2

2

 I  I ∑ ∆P = P1 − P = ∆Pihkl. + ∆Pkl.g ⋅  I  + ∆P\.g ⋅  I \  .  g  \ .g 

I

LhdklZlhjZijbghfbgZevghfgZijy`_gbbhij_^_ey_lky

P2 + Q2 I= = I g ⋅ β 2 ⋅ cos 2 ϕ g + α 2 ⋅ sin 2 ϕ g , 3 ⋅ Ug ]^_αbβ –dhwnnbpb_gluaZ]jmadbklZlhjZkhhl\_lkl\_gghihj_Zdlb\ghcbZdlb\ghc fhsghklb

167

Ijbeh`_gb_

β=

P1 , P1g

α=

Q . Qg

I = β2 ⋅ cos 2 ϕg + α 2 ⋅ sin 2 ϕg . Ig

I

Dhwnnbpb_glu α b β lZd`_ ij_^klZ\eyxl kh[hc agZq_gby j_Zdlb\ghc b Zdlb\ghcfhsghklb\hlghkbl_evguo_^bgbpZo Bamijhs_gghc\_dlhjghc^bZ]jZffuKF>@

I \2. 1 + β 2 ⋅ x d2 ⋅ cos 2 ϕ G + α 2 ⋅ x d2 ⋅ sin 2 ϕ G + 2 ⋅ α ⋅ x d ⋅ sin ϕ G 2 , I = k\ = I \2.g 1 + x d2 + 2 ⋅ x d ⋅ sin ϕ G ]^_

k\ –dhwnnbpb_gl\ha[m`^_gby xd –bg^mdlb\gh_khijhlb\e_gb_K>ihijh^hevghchkb

Dhwnnbpb_glk\y\ey_lkylZd`_blhdhf\ha[m`^_gby\hlghkbl_evguo_^bgbpZo <I agZf_gZl_evij_^klZ\ey_lkh[hcd\Z^jZlhlghr_gbyghfbgZevgh]h lhdZ\ha[m`^_gbydlhdm\ha[m`^_gbyohehklh]hoh^Z

I \ .g 1 = = 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG . I \.o k \. o BaI ke_^m_lqlh^eyhij_^_e_gbyihl_jv\K>ijbjZaebqguoj_`bfZo_]h j_`bfZo g_h[oh^bfh agZlv oZjZdl_j baf_g_gby lhdZ \ha[m`^_gby b lhdZ klZlhjZ JZkkfhljbfg_dhlhju_j_`bfujZ[hluK> :J?@BFIJB&26ϕ = 1 Ijb FRVϕ j_Zdlb\gZy fhsghklv 4 khhl\_lkl\_ggh α Lhd \ha[m`^_gby

1 + β 2 ⋅ x d2 ⋅ cos 2 ϕG I \1 . = k \1 = I \ .g 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG

I

Lhd \ha[m`^_gby ih mjZ\g_gbx I fh`_l [ulv ij_^klZ\e_g \ \b^_ ]_hf_ljbq_kdhc kmffu ^\mo khklZ\eyxsbo i_j\Zy ba dhlhjuo jZ\gZ djZlghklb lhdZ ohehklh]hoh^Z

1 , 1 + x + 2 ⋅ x d ⋅ sin ϕG 2 d

Z\lhjZyijhihjpbhgZevgZZdlb\ghckhklZ\eyxs_clhdZklZlhjZ

168

Ijbeh`_gb_

β ⋅ x d ⋅ cos ϕG . 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG Ijbwlhfj_`bf_dZdwlhke_^m_lbaI ijbα lhdklZlhjZebg_cgh baf_gy_lky\aZ\bkbfhklbhlaZ]jmadbihZdlb\ghcfhsghklb

I = β ⋅ cos ϕg . Ig

:J?@BFIJBGHFBG:EVGHFLHD??GBY(I< = I<.G, K< = 1) J_Zdlb\gZyfhsghklvbamjZ\g_gbyI ijbN\ = 1

1 + x d2 ⋅ (1 − β 2 ⋅ cos 2 ϕg ) + 2 ⋅ x d ⋅ sin ϕg − 1 Q` . α`= = Qg x d ⋅ sin ϕg

I

LhdklZlhjZijbN\ =1

I = β 2 ⋅ cos 2 ϕg + α`2 ⋅ sin 2 ϕg . Ig :J?@BFJ:;HLUK>K&26ϕ = COSϕG Ijbwlhfα = β, lhdklZlhjZbaI

I = β, Ig lhd\ha[m`^_gbybaI

1 + β 2 ⋅ x d2 + 2 ⋅ β ⋅ x d ⋅ sin ϕG . k \ϕ = 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG :J?@BFKGHFBG:EVGUFAG:Q?GB?FJ?:DLB
k \4

1 + x d2 + 2 ⋅ x d ⋅ sin ϕG − x d2 ⋅ cos 2 ϕg ⋅ (1 − β 2 ) . = 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG

LhdklZlhjZgZhkgh\ZgbbI ijbα = 1

I = β 2 ⋅ cos 2 ϕg + sin 2 ϕg . Ig 169

Ijbeh`_gb_

:KHKL:<EYXSB?IHL?JV< K> >ey mklZgh\e_gby gZb[he__ \u]h^gh]h j_`bfZ jZ[hlu K> g_h[oh^bfh h[sb_ ihl_jbZdlb\ghcfhsghklbjZa^_eblvgZihl_jbaZ\bkysb_hlZdlb\ghcbj_Zdlb\ghc fhsghklb>eywlhcp_ebg_h[oh^bfhbkihevah\Zlvijb\_^_ggu_\ur_\ujZ`_gby^ey lhdh\klZlhjZbjhlhjZq_j_akhklZ\eyxsb_hij_^_e_ggu_khhl\_lkl\_gghihZdlb\ghc bj_Zdlb\ghcfhsghklyf Kh]eZkgh >@ \ k\yab k baf_g_gb_f gZkus_gby ijb jZaebqguo j_Zdlb\guo gZ]jmadZo [he__ lhqgh_ \ujZ`_gb_ ^ey lhdZ \ha[m`^_gby ih kjZ\g_gbx k ZgZeblbq_kdbfI ihemqZxl]jZnhZgZeblbq_kdbff_lh^hf K ^hklZlhqghc kl_i_gvx lhqghklb wlZ aZ\bkbfhklv fh`_l [ulv \ujZ`_gZ mjZ\g_gb_f

I \ = I \1 + (I \.g − I \1 ) ⋅

Q , α`⋅Q g

beb

k \ = k \ + (1 − k \ ) ⋅

α , α`

I

]^_ α` – j_Zdlb\gZy fhsghklv hl^Z\Z_fZy \ k_lv ijb ghfbgZevghf lhd_ \ha[m`^_gbybZdlb\ghcfhsghklb31 = β⋅Pg. Baf_g_gb_j_Zdlb\ghcfhsghklb\aZ\bkbfhklbhllhdZ\ha[m`^_gbybaI

α = α`⋅

k \ − k \ , 1 − k \

blh]^ZlhdklZlhjZijbbaf_gyxs_fkylhd_\ha[m`^_gby 2

 k − k \1  I sin 2 ϕg . = β 2 ⋅ cos 2 ϕg + α`⋅ \  Ig  1 − k \1  D\Z^jZllhdZ\ha[m`^_gby

2 ⋅ k \1 ⋅ (1 − k \1 )  1 − k \1  2 k = k + ⋅α ,  ⋅α + α'  α'  2

2 \

I

2 \1

bebijbih^klZgh\d_I \I 1 2 ⋅ k \1 ⋅ (1 − k \1 ) β2 ⋅ x d2 ⋅ cos 2 ϕG  1 − k \1  2 k = + ⋅α +  ⋅α + 2 2 1 + x d + 2 ⋅ x d ⋅ sin ϕG 1 + x d + 2 ⋅ x d ⋅ sin ϕG  α'  α' I 2

2 \

Ijbih^klZgh\d_I bI \I \ujZ`_gb_I ijbgbfZ_l\b^

170

Ijbeh`_gb_

∆P\.g ∆P\.g ⋅ x d2 ⋅ cos 2 ϕg ∑ ∆P = ∆Pihkl. + 1 + x 2 + 2 ⋅ x ⋅ sin ϕ + 1 + x 2 + 2 ⋅ x ⋅ sin ϕ ⋅ β2 + d d d d g g 2   2  1 − k \1  2 + ∆Pkl.g ⋅ β ⋅ cos ϕg + ∆Pkl.g ⋅ sin ϕg +   ⋅ ∆P\.g  ⋅ α +  α'    2 ⋅ ∆P\.g ⋅ k \1 ⋅ (1 − k \1 ) + ⋅ α. α' 2

2

I

beb

∑ ∆P = C + D ⋅ β

2

+ A ⋅ α 2 + B ⋅ α,

I

]^_

C = ∆Pihkl. +

∆P\.g ; 1 + x + 2 ⋅ x d ⋅ sin ϕg 2 d

∆P\.g ⋅ x d2 ⋅ cos 2 ϕg D= + ∆Pkl.g ⋅ cos 2 ϕg ; 2 1 + x d + 2 ⋅ x d ⋅ sin ϕg  1 − k \1  A = ∆Pkl.g ⋅ sin ϕg +   ⋅ ∆P\.g ;  α'  2

2

B=

2 ⋅ ∆P\.g ⋅ k \1 ⋅ (1 − k \1 ) ; α'

K–khklZ\eyxsZyihl_jvg_aZ\bkysZyhlZdlb\ghcbj_Zdlb\ghcfhsghklb D⋅β2 –khklZ\eyxsZyihl_jvbaf_gyxsZykyijhihjpbhgZevghd\Z^jZlmZdlb\ghc fhsghklb A⋅α2 –khklZ\eyxsZyihl_jvbaf_gyxsZykyijhihjpbhgZevghd\Z^jZlmj_Zdlb\ghc fhsghklb B⋅α –khklZ\eyxsZyihl_jvbaf_gyxsZykyijhihjpbhgZevghj_Zdlb\ghcfhsghklb :IHL?JBIJBJ?@BF?J:;HLUK&26ϕ = 1 GZhkgh\ZgbbI ijbα ihemqbf

∆P\.g ⋅ (1 + β 2 ⋅ x d2 ⋅ cos 2 ϕg ) ∑ ∆P = ∆Pihkl. + 1 + x 2 + 2 ⋅ x ⋅ sin ϕ + ∆Pkl.g ⋅ β2 ⋅ cos 2 ϕg g d d bebkmq_lhfI

∑ ∆P = ∆P

ihkl .

+ ∆P\.g ⋅ k \21 + ∆Pkl.g ⋅ β 2 ⋅ cos 2 ϕg

I

171

Ijbeh`_gb_

:IHL?JBIJBGHFBG:EVGHFLHD??GBY BaI ijbk\ = 1

∑ ∆P = ∆P

ihkl .

+ ∆P\.g + ∆Pkl.g ⋅ (β 2 ⋅ cos 2 ϕg + α`2 ⋅ sin 2 ϕg ) .

I

: IHL?JBIJB&26ϕ = COSϕG IjbjZ[hl_\wlhfj_`bf_α = βh[sb_ihl_jb\wlhfkemqZ_baI

1 + β 2 ⋅ x d2 + 2 ⋅ β ⋅ x d ⋅ sin ϕg ∑ ∆P = ∆Pihkl. + ∆Pkl.g ⋅ β + ∆P\.g ⋅ 1 + x 2 + 2 ⋅ x ⋅ sin ϕ , d d g 2

IZ

bebkmq_lhfI

(1 − k ) ⋅ β   ∑ ∆P = ∆Pihkl. + ∆Pkl.g ⋅ β + ∆P\.g ⋅ k \1 + α\`1  .   2

2

I[

:IHL?JBIJBGHFBG:EVGHCJ?:DLB
∑ ∆P = ∆P

ihkl .

+ ∆P\.g ⋅

+ ∆Pkl.g ⋅ (β 2 ⋅ cos 2 ϕg + sin 2 ϕg ) +

1 + x d2 + 2 ⋅ x d ⋅ sin ϕG − x d2 ⋅ cos 2 ϕg ⋅ (1 − β 2 ) . 1 + x d2 + 2 ⋅ x d ⋅ sin ϕG

: J:KQ?L

IHL?JV < >
I

KL>–8000–2

< J:AEBQGUO J?@BF:O

Bkoh^gu_^Zggu_g_h[oh^bfu_^eyjZkq_lZ - ghfbgZevgZyfhsghklv^\b]Zl_ey3g; - ghfbgZevgZyihegZyfhsghklv^\b]Zl_ey6g; - ghfbgZevgucDI>^\b]Zl_eyηg; - bg^mdlb\gh_khijhlb\e_gb_^\b]Zl_eyihijh^hevghchkb[d; - ihklhyggu_ihl_jbihl_jb\klZebbf_oZgbq_kdb_ihl_jb ∆Pihkl; - ihl_jb \ h[fhld_ klZlhjZ ijb ghfbgZevghf lhd_ klZlhjZ ,g \dexqZy ^h[Z\hqgu_ihl_jb∆Pklg; - ihl_jbgZ\ha[m`^_gb_ijbghfbgZevghflhd_\ha[m`^_gby,\g, ∆P\g. Bkoh^gu_ ^Zggu_ ^ey jZkq_lZ ihl_jv fhsghklb \ kbgojhgghf ^\b]Zl_e_ lbiZ KL>8000-ijb\_^_gu\lZ[ebp_I LZ[ebpZI >Zggu_^\b]Zl_eylbiZKL>-8000-2 Pgd
Sgd<⋅:

ηg

xd

∆Pihkld
∆Pklgd
∆P\gd
8000

9300

0,978

2,192

77382

57587

44990

172

Ijbeh`_gb_

Dhwnnbpb_glfhsghklb

cos ϕG =

Pg , Sg ⋅ ηg

cos ϕg = 0,88.

sin ϕg = 1 − cos 2 ϕg , sin ϕg = 0,48. >Ze__jZkq_l^eykhhl\_lkl\mxs_]hj_`bfZijhba\h^blkyihnhjfmeZfI – J_amevlZlujZkq_lZk\_^_gu\lZ[ebpmI LZ[ebpZI GZ]jmahqgu_ihl_jbd-8000-2 β

0,1

I 83,74

0,2

0,3

0,4

85,71

89,00

93,60

0,5

0,6

0,7

0,8

0,9

1,0

99,52 106,75 115,30 125,16 136,34 148,83

I 161,75 162,23 163,04 164,18 165,68 167,57 169,88 172,65 175,98 179,96 IZ 85,12

88,86

94,30 101,44 110,28 120,81 133,05 146,97 162,62 179,96

I[ 85,14

88,96

94,57 101,97 110,97 121,90 134,28 148,16 163,43 179,96

I 114,87 116,84 120,13 124,73 130,65 137,88 146,43 156,29 167,47 179,96 DZd\b^ghbalZ[ebpuIIZ bI[ ^ZxlijZdlbq_kdbh^bgblhl`_ qbke_ggucj_amevlZl Ihj_amevlZlZfjZkq_lh\kZfufbwdhghfbqgufbj_`bfZfby\eyxlkyj_`bfuk ihklhyggufdhwnnbpb_glhffhsghklbGZb[he__wdhghfbqgufbagboy\ey_lkyj_`bf k FRV ϕ lZd dZd \ wlhf j_`bf_ hlkmlkl\mxl ihl_jb h[mkeh\e_ggu_ i_j_^Zq_c j_Zdlb\ghcfhsghklbqlhkgb`Z_lgZ]j_\h[fhlhdklZlhjZbjhlhj AZ\bkbfhklvkmffZjguoihl_jv\^\b]Zl_e_lbiZKL>-8000-hlaZ]jmadb^ey jZaebqguoj_`bfh\_]hjZ[hluij_^klZ\e_gZgZjbkmgd_I

173

Ijbeh`_gb_

JbkmghdI–AZ\bkbfhklvh[sboihl_jv\K>hlaZ]jmadb : g_ \k_]^Z h[_ki_qb\Z_l fbgbfZevgu_ ihl_jb \ k_lb \ p_ehf lZd dZd d rbgZf djhf_ K> h[uqgh ih^dexq_gu Zkbgojhggu_ ^\b]Zl_eb we_dljhijb\h^u ih^ihjguo gZkhkh\ b ^jm]b_ ihlj_[bl_eb j_Zdlb\ghc fhsghklb JF Ijb hij_^_e_gghf agZq_gbb JF ihlj_[ey_fhc klhjhggbfb ihlj_[bl_eyfbihl_jb\k_lbgZi_j_^ZqmJFbihl_jb\K>fh]ml[ulvkhbaf_jbfu beb^Z`_ij_\urZlvihl_jb\K> < wlhf kemqZ_ \u]h^g__ bkihevah\Zlv K> dZd bklhqgbd JF lh _klv ijbjhkl ihl_jv\^\b]Zl_e_k\yaZgguckm\_ebq_gb_faZ]jmadbihJF[m^_lf_gvr_ihl_jvgZ i_j_^ZqmJF Kfh^_ebjm_fkblmZpbxkihfhsvxjZajZ[hlZgghcijh]jZffuImklvgZrbgZo \f_kl_kK>ijbkmlkl\m_lklhjhggbcihlj_[bl_evkhke_^mxsbfboZjZdl_jbklbdZfb -

Zdlb\gZyfhsghklvihlj_[bl_eyPihlj d
-

j_Zdlb\gZyfhsghklvihlj_[bl_eyQihlj d<⋅:j

Wd\b\Ze_glgh_ Zdlb\gh_ khijhlb\e_gb_ k_lb Rc Hf aZ]jmadZ K> ih Zdlb\ghcfhsghklbβ = 0,8. Lh]^Zihl_jb\k_lbgZi_j_^ZqmJFhibku\Zxlky\ujZ`_gb_f

174

Ijbeh`_gb_

∆PQ = ]^_

(Pg ⋅ β + ∆PK> + Pihlj ) 2 + (Qihlj − Qg ⋅ α) 2 U g2

⋅ Rc ,

I

Pg, Qg –khhl\_lkl\_gghZdlb\gZybj_Zdlb\gZyghfbgZevgu_fhsghklbK> Ug –gZijy`_gb_gZrbgZo ∆PK> –ihl_jbfhsghklb\K>ijb^Zgguoαbβ.

Ijh]jZffZjZkkqblu\Z_lihl_jb\^\b]Zl_e_∆PK> ihI ihl_jbhli_j_^Zqb JF ∆PQ ^ey α ∈ > @ k rZ]hf B ih fbgbfZevghc kmff_ ∆PQ + ∆PK> gZoh^bl hilbfZevgmxaZ]jmadmihJFbkhhl\_lkl\mxsbclZdhfmj_`bfmk\>ey[he__lhqgh]h ihbkdZαhilfh`gh\hkihevah\Zlvkyih^ijh]jZffhcjZkkqblu\Zxs_cihl_jb\K>^ey aZ^Zgguo agZq_gbc α b β Ih j_amevlZlZf jZkq_lh\ ^ey ij_^eh`_gguo bkoh^guo ^Zgguoαhil Zk\ = 0,698. Ke_^m_l hlf_lblv qlh ihbkd hilbfZevgh]h j_`bfZ ih fbgbfZevguf ihl_jyf Zdlb\ghcfhsghklbg_mqblu\Z_l\ebygb_kgb`_gbylhdZ\ha[m`^_gbygZmklhcqb\hklv jZ[hlu K> Ihwlhfm bkihevah\Zgb_wlh]hf_lh^Z^eyj_Zevguomkeh\bc[_aijh\_jdb g_h[oh^bfh]h^eymklhcqb\hcjZ[hluK>mjh\gylhdZ\ha[m`^_gbyg_j_dhf_g^m_lky GZ jbkmgd_ I ij_^klZ\e_gh hdgh ijh]jZffu ]jZnbq_kdb hlh[jZ`Zxs__ ihl_jb\K>ihl_jb\k_lbhli_j_^ZqbJFZlZd`_kmffZjgu_ihl_jbijbi_j_f_gghc aZ]jmad_K>ihJF

JbkmghdI–Ihl_jbfhsghklbijbgZebqbbklhjhgg_]hihlj_[bl_ey

175

Ijbeh`_gb_

<IMKDH fh`gh hij_^_eblv ih ko_f_ aZf_s_gby ij_^eh`_gghc \ >@ jbkmghd I < ^Zgghc ko_f_ baf_g_gb_ iZjZf_ljh\ ko_fu \ ijhp_kk_ imkdZ mqblu\Z_lky aZ\bkbfhklvx hl kdhev`_gby Zdlb\guo khijhlb\e_gbc h[fhldb\ha[m`^_gbyb^_fin_jghch[fhldb

JbkmghdI–Ko_fZaZf_s_gbyg_y\ghihexkgh]hK> GZko_f_h[hagZq_gh xafd –khijhlb\e_gb_\aZbfhbg^mdpbbf_`^mdhglmjZfbklZlhjZbjhlhjZih ijh^hevghchkb rf, xffd –Zdlb\gh_bbg^mdlb\gh_khijhlb\e_gbyh[fhldb\ha[m`^_gby r11d, x11d –Zdlb\gh_bbg^mdlb\gh_khijhlb\e_gby^_fin_jghch[fhldbihijh^hevghc hkb rs –Zdlb\gh_khijhlb\e_gb_h[fhldbklZlhjZ xs –khijhlb\e_gb_jZkk_ygbyh[fhldbklZlhjZ Qlh[u hij_^_eblv imkdh\u_ ihl_jb ih ^Zgghc ko_f_ aZf_s_gby g_h[oh^bfh agZlv hibkZggu_ \ur_ iZjZf_lju ^ey hij_^_e_gby lhdh\ \ dZ`^hc ba \_l\_c >Ze__ hij_^_eyxlkyihl_jbfhsghklbgZdZ`^hfZdlb\ghfkhijhlb\e_gbbdZd ∆Pi = Ii2⋅Ri. Qlh[u hij_^_eblv ihl_jb we_dljhwg_j]bb g_h[oh^bfh ihkljhblv djb\mx jZa]hgZgZkhkgh]hZ]j_]ZlZlh]^Zihl_jbwe_dljhwg_j]bbhij_^_eyxlky ∆Wi = ∆Pi ⋅ti, ]^_

ti –\j_fyjZ[hluK>gZdZ`^hfbamqZkldh\djb\hcjZa]hgZ Ihke_wlh]hh[sb_ihl_jbhij_^_eyxlkykmffbjh\Zgb_fhl^_evguo∆Wi. <HIJ?>?E?GB?I:J:F?LJH
>eyhij_^_e_gbyiZjZf_ljh\ko_fuaZf_s_gbyko_ffh`ghbkihevah\Zlv khhlghr_gbyijb\_^_ggu_\>@ xd = xs + xafd;

176

I.16)

Ijbeh`_gb_

x 'd = x s +

x ffd ⋅ x afd ; x ffd + x afd

I

x 'd = x s +

(x 'd − x s ) ⋅ x11d ; (x 'd − x s ) + x11d

I

Qlh[u ih khhlghr_gbyf I – I hij_^_eblv \k_ j_Zdlb\gu_ khijhlb\e_gby ko_fu aZf_s_gby K> g_h[oh^bfh agZlv khijhlb\e_gb_ klZlhjZ [l. :dlb\gu_khijhlb\e_gbyfh`ghhij_^_eblvba\ujZ`_gbc^eyihklhygguo\j_f_gb Td` = x1/rf; Td``= x2/r11d; Ta = xs/rs, ]^_

x1 =

x d ⋅ x 'd ; x d − x 'd

x2 =

x 'd ⋅ x ''d . x 'd − x ''d

Khijhlb\e_gb_ h[fhldb \ha[m`^_gby fh`gh lZd`_ hij_^_eblv ba iZkihjlguo ^Zgguo \ha[m^bl_ey LZd gZ GIK ©KZfZjZª ^ey ^\b]Zl_e_c lbiZ KL>-8000-2 bkihevamxlky lbjbklhjgu_ \ha[m^bl_eb lbiZ L?- >ey wlh]h lbiZ \ha[m^bl_e_ckhijhlb\e_gb_p_ib\ha[m`^_gbyjZ\ghHf LZddZd\jZ[hl_bkihevamxlkylhevdhiZkihjlgu_^Zggu_^\b]Zl_eylhjZkq_l iZjZf_ljh\ko_fuaZf_s_gbyg_ij_^klZ\ey_lky\hafh`gufbkihevam_lkywd\b\Ze_glgh_Zdlb\gh_khijhlb\e_gb_^\b]Zl_ey < HIJ?>?E?GB?

IHL?JV FHSGHKLB < KHIJHLB<E?GB?

K>

Q?J?A WD
<>@ijb\h^blkyf_lh^bdZhij_^_e_gbyiZjZf_ljh\K>ihdZlZeh`guf ^Zggufijb\h^ylkyke_^mxsb_\_ebqbgu Ug –ghfbgZevgh_gZijy`_gb_d< Ig –ghfbgZevguclhd: Pg –ghfbgZevgZyfhsghklv Sg –ghfbgZevgZyihegZyfhsghklvd<⋅: cos ϕg –ghfbgZevgucdhwnnbpb_glfhsghklb ηg –DI>ijbghfbgZevghcgZ]jmad_ Ii –djZlghklvimkdh\h]hlhdZhlrbg[_kdhg_qghcfhsghklbkgZijy`_gb_f8g; mi –djZlghklvimkdh\h]hfhf_glZ ng –ghfbgZevgZykbgojhggZyqZklhlZ\jZs_gbyfbg-1. GhfbgZevgucfhf_glhij_^_ey_lkyjZkq_lgufiml_fba\ujZ`_gby 177

Ijbeh`_gb_

Mg =

Pg . ωg

<_ebqbguijb\_^_ggu_\dZlZeh]_k\yaZguf_`^mkh[hcke_^mxsbfb aZ\bkbfhklyfb

Sg = 3 ⋅ U g ⋅ Ig ; Pg = Sg⋅cos ϕg⋅ηg. JZkkfhljbfg_dhlhju_khhlghr_gby\hlghkbl_evguo_^bgbpZoIhegh_ khijhlb\e_gb_^\b]Zl_ey\i_j\ucfhf_glimkdZ

z ''d = ]^_

Ug I ⋅ 3 I 1 ⋅ g = g = , I imkd I i 3 ⋅ Iimkd U g

Iimkd –lhdklZlhjZ\i_j\ucfhf_glimkdZ: Ii –djZlghklvimkdh\h]hlhdZ DjZlghklvimkdh\h]hfhf_glZ

mi = hldm^Z

3 ⋅ U g ⋅ Iimkd ⋅ cos ϕi M i Pi cos ϕi , = = = Ii ⋅ Fg Jg FRV ϕg 3 ⋅ U g ⋅ Ig ⋅ cos ϕg cos ϕi =

m i ⋅ cos ϕg . Ii

:dlb\gh_khijhlb\e_gb_^\b]Zl_ey\i_j\ucfhf_glimkdZ

r ''d = z ''d ⋅ cos ϕi =

1 m i ⋅ cos ϕg m i ⋅ cos ϕg . ⋅ = Ii Ii Ii2

Qlh[u i_j_clb hl hlghkbl_evguo _^bgbp d bf_gh\Zgguf g_h[oh^bfh ihemq_ggh_\h_khijhlb\e_gb_mfgh`blvgZ[Zabkgh_khijhlb\e_gb_

R ''d = r ''d ⋅ R [ = r ''G ⋅

U g2 . Sg

I

Wd\b\Ze_glgh_ Zdlb\gh_ khijhlb\e_gb_ K> ijb ex[hf kdhev`_gbb hlebqghf hl_^bgbpufh`_l[ulvhij_^_e_ghihnhjfme_>@

r^\ (s) =

m i (s) ⋅ cos ϕg , Ii2 (s)

I

i_j_oh^dbf_gh\Zgguf_^bgbpZfhkms_kl\ey_lkyZgZeh]bqghI <IHKLJH?GB?IMKDH >ey Z\lhfZlbabjh\Zggh]h jZkq_lZ ij_^ihqlbl_evg__ _keb f_oZgbq_kdZy oZjZdl_jbklbdZK>aZ^Z_lkyZgZeblbq_kdbf\ujZ`_gb_fKh]eZkgh>@\ujZ`_gb_^ey kj_^g_]hZkbgojhggh]hfhf_glZg_y\ghihexkgh]hK>bf__l\b^ 178

Ijbeh`_gb_

ma =

  1 1 2  1 1  1  τ 'd τ ''d . ⋅ u ⋅  − ⋅ + − ⋅   2 2 2 x ' x 1 ( ' s) x '' x ' 1 ( '' s) + τ ⋅ + τ ⋅ d d d d d d      

I

DZd \b^gh ba I Zkbgojhgguc fhf_gl g_y\ghihexkgh]h K> khklhbl ba ^\mo keZ]Z_fuo i_j\h_ ba dhlhjuo h[mkeh\e_gh baf_g_gb_f h[s_]h ihlhdZ jhlhjZ \ ijh^hevghchkbZ\lhjh_keZ]Z_fh_–baf_g_gb_fihlhdh\jZkk_ygbyf_`^mdhglmjZfb jhlhjZihijh^hevghchkb Ihkljh_ggZyihI f_oZgbq_kdZyoZjZdl_jbklbdZ^eyK>lbiZKL>-8000-2 ij_^klZ\e_gZgZjbkmgd_I

ma

s JbkmghdI–Imkdh\Zyf_oZgbq_kdZyoZjZdl_jbklbdZK>ihZgZeblbq_kdhfm \ujZ`_gbx H^gZdh nZdlbq_kdZy f_oZgbq_kdZy oZjZdl_jbklbdZ g_ khhl\_lkl\m_l ihkljh_gghcih\ujZ`_gbxI Wlhh[tykgy_lkyl_fqlhjhlhjKF\uihegy_lky rbolh\Zgguf gh eZdh\Zy baheypby f_`^m ebklZfb klZeb hlkmlkl\m_l ihwlhfm \ Zkbgojhgghf j_`bf_ \ `_e_a_ jhlhjZ gZ\h^ylky agZqbl_evgu_ \boj_\u_ lhdb kha^Zxsb_ ^hihegbl_evguc Zkbgojhgguc fhf_gl NZdlbq_kdZy f_oZgbq_kdZy oZjZdl_jbklbdZK>lbiZKL>-8000-ijb\_^_gZgZjbkmgd_I

179

Ijbeh`_gb_

3

2.5

2

1.5

ma 1

0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s JbkmghdI–NZdlbq_kdZyimkdh\Zyf_oZgbq_kdZyoZjZdl_jbklbdZK> lbiZKL>-8000-2 <\b^mlh]hqlhimkdh\Zyf_oZgbq_kdZyoZjZdl_jbklbdZihemq_ggZyihI g_ khhl\_lkl\m_l nZdlbq_kdhc ^ey ^Zevg_cr_]h jZkq_lZ [m^_l bkihevah\ZgZ nZdlbq_kdZyf_oZgbq_kdZyoZjZdl_jbklbdZaZ^Z\Z_fZylZ[ebqgh LZd dZd f_oZgbq_kdZy oZjZdl_jbklbdZ ^\b]Zl_ey ijb\h^bfZy \ dZlZeh]_, ij_^iheZ]Z_l bklhqgbd iblZgby [_kdhg_qghc fhsghklb lh iZ^_gb_ gZijy`_gby gZ rbgZo ijb imkd_ g_ mqblu\Z_lky >ey mq_lZ iZ^_gby gZijy`_gby ke_^m_l \\_klb ihijZ\hqgu_dhwnnbpb_gluLZddZdkhijhlb\e_gb_fdZ[_eybrbgfh`ghij_g_[j_qv mqblu\Z_lkylhevdhkhijhlb\e_gb_ljZgknhjfZlhjZGZGIK©KZfZjZªrbguiblZxlky hl lj_oh[fhlhqguo ljZgknhjfZlhjh\ lbiZ L>GL- gZijy`_gb_f dhjhldh]h aZfudZgbyUd
XT Hf khijhlb\e_gb_ljZgknhjfZlhjZijb\_^_ggh_dghfbgZevgufiZjZf_ljZfK>\h_

x T = XT ⋅

Sg , U g2

xT = 0,041.

180

Ijbeh`_gb_

Lh]^Z gZijy`_gb_ gZ klhjhg_ \ukr_]h gZijy`_gby ljZgknhjfZlhjZ ijb ghfbgZevghflhd_klZlhjZ ug = 1 + xT. Ijbf_fgZijy`_gb_ugihklhyggufbg_aZ\bkysbfhlj_`bfZjZ[hluK>Lh]^Z gZijy`_gb_ gZ \\h^Zo ^\b]Zl_ey ijb imkd_ [m^_l baf_gylvky \ khhl\_lkl\bb k \ujZ`_gb_f u = ug – xT⋅Ii(s).

I

LZd dZd Zkbgojhgguc fhf_gl K> ijhihjpbhgZe_g d\Z^jZlm gZijy`_gby k mq_lhf I Zkbgojhgguc fhf_gl ijb gZijy`_gbb gZ \\h^Zo ^\b]Zl_ey g_ jZ\ghf ghfbgZevghfm ma(u) = u2⋅ ma(ug) AgZq_gby Zkbgojhggh]h fhf_glZ ijb imkd_ k mq_lhf iZ^_gby gZijy`_gby gZ ljZgknhjfZlhj_ijb\_^_gu\lZ[ebp_I LZ[ebpZI F_oZgbq_kdZyoZjZdl_jbklbdZK>kmq_lhfk_lb s

1,00

0,90

0,80

0,70

0,60

0,50

0,40

0,30

0,20

0,10

0,05

0,02

Ii

6,93

6,85

6,72

6,6

6,42

6,2

5,92

5,5

4,95

3,95

3,01

1,93

u

0,759 0,762 0,767 0,772 0,779 0,788

0,8

0,817 0,839 0,88 0,918 0,968

ma(ug) 1,76

1,82

1,89

1,95

2,05

2,13

2,21

2,28

2,29

2,14

1,83

1,26

ma(u) 1,01

1,06

1,11

1,16

1,25

1,32

1,41

1,52

1,61

1,66

1,54

1,17

F_oZgbq_kdZy oZjZdl_jbklbdZ gZkhkZ GF-10000- ih >@ ijb\_^_gZ \ lZ[ebp_I LZ[ebpZI F_oZgbq_kdZyoZjZdl_jbklbdZgZkhkZGF-10000-210 s mc

1,00

0,90

0,80

0,70

0,60

0,50

0,40

0,30

0,20

0,10

0,05

0,02

0,190 0,120 0,087 0,092 0,149 0,230 0,330 0,442 0,572 0,727 0,811 0,865

NZdlbq_kdZy f_oZgbq_kdZy oZjZdl_jbklbdZ ^\b]Zl_ey f_oZgbq_kdZy oZjZdl_jbklbdZ gZkhkZ b kh\f_klgZy f_oZgbq_kdZy oZjZdl_jbklbdZ ij_^klZ\e_gu gZ jbkmgd_I

181

Ijbeh`_gb_

3

2.5

ma 2

1.5

m md 1

0.5

mc 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s JbkmghdI–Kh\f_klgZyf_oZgbq_kdZyoZjZdl_jbklbdZgZkhkgh]hZ]j_]ZlZ <IHKLJH?GB?DJB
Md = J ⋅ ]^_

dω , dt

dω , dt

I

Md –^bgZfbq_kdbcfhf_gl J –fhf_glbg_jpbbgZkhkgh]hZ]j_]ZlZ dω/dt –ijbjZs_gb_kdhjhklbih^^_ckl\b_f^bgZfbq_kdh]hfhf_glZ

Ijbgy\\I

τj = J ⋅ ]^_

ω0 , Mg

τj –f_oZgbq_kdZyihklhyggZy\j_f_gbgZkhkgh]hZ]j_]ZlZk ω0 –kbgojhggZykdhjhklv^\b]Zl_eyk-1; Mg –ghfbgZevgucfhf_gl^\b]Zl_eyG⋅f

ihemqbf

182

I1.24)

Ijbeh`_gb_

m d = −τ j ⋅

ds , dt

>eyhij_^_e_gby\j_f_gbimkdZgZkhkgh]hZ]j_]ZlZg_h[oh^bfh\uqbkeblv 0

ds . m d 1

t i = −τ M ⋅ ∫

LZd dZd nmgdpbhgZevgZy aZ\bkbfhklv md hl kdhev`_gby g_ba\_klgZ bgl_]jbjh\Zgb_aZf_gy_lkykmffbjh\Zgb_f

t i = −τ M ⋅ ∑ i

s dL − s gL , m di

I

]^_ sdL b VgL – khhl\_lkl\_ggh dhg_qgh_ b gZqZevgh_ agZq_gby kdhev`_gby gZ L-f mqZkld_f_oZgbq_kdhcoZjZdl_jbklbdb mdi –kj_^g__agZq_gb_^bgZfbq_kdh]hfhf_glZgZwlhfmqZkld_ >ey ihkljh_gby djb\hc jZa]hgZ ba kmffu \ \ujZ`_gbb I g_h[oh^bfh\u^_eblv hl^_evgu_keZ]Z_fu_–bgl_j\Zeu\j_f_gb

∆t i = τ j ⋅

si−1 − si . 0,5 ⋅ (m di−1 + m di )

I1.26)

GZihemq_gguoihI bgl_j\ZeZo\j_f_gbijbihkljh_gbbdjb\hcjZa]hgZ mkdhj_gb_ ijbgbfZ_lky ihklhygguf ijb ^hklZlhqgh [hevrhf dhebq_kl\_ lZdbo mqZkldh\\f_klhehfZghcebgbbihemqZ_lkyieZ\gZydjb\Zy 350

k-1 300

250

200

ω 150

100

50

0

0.5

1

1.5

t

2

JbkmghdI–Djb\ZyjZa]hgZgZkhkgh]hZ]j_]ZlZ

k

2.5

183

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1

2

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4

5

6

7

8

9

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Информационно-аналитические системы магистральных трубопроводов

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