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Turbo machines
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VTU
Mechanical Engineering
5 Semester
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Turbo Machines [10ME56]
2010 Scheme
Branch Name: Mechanical Engineering SEM: 5 University: VTU Syllabus: 2010 Table of Contents: Turbo Machines (10ME56)
Sl. No. Units 1 Introduction 2 Thermodynamics of fluid flow 3 Energy exchange in Turbomachines 4 General Analysis of Turbomachines 5 Steam Turbines 6 Hydraulic Turbines 7 Centrifugal Pumps 8 (a)Centrifugal Compressors
(b)Axial flow compressors Download notes for other subjects from the link below: www.studyeasy.in
T&C - All rights reserved-studyeasy.in - 2014
ENIHCAMOBRUT ]65EM01[
egaP 1
SENIHCAM OBRUT :edoC tcejbuS 65EM01 52 :skraM AI
:keeW/sruoH 40 30 :sruoH maxE :sruoH latoT 25 001 :skraM maxE
TRAP - A TINU -1
:noitcudortnI ,enihcam obrut fo noitinifeD ,senihcam obrut fo strap htiw nosirapmoC,noitacifissalC ,senihcam tnemecalpsid evitisop rieht dna sretemarap sselnoisnemiD
sdlonyeR fo tceffE ,ecnacifingis .seiduts ledom ,seititnauq cificeps dna tinU ,rebmundna tsrif fo noitacilppA reht fo swal dnoces fo seicneiciffE ,senihcam obrut ot scimanydom
senihcam obrut smelborP . sruoH 70
TINU 2 :wolf diulf fo scimanydomrehT setats noitangatS dna citatS - erpmocnI dna sdiulf elbiss
,sesag tcefrep rieht( ycneiciffe egats ,ycneiciffe ciportnesi llarevO )nosirapmoc dnanoisnapxe dna noisserpmoc htob rof ycneiciffe cihportylop rof rotcaf taeheR .sessecorp
.ssecorp noisnapxe sruoH 70
TINU 3 :senihcamobruT ni egnahcxe ygrenE etanretlA ,noitauqe enibrut sreluE sreluE fo mrof
rof selgnairt yticoleV ,noitauqe enibrut fo seulav tnereffid fo stnenopmoC ,noitcaer fo eerged,noitcaeR fo eergeD ,refsnart ygrene noitcaer fo eerged neewteb noitaleR ,rotcaf noitazilitu
,rotcaf noitazilitU dna .smelborP sruoH 60
TINU 4 :senihcamobruT fo sisylanA lareneG wolf laidaR spmup dna srosserpmoc lareneg
,selgnairt yticolev ,noitcaer fo eerged rof noisserpxE ,sisylana elgna egrahcsid edalb fo tceffE,noitcaer fo eerged dna refsnart ygrene no ,ecnamrofrep no elgna egrahcsid edalb fo tceffE
daeh laciteroehT yticapac snoitaler dna spmup wolf laixa fo sisylana lareneG ,piheerged ,srosserpmoc .smelborP ,selgnairt yticolev ,noitcaer fo
sruoH 60 TRAP B
TINU 5 :senibruT maetS rof noitidnoc ,enibrut eslupmi egats elgniS ,noitacifissalC edalb mumixam
,ycneiciffe egats ,ycneiciffe fo sdohtem dna deeN itluM ,gnidnuopmoc - ,enibrut eslupmi egatsmumixam rof noisserpxe enibrut noitcaeR ,rotcaf noitazilitu noitidnoc ,enibrut ssnosraP
rof .smelborP .gnigats noitcaer ,rotcaf noitazilitu mumixam sruoH 70
TINU 6 :senibruT ciluardyH ssalC enibrut notleP ,seicneiciffe tnereffiD ,noitacifi yticolev
ixaM ,sretemarap ngised ,selgnairt enibrut sicnarF .ycneiciffe mum - ngised ,selgnairt yticolevedalb tnereffid rof sepahs rennur ,sretemarap sebut tfarD .sdeeps - .snoitcnuf dna sepyT
porP dna nalpaK senibrut relle - .smelborP .sretemarap ngised ,selgnairt yticolev sruoH 70
TINU 7 :spmuP lagufirtneC tnereffid ,pmup lagufirtnec fo strap dna noitacifissalC dna sdaeh
eht gnitrats rof deeps muminiM ,pmup lagufirtnec fo seicneiciffe l noitcus mumixaM ,wolf ,tfi ,daeh noitcus evitisop teN snoitativaC rof deeN , .lellarap dna seires ni spmuP ,gnimirp
.smelborP sruoH 60
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ENIHCAMOBRUT ]65EM01[
egaP 2
TINU 8 :srosserpmoC lagufirtneC tupni rewop ,rotcaf pils ,selgnairt yticolev egatS egatS ,rotcaf
fe egats ,depoleved erusserP ,krow dna gnigrus dna ycneicif .smelborp srosserpmoC wolf laixA ,egats a ni depoleved oitar erusserp rof noisserpxE : enod krow
.smelborP .gnillats dna seicneiciffe ,rotcaf sruoH 60
( :etoN ,tcejbus scinahceM diulF ni derevoc si sisylana lanoisnemid ecniS no snoitseuqlanoisnemid ,revewoH .nevig eb ton yam sisylana lanoisnemid ledom dna sretemarap
erom nevig eb yam seiduts ega thgiew .)
:SKOOB TXET .1 noisrevnoC ygrenE ot noitcudortnI nA ,yrenihcamobruT ,III emuloV , V dna ibmadaK .
egA weN ,dasarP rahonaM nI .8002 tnirper ,srehsilbuP lanoitanret .2 snaF & srosserpmoC ,senibruT ,noitide dn2 ,.dtL .oClliH warGcM ataT ,ayhaY .M .S ,
2002 :SKOOB ECNEREFER
.1 senihcamobruT fo slapicnirP nallimcaM ehT ,drehpehS .G .D , .)4691( ynapmoC
.2 & scinahceM diulF senihcamobruT fo scimanydomrehT .)5002( reiveslE ,noxiD.L .S ,
.3 enihcamobruT .9002 ihleD weN ,IHP annakneV.K.B ,
.4 ,senihcamobruT fo kooB txeT .M .M ,jaragaN.M .A dna aduogdnivoG .S .M.8002 ,dE hT4 ,snoitacilbuP
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ENIHCAMOBRUT ]65EM01[
egaP 3
STNETNOC
.1 noitcudortnI 4 31
.2 wolf diulf fo scimanydomrehT 41 - 42
.3 obruT ni egnahcxe ygrenE senihcam 52 - 33
.4 obruT fo sisylanA lareneG senihcam 43 - 34
.5 senibruT maetS 44 - 25
.6 senibruT ciluardyH 35 - 46
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ENIHCAMOBRUT ]65EM01[
egaP 4
1 :TINU
NOITCUDORTNI
enihcam obruT a fo noitinifeD
A diulf gniwolf a neewteb srucco refsnart ygrene hcihw ni ecived a si enihcam obrut
dna erusserp fo egnahc ni stluser sihT .noitca cimanyd ot eud tnemele gnitator dna
.diulf eht fo mutnemom
enihcam obrut a fo straP
.1.1 :giF ssorc citamehcS - lanoitces eht fo strap lapicnirp eht gniwohs enibrut a fo weiv .enihcamobrut
:era enihcam obrut a fo stnenopmoc elpicnirp ehT
.1 tnemele gnitatoR )sedalb ro rellepmi ,enav( .diulf fo maerts a ni gnitarepo
.2 stnemele yranoitatS ni diulf eht ediug yllausu hcihw tneiciffe rof noitcerid reporp
.ssecorp noisrevnoc ygrene
.3 tfahS cimanyd rednu diulf morf rewop tuptuo sekat ro rewop tupni sevig rehtie sihT
.deeps deriuqer ta snur dna snoitidnoc
.4 gnisuoH as segassap rehto dna yrenoitats ,gnitator suoirav peek ot cimanyd rednu ylef
.diulf gniwolf eht fo snoitidnoc
.strap enibrut notleP dna strap enibrut maetS .g.E
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ENIHCAMOBRUT ]65EM01[
egaP 5
senihcam obrut fo noitacifissalC
refsnart ygrene no desaB.1
rotor eht ot diulf yb nevig si ygrenE)a - .g.E enihcam obrut gnitareneg rewoPsenibruT
diulf eht ot rotor eht yb nevig ygrenE)b enihcam obrut gnibrosba rewoP
srosserpmoc dna srewolb ,spmuP .g.E)c
enihcam obrut ni gniwolf diulf no desaB.2
retaW)a
riA)b
maetS)c
sesag toH)d
.cte lortep ekil sdiuqiL)e
orht wolf fo noitcerid no desaB.3 ot ecnerefer htiw ,sedalb ro senav ro rellepmi eht hgunoitator tfahs fo sixa eht
wolf laixA)a enibrut ro rosserpmoc ,pmup laixA
wolf dexiM)b enibrut sicnarF ,pmup wolf dexiM
wolf laidaR)c rosserpmoc ro pmup lagufirtneC
wolf laitnegnaT)d notleP enibrut retaw
enihcam obrut ni diulf fo noitidnoc no desaB.4
enibrut retaw notleP .g.E )erusserp tnatsnoc( epyt eslupmI)a
enibrut noitcaer sicnarF .g.E )erusserp elbairav( epyt noitcaeR)b s
tfahs gnitator fo noitisop no desaB.5
tfahs latnoziroH)a tS senibrut mae
tfahs lacitreV)b senibrut retaw nalpaK
tfahs denilcnI)c orcim blub nredoM
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ENIHCAMOBRUT ]65EM01[
egaP 6
dna senihcam tnemecalpsid evitisop neewteb nosirapmoC senihcam obruT
dna senihcam tnemecalpsid evitisop neewteb nosirapmoC senihcam obruT
senihcam obruT P senihcam tnemecalpsid evitiso x tI cimanyD & cimanydomrehT setaerc ,diulf gniwolf & tnemele gnitator w/b noitca dna erusserp fi ecalp sekat refsnart ygrene
segnahc mutnemom
& cimanydomrehT setaerc tI lacinahceM w/b noitca rebmem gnivom & citats ,diulf
ecalp sekat refsnart ygrene tnemecalpsid htiwdiulf fo x gnitator & diulf fo wolf ydaets a sevlovni tI
tnemele lacinahcem fo noitom & diulf fo wolf ydaetsnu a sevlovni tI
noitom gnitacorpicer x yehT deeps lanoitator hgih ta etarepo yehT deeps wol ta etarepo x fo egnahC sesuac wolf diulf gnirud esahpmelborp suoires enihcamobrut ni s
fo egnahC sesuac wolf diulf gnirud esahp ni smelborp ssel tnemecalpsid evitisoP
senihcam x ycneiciffE ssel yllausu si ycneiciffE rehgih si x ni elpmis si tI ngised ngised ni xelpmoc si tI x era smelborp noitarbiv noitom yrator ot euDssel
noitarbiv noitom gnitacorpicer ot euDerom era smelborp
maetS ,senibrut saG ,senibrut ciluardyH .g.E .cte senibrut
ria gnitacorpiceR ,senigne C.I .g.E.cte spmup ,rosserpmoc
rebmuN sdlonyeR fo tceffE rotcaf ssol eht ,rebmun sdlonyeR gnisaerced htiw ,noitcirf htiw sepip ni wolf ekil tsuJ
neht ,ylwols tsrif ta sesaercni .senihcam obruT ni yldipar erom dna erom
ets ,ria ,retaw gnildnah( ,senihcam obrut yranidro fo ytirojam ehT dnuof era )sag ro ma
.noiger hguor ylluf ni etarepo ot
eht htiw seirav ,hguor ylluf semoceb wolf eht hcihw ta ,rebmun sdlonyeR lacitirc ehT
sdneped ti( enihcam eht fo ezis nevig a rof noitacol tcaxe sti dna )ssenhguor evitaler no
ot tluciffid si enihcam .tciderp
ssol ni ecnatropmi fo si noitarapes sti dna reyal yradnuob fo gnidnatsrednu ehT
.stceffe
lagufirtnec ezis etaredom a fo ycneiciffe dna daeh ni rotcaf ssol eht swohs hparg ehT
pmup
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ENIHCAMOBRUT ]65EM01[
egaP 7
seititnauQ tinU
rednu era hcihw deeps tinu dna rewop tinu ,wolf tinu era seititnauq tinU tinu eht ,sdrow rehto nI .senibrut ciluardyh htiw noitcennoc ni retem tinu fo snoitaredisnoc
.m1 fo daeh eht rof denifed era seititnauq
)a( :wolf tinU wolf tinU m1 fo wolf eht si 3 taht s/ elihw enihcamobrut eht hguorht srucco.m1 fo daeh a rednu gnikrow
yb nevig si enibrut a hguorht egrahcsid eht t.k.W =
tnatsnoc si enibrut a rof wolf fo aera eht ecniS
= 2
=
,m1=H nehW Q=Q ,u noitauqe evoba ni noitidnoc eseht gnitutsbus
= 1
nehT =
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ENIHCAMOBRUT ]65EM01[
egaP 8
=
)b( :deepS tinU .daeh tinu a rednu gnikrow enibrut eht fo deepS
,yb nevig si senav eht fo yticolev larehpirep eht t.k.W
= 2
oslA
=
06
gnirapmoC snoitauqe owt evoba
=
,m1=H nehW U=U ,u noitauqe evoba ni noitidnoc eseht gnitutsbus
= 1
= nehT
=
)c( rewoP tinU : .daeh tinu a rednu gnikrow enibrut eht yb depoleved rewop ehT
si enibrut eht fo ycneiciffe llarevo eht t.k.W ,yb nevig
=
0001
=
0001
3/2
= 3/2 ,m1=H nehW P= , noitauqe evoba ni noitidnoc eseht gnitutsbus
= 13/2
= = 3/2
nehT
=
3/2
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ENIHCAMOBRUT ]65EM01[
egaP 9
ecnacifingis rieht dna spuorg sselnoisnemiD
ehT rof srewolb ro snaf ,senibrut retaw ,spmup ekil enihcamobrut a fo ecnamrofreP
eb nac wolf elbisserpmocni :fo noitcnuf a sa desserpxe
)i( D diulf eht fo ytisne
N rotor eht fo deepS )ii(
D retemaid citsiretcarahC )iii(
Q egrahcsiD )vi(
Hg( daeh ytivarG )v( )
dna P depoleved rewoP )iv(
. ytisocsiV )iiv(
.ecnacifingis rieht nialpxe dna spuorg sselnoisnemid niatbO
noituloS meroeht p mahgnikcuB gnisU
[ f = enihcamobruT ] ,P ,Hg ,Q ,D ,N , ecnamrofreP
rehto htiw gnipuorg dna selbairav gnitaeper sa D ,N gnikaT lanoisnemid non sa selbairavspuorg
1 = [1, 1, 1, ]
2 = [2, 2, 2, ]
3 = [3, 3, 3, ]
4 = [4, 4, 4, ]
1 =
3
2 =
22
3 =
35
4 =
2
esu nac ew ,senihcamobrut ralimis rof seiduts ledom roF
1131
= 2
232
12121
=2
2222
113151
=2
23252
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ENIHCAMOBRUT ]65EM01[
egaP 01
11121
=2
2222
lanoisnemiD noN fo ecnacifingiS spuorG
.1 tneiciffeoc yticapac ro tneiciffeoc egrahcsiD
1 =
3 C = 1 senihcam obruT ralimis rof tneiciffeoc wolf ro tneiciffeoc yticapac si .
1 =
3
2
3
= =
2
4
1 =
=
1
erehW =oitar deeps dellac si
.dexif si oitar deeps ,enihcam obrut revig yna roF
ta gninnur retemaid niatrec fo naf ro pmup nevig a roF si egrahcsid eht sdeeps suoirav
.deeps si lanoitroporp
.2 tneiciffeoc daeH
2 =
22 tneiciffeoc daeh dellac sI .
2 =
22=
U2i. e U DN
ro spmup fo epyt emas rof ralimis eb lliw tneiciffeoc daeh taht swohs oitar evoba ehT
.rotor eht fo deeps laitnegnat eht fo erauqs sa seirav daeh dna ezis rellepmi nevig rof senibrut
.3 tneiciffeoc rewoP
3 =
35 i s .rewop cificepS ro tneiciffeoc rewop dellac
eht fo ebuc eht ot lanoitroporp yltcerid si rewop eht ,enibrut retaw a ro pmup nevig a roF
.rennur fo deeps
DEEPS CIFICEPS srosserpmoc dna srewolb ,snaf ,spmuP
( deepS cificepS aerg fo mret sselnoisnemid a si ) dna srewolb ,snaf ,spmup ni ecnatropmi t
srosserpmoc
erehW 5 =(1)1/2
(2)3/4=
1/2
(3)1/2
(22)3/4
( )3/4=
1/2
( )3/4
,sa desserpxe eb osla nac sihT
=
3/4
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ENIHCAMOBRUT ]65EM01[
egaP 11
deeps cificeps eht si noitauqe evoba ehT a sa denifed si tI .pmup a rof noitauqe
m 1 gnigrahcsid enihcam ralimis yllacirtemoeg a fo deeps 3 m1 fo daeh a rednu retaw fo s/
enibruT a fo deepS cificepS
( enibrut a fo deeps cificeps ehT tneiciffeoc daeh fo noitanibmoc eht yb deniatbo si )
rewop dna sa tneiciffeoc .swollof
6 =(3)
1/2
(2)5/4=
1/2
(35)1/2
(22)5/4
( )5/4=
1/2
1/2( )5/4
mret eht ,diulf elbisserpmocni eht rof tuB1
1/2( )5/4 si tnatsnoc sa ffo deppord
semoceb deeps cificeps eht nehT
=
5/4
evoba ehT deeps cificeps eht si noitauqe a sa denifed si tI .enibrut a eof noitauqe
m1 fo daeh a rednu rewop WK 1 secudorp hcihw enihcam ralimis yllacirtemoeg a fo deeps
senihcaM obruT ot swaL dnoceS dna tsriF fo noitacilppA
ygrene wolf ydaetS 2.1 giF enihcam obrut ni ssecorp
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ENIHCAMOBRUT ]65EM01[
egaP 21
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ENIHCAMOBRUT ]65EM01[
egaP 31
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ENIHCAMOBRUT ]65EM01[
egaP 41
TINU : 2
DIULF FO SCIMANYDOMREHT WOLF
setats noitangatS dna citatS
obruT nI .sdiulf elbisserpmocni dna elbisserpmoc fo esu eht evlovni senihcam
seiticolev htiw evom diulf sMT elbisserpmoc nI .snoitacol ynam ta eno hcaM naht erom
eht fo .E.P dna .E.K ,revewoh ,wol yllareneg era seiticolev diulf eht sMT elbisserpmocni
oitauqe etalumrof oT detcelgen eb tonnac dna egral yrev era diulf gnivom lautca no desab sn
eht fo etats swal no desab diulf .desu era setats owt scimanydomreht fo
.setats noitangats dna etats citats era setats ehT
etatS citatS
derusaem eht ,diulf eht ot tcepser htiw citats si tnemurtsni gnirusaem eht fI si ytitnauq
dluoc ytreporp citats derusaem ehT .ytreporp citats sa nwonk eb colev ,erusserp yti
.cte yplahtne ,erutarepmet a yb dexif elcitrap eht fo etats ehT dellac si seitreporp citats fo tes
.etats citats
etatS noitangatS
krow ciportnesi ,suoititcif a fo etats lanimret eht sa denifed si tI - ydaets dna eerf wolf
irud ssecorp elcitrap diulf eht fo .E.K dna .E.P cipocsorcam lanif eht hcihw gn ecuder era ot d
.orez
si ssecorp laer on esuaceb etats noitangats ot dael ton seod ssecorp laeR .ciportnesi
laer eht hcihw tsniaga eulav laedi edivorp segnahc ytreporp noitangatS ep enihcam ecnamrofr
noitangats niatbo ot elbissop si tI .derapmoc eb nac yb seitreporp citats fo smret ni seitreporp
.etats noitangats fo noitinifed eht gnisu rp wolf ydaets eht redisnoC tsrif eht yb nevig sseco
fo wal .scimanydomreht
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ENIHCAMOBRUT ]65EM01[
egaP 51
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ENIHCAMOBRUT ]65EM01[
egaP 61
obruT fo seicneiciffE senihcam :
yb nevig si enihcamobrut a fo ycneiciffE
=
erehW
= ycneiciffe citabaidA = ycneiciffe lacinahceM
%001 tsomla erA ? h eht morf detaluclac eb nac MT a fo ycneiciffe citabaida ehT -s htob rof margaid eht
gnisu laedi ehT .ssecorp noisserpmoc dna noisnapxe krow gnisu eb nac tuptuo ro tupni rehtie
.setats noitangats ro citats
)a( obruT gnitareneG rewoP )MTGP( senihcam
MTGP rof tuptuo krow lautcA = 10 20
si noitauqe reporp ehT .noitseuq ni enihcamobruT fo snoitidnoc eht yb denimreted
rof desu si eK tixe dna elbigilgen si eK telni eht fi enibrut a ni elpmaxe roF fo noitcudorp
si noitinifed latot ot citats neht ,esle erehwemos ygrene lacinahcem tixe eht fI .desu Ke si
.desu si noitinifed citats ot citats neht detsaw
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ENIHCAMOBRUT ]65EM01[
egaP 71
)b( obruT gnibrosbA rewoP )MTAP( senihcam
MTAP rof tupni krow lautcA = 20 10
ycneiciffe egats etiniF
.1 .egats etinif a si pord erusserp etinif a htiw egats A
.2 itlum a nI - eht htiw gnola enibrut egats fo seicneiciffe eht ycneiciffe ciportnesi llarevo
.tnatropmi era segats laudividni
.3 llarevo eht tceffe cimanydomreht detaicossa dna pord erusserp egral fo tnuocca nO
fo ecnamrofrep ciluardyh ro cimanydorea fo xedni eurt a ton si ycneiciffe ciportnesi
ihcam .en
.4 h fo snoiger tnereffid ni detacol pord erusserp emas eht htiw segats tnereffiD - enalp s
tuptuo krow fo seulav tnereffid evig lliw .
)senibruT( taeheR fo tceffE
.gif ni nwohs sa setats owt neewteb segats fo srebmun ruof redisnoC eht taht demussa si tI
emas era ycneiciffe egats dna oitar erusserp segats ruof eht lla rof . 1
=
=
=2
= ------- 1
ycneiciffe llarevO = =
si 2 etats ot 1 etats morf noisnapxe gnirud krow lautca ehT
= 2
fo seulav ehT era segats eht ni krow ciportnesi ro laedi 1, 2, 3, 4
era segats eseht ni enod krow lautca fo seulav latot ehT
= = ( 1 + 2 + 3 + 4) 3
= 2
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ENIHCAMOBRUT ]65EM01[
egaP 81
& 2 noitauqe morF 3 noitauqe
fo epols ehT h no senil erusserp tnatsnoc - yb nevig si enalp s
(
) = 5
thgir eht sdrawot egrevid tsum senil erusserp tnatsnoc taht swohs noitauqe evoba ehT ? 4=1
> 1 6 laudividni eht naht retaerg enibrut eht fo ycneiciffe llarevo eht sekam sihT seicneiciffe egats
>
ytitnauq sihT
4=1
eno naht retaerg syawla si dna rotcaf taeher sa nwonk si
tnatsnoc gnirud yplahtne desaercni sa sessol egats fo ecnaraeppaer eht ot eud si taeheR.ssecorp gnitaeh erusserp
=
> 1
ycneiciffe ciportyloP ro ycneiciffe egats lamisetinifnI )senibruT( x llams fo tpecnoc eht egats a fo ecnamrofrep cimanydorea eurt eht niatbo oT rodesu si egats lamisetinifni x erofereht si dna pord erusserp lamisetinifni htiw egats yranigami na si sihT
epedni tceffe taeher fo tnedn
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ENIHCAMOBRUT ]65EM01[
egaP 91
x serusserp neewteb egats llams a swohs .giF p dna p- pd si egats siht fo ycneiciffe ehT
=
=
Td
Td s
ciportnesi lamisetinifni roF noisnapxe
dnoyeb smret gnitcelgen dna noisserpxe laimonoib gnisu .s.h.r no smret eht gnidnapxEdnoces
2 dna 1 stimil neewteb 2.qe eht gnitargetnI
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ENIHCAMOBRUT ]65EM01[
egaP 02
a ot tnelaviuqe sa deredisnoc eb nac ssecorp noisnapxe )lautca( citabaida elbisreverri ehT
ciportylop .n xedni htiw ssecorp
si ssecorp lautca ni noisnapxe fo xedni ehT
nehW p ,1= =n ycneiciffe ehT .noisnapxe ciportnesi eht htiw sedicnioc enil noisnapxe eht
seulav citats gnikaT .ycneiciffe egats llams fo smret ni desserpxe eb won nac egats etinif a fo
fo T dna p sag tcefrep gnimussa dna
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ENIHCAMOBRUT ]65EM01[
egaP 12
htiw sessecorp noisnapxe etinif suoirav fo seicneiciffe eht evig nac 8 dna 7 snoitauqE
ycneiciffe egats llams dna oitar erusserp fo seulav tnereffid
)rosserpmoC( ycneiciffe egats etiniF x etinif a htiw rosserpmoc A egats etinif a sa nwonk si esir erusserp x oitar erusserp dna erutarepmet laitini fo noitcnuf a si krow egatS x rehgih htiw krow fo eulav rehgih a seriuqer egats a ,oitar erusserp emas eht roFerutarepmet x oiger erutarepmet rehgih eht ni segats rosserpmoc suhT siht fo tnuocca no reffus n
rosserpmoc egatsitlum fo ycneiciffe eht no tceffe evitalumuc a evah srotcaf evoba ehT
)rosserpmoC( taeherp fo tceffE
eht evah segats eht lla taht demussa si tI .nwohs sa segats ruof htiw rosserpmoc a redisnoC
seicneiciffe emas .soitar erusserp dna
si s2 ot 1 etats morf krow ciportnesi latot ehT era segats laudividni eht ni skrow ciportnesi ehT 1, 2, 3, 4
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ENIHCAMOBRUT ]65EM01[
egaP 22
si rosserpmoc eht fo ycneiciffe llarevo ehT =WS
Wa
eht fo ycneiciffe llarevo eht sekam sihT ycneiciffe egats naht rellams rosserpmoc
<
rp dellac tceffe cimanydomreht eht ot eud si sihT - (detaeh yllanoitnetni ton si sag eht gnitaeh
hcae fo dne eht ta )detaeherp ehT.egats noisserpmoc erusserp tnatsnoc llams ni taeherp
na sniamer llits ssecorp noisserpmoc eht dna anemonehp lanretni na ylno si sessecorp
.ssecorp citabaida
)rosserpmoC( ycneiciffE ciportyloP ro lamisetinifnI x s fo rebmun etinifni fo pu edam eb nac egats rosserpmoc etinif A segats llam x ycneiciffe na evah segats lamisetinifni eseht fo hcaE lamisetinifni ro ycneiciffeycneiciffe egats x cimanydorea eht erofereht si dna tceffe cimanydomreht fo tnednepedni si tI
rosserpmoc eht fo ecnamrofrep x c si ria hcihw ni egats a redisnoC na swohs osla tI .2 etats ot 1 etats morf desserpmoserusserp neewteb gnitarepo egats etinifni +
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ENIHCAMOBRUT ]65EM01[
egaP 32
1 noitauqe otni sTd fo eulav eht gnitutitsbuS
2 ot 1 etats neewteb 2.qe gnitargetnI
citabaida elbisreverri eht gnimussA htiw ssecorp ciportylop a ot tnelaviuqe sa noisserpmoc
sa nettirw eb nac 3 noitauqe ,n xedni
lautca ehT .ycneiciffe egats llams ot detaler eb nac egats rosserpmoc etinif fo ycneiciffe ehT
yb nevig si esir erutarepmet
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ENIHCAMOBRUT ]65EM01[
egaP 42
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ENIHCAMOBRUT ]65EM01[
egaP 52
:TINU 3
MOBRUT NI EGNAHCXE YGRENE SENIHCA
noitauqe enibrut sreluE
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ENIHCAMOBRUT ]65EM01[
egaP 62
ralugna ehT .MT lareneg a fo tixe dna yrtne ta selgnairt yticolev eht swohs erugif evoba ehT
si rotor eht fo yticolev ces/dar yb nevig si dna
=2
06 1
retemaid eht ot gnidnopserroc tixe dna yrtne eht ta edalb eht fo yticolev larehpirep ehT
1 2 yb nevig era
1 =1
06 2
2 =2
06 3
V dna u ,V rotcev yticolev eerht ehT r noitauqe rotcev elpmis a yb detaler era noitces eht ta
= + 4
evah ew emit tinu ni gnivael dna gniretne diulf eht fo ssam tinu gniredisnoC
telni eht fo mutnemom ralugnA = 1 1 5
ylralimiS
teltuo eht fo mutnemom ralugnA = 2 2 6
egnahc fo etar = decudorp euqroT mutnemom ralugnA fo
= { ralugnA mutnemom ta telni } { ralugnA mutnemom ta teltuo }
= (11) (22) 7
yb nevig si enod krow eht eroferehT
=
= (11 22)
= [1(1) 2(2)]
= 1 2
061 2
2
062
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ENIHCAMOBRUT ]65EM01[
egaP 72
= 11
06
22
06
= [11 22] 8
sa nwonk si 8 noitauqE noitauqe enibrut sreluE
etanretlA noitauqe enibrut sreluE fo mrof
selgnairT yticoleV teltuO dna telnI
selgnairt yticolev ot gnirrefeR
1 2 ,telnI teltuo
)senav rotor eht gniretne erofeb( telni ta diulf eht fo yticolev etulosbA = 1V
telni rotor ta diulf eht fo yticolev evitaleR = 1rV
yticolev etulosba fo tnenopmoc laitnegnaT = 1uV
RO
telni ta yticolev fo tnenopmoc lrihW
losba fo tnenopmoc wolF = 1fV telni ta yticolev etu
telni ta yticolev evitaler fo tnenopmoc lrihW = 1urV
telni ta yticolev enav rotor raeniL = 1U
1 telni ta elgna tej etulosbA =
1 telni ta elgna )edalb( enaV =
elgnairt yticolev teltuo ot gnirrefeR
2 teltuO
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ENIHCAMOBRUT ]65EM01[
egaP 82
o yticolev etulosbA = 2V rotor eht gnivael retfa teltuo ta diulf eht f .senav
evael ot tuoba tsuJ( teltuo rotor diulf eht fo yticolev evitaleR = 2rV )rotor eht
teltuo ta yticolev etulosba fo tnenopmoc lrihW = 2uV
teltuo ta yticolev etulosba fo tnenopmoc wolF = 2fV
moc lrihW = 2urV teltuo ta yticolev evitaler fo tnenop
teltuo ta yticolev rotor raeniL = 2U
1 )noitator leehw fo noitcerid eht oT( teltuo ta elgna tej ro diulF =
1 )noitator leehw fo noitcerid eht oT( teltuo ta elgna )edalb( enaV =
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ENIHCAMOBRUT ]65EM01[
egaP 92
ygrene fo stnenopmoC refsnart
.1
m ni ygrene citenik etulosba ni egnahc si 2 s/ 2 gk/mN ro
.2
rotor ni egnahc erusserp citats sa tlef diulf fo ygrene lagufirtnec ni egnahc si
m ni sedalb 2 s/ 2 gk/mN ro
.3
yticolev evitaler ni egnahc sI erp citats sa tlef ygrene rotor ni egnahc eruss
ni sedalb gk/mN ro 2s/2m
:2 ESAC
V fI 2u si ev
V = gk/DW = E 1u U 1 V + 2u U2 )erom eb lliw enod kroW(
= 1
2 22
2 +
12 2
2
2 +
22 1
2
2
:3 ESAC
V fI 2u 0 =
ni desu ylnommoc teltuo ta lrihw oN senibrut yticapac hgih
V( = gk/DW = E 1u U1 ylno gk/mN )
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ENIHCAMOBRUT ]65EM01[
egaP 03
R noitcaeR fo eergeD
ot eud refsnarT ygrenE fo oitar eht si R noitcaeR fo eergeD ot egnahc yplahtnE citatS
latoT ot eud refsnarT ygrenE latoT .rotor a ni egnahc yplahtnE
=
=
citatS yplahtne egnahc
latoT yplahtne egnahc=
h
h0
h =1
2 22
2+
22 1
2
2
h0 = 1
2 22
2 +
12 2
2
2 +
22 1
2
2
=1
2 22 + 2
2 12
12 2
2 + 12 2
2 + 22 1
2
gnikaT
1
222
2 + 2
2 12
2 = citatS dna tnenopmoc
122
2
2= . )seigrene egnahc yticolev etulosbA( tnenopmoC ygrenE citeniK
=
+ =
1
1 +
+ 1 =
1
=
1
1 =
1
=
1
rotor yb tlef ygrene citatS = S nehW
dna 1V fo smret ni( rotor ni egnahc ygrene citeniK = EK )seiticolev etulosbA ,2V
elgnA egrahcsiD edalB fo tceffE no R noitcaeR fo eergeD dna E refsnarT ygrenE
si 2 ,telni si 1 erehw ,erugif ni nwohs sa enihcam obrut wolf laidar drawtuo na redisnoC
teltuo
snoitpmussA
,tnatsnoc si wolf fo yticolev laidaR)1 .e.i
V 1f V = 2f V = f
telni ta tnenopmoc lrihw oN)2
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ENIHCAMOBRUT ]65EM01[
egaP 13
V 1u 0 =
.e.i ,telni ta sa eciwt si teltuo ta retemaiD)3
D 2 D2 = 1 U ro 2 U2 = 1
telni ta elgna edalB)4 54 =0 V , 1 V = 1f U = 1
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ENIHCAMOBRUT ]65EM01[
egaP 23
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ENIHCAMOBRUT ]65EM01[
egaP 33
R noitcaeR fo eergeD
suoirav rof teltuo ta elgnairt yticolev morF
.1 b nehW 2 09 < 0 enav sevruc drawkcab
V 2u U < 2
5.0 > 1 < R
.2 b sedalb laidaR roF 2 09 = 0
V 2u U = 2
1 = R 5.0 =
.3 b senav devruc drawrof roF 2 09 > 0
V 2u U > 2
5.0 < R
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ENIHCAMOBRUT ]65EM01[
egaP 43
4 :TINU
SENIHCAMOBRUT FO SISYLANA LARENEG
spmup dna srosserpmoc wolf laixA
obrut gnibrosba rewop era spmup dna srosserpmoc wolf laixA esehT .senihcam
laixA .diulf gniwolf eht fo yplahtne eht esaercni ybereht dna rewop lanretxe brosba senihcam
obrut wolf rapmoc diulf fo ytitnauq egral esu senihcam fo epyt lagufirtnec dna dexim ot de
obrut obrut wolf laixa fo esac ni rewol si egats rep esir erusserp eht ,revewoH .senihcam
obrut wolf lagufirtnec dna dexim naht senihcam desu era srosserpmoc wolf laixA .senihcam
eg rewop enola dnats ,senigne tfarcria ni noitaren .cte senigne eniram ,stinu
senibrut fo ngised eht naht lacitirc erom si srosserpmoc wolf laixa fo ngiseD rewop(
obrut gnitareneg wolf eht srosserpmoc ni ,taht si nosaer ehT .)senihcam eht ni sevom
erusserp esrevda( erusserp gnisaercni fo noitcerid eht fI .)tneidarg yb dezirusserp si wolf
eht ot dehcatta sreyal yradnuob eht ,rewop erom gniylppus dehcated teg gnisac dna sedalb
hcihw strats wolf esrever dna dael wolf ot eht fo eruliaf elbissop ot gnidael ytilibatsni
f eht senibrut ni ,revewoH .enihcam diul ( erusserp gnisaerced eht ni sevom elbarovaf erusserp
a refsnart oT .)tneidarg segats fo rebmun erom ygrene fo tnuoma nevig si ni deriuqer
ni naht srosserpmoc gninrut diulf eht ,yllareneG .senibrut 02 ot detimil era selgna ni
srosserpmoc dna era 051 si egats rep esir erusserp eht suhT .senibrut fo esac ni 561 ot
ni detimil sesaercni siht ,erusserp gnisaercni fo noitcerid ni swolf diulF .srosserpmoc fo esac
,diulf eht fo ytisned eht suht dna ecnartne eht morf sesaerced edalb eht fo thgieh eht ot eht
dna ecnartne eht ta senav ediug telni evah srosserpmoc wolf laixA .tixe .tixe eht ta resuffid
eht swohs 2 .gif dna rosserpmoc eht hguorht wolf eht swohs 1 erugiF gnidnopserroc
eht rosserpmoc a rof yllareneG .selgnairt yticolev tixe dna telni ra selgna htiw denifed e
eb nac tI .)selgna ria sa nwonk( noitcerid laixa ot tcepser si elgna gninrut diulf eht taht nees
eht swohs 3 erugiF .srosserpmoc fo esac ni wol eht 4 .gif dna edalb enibrut eht hguorht wolf
yticolev tixe dna telni gnidnopserroc rof selgnairt .enibrut a
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ENIHCAMOBRUT ]65EM01[
egaP 53
edalb rosserpmoc a ssorca wolF 1 .giF
selgnairt yticolev tixe dna telnI 2 .giF
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ENIHCAMOBRUT ]65EM01[
egaP 63
edalb enibrut a ssorca wolF 3 .giF
enibrut rof selgnairt yticolev tixe dna telnI 4 .giF
rof noitcaer fo eerged rof noisserpxE rosserpmoc wolf laixa
citats fo erusaem a sa denifed si noitcaer fo eergeD rotor eht ni srucco taht esir yplahtne
yplahtne citats latot eht fo egatnecrep a sa desserpxe .rotor eht ssorca
=
:snoitpmussA x 2 rof si sisylana ehT - lanoisnemid wolf . ehT larehpirep ekat ot demussa si wolf x noitcerid laidar eht ni wolf on si ereht dna emas era teltuo dna telni ta seiticolev
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ENIHCAMOBRUT ]65EM01[
egaP 73
x ot nommoc si tI wolf laixa fo esac ni noitcerid laixa .t.r.w selgna edalb sserpxe)selgna ria( rosserpmoc x tnatsnoc niamer ot demussa si yticolev laixA
srosserpmoc wolf laixa rof selgnairt yticolev tixe dna telni eht swohs 2 erugiF .
egnahc = rosserpmoc eht no enod krow ehT yplahtne noitangats ni
0 = (2 1) 1
elgnairt yticolev telni morf ,MT swolf laixa na roF
elgnairt yticolev tixe eht morf ralimiS
gniyfilpmis dna 3 uqe dna 2 .uqe gnitauqE
5 .qe ni 7.qe dna 6 .qe gnitutsbuS
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ENIHCAMOBRUT ]65EM01[
egaP 83
rof selgnairt yticoleV ereffid noitcaer fo eerged fo seulav tn
hcihw ni senihcam obrut wolf laixa rof nward era selgnairt yticoleV 1 = 2 =
=2
2 12
(12 2
2) + (22 1
2 )
= =(1
2 22) + (2
2 12 )
2
)1( nehW < 0 ( )
nehw evitagen semoceb R 1 > 2
evitisop eb nac DW ro E
)2( ;0=R nehW 1 > 2 erusserp citats oN ;MT eslupmi ; rotor ssorca egnahc
)3( ;5.0=R nehW 1 = 2 2 = 1 yb %05 dna eslupmi yb %05 ;MT eslupmI ;
;elgnairt yticolev lacirtemmyS ,noitcaer 1 = 2; 2 = 1
)4( ;1=R nehW 1 = 2 ot eud ylerup srucco noitamrofsnart ygrene ;MT noitcaer ylerup ;
diulf fo E.K evitaler ni egnahc
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ENIHCAMOBRUT ]65EM01[
egaP 93
)5( nehW > 1.0; 2 > 1; evitisop ro evitagen eb nac noitamrofsnart ygrene
senibruT - rotcaf noitazilitU
.1 rotcaf noitazilitU si MTGP rof ylno denifed - senibruT
.2 eht si ycneiciffe citabaidA senibrut ni tseretni fo ytitnauq
.3 dna ycneiciffe citabaida fo tcudorp si ycneiciffe llarevO lacinahceM ycneiciffe
.4 %001 ylraen si sMT fo ytirojam fo ycneiciffe lacinahceM
.5 ffe llarevo ,eroferehT ot lauqe tsomla si ycneici ycneiciffe citabaida
.6 rotcaf noitazilitu fo tcudorp si ycneiciffe citabaida ,revewoH nac taht ygrene margaid(
enibrut a morf deniatbo eb sessol suoirav htiw detaicossa ycneiciffe dna )ycneiciffe
.7 tahw htiw slaed rotcaf noitazilitU mumixam si enibrut a morf deniatbo tuohtiw
enibrut eht ni sessol eht gniredisnoc
.8 krow laedi fo oitar eht si rotcaf noitazilitU krow ot noisrevnoc rof
.9 esaercni dna telni ta .E.K eht lla ezilitu ot elbissop eb dluohs ti snoitidnoc laedi rednU
ot eud .E.K eht tceffe noitcaer
.01 krow otni noisrevnoc rof elbaliava ygrene laedi ehT
.11 si noitauqE enibruT sreluE yb nevig tuptuo krow ehT
.21 yb nevig si rotcaf noitazilitU
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ENIHCAMOBRUT ]65EM01[
egaP 04
.31 %59 ot %09 neewteb si sMT nredom rof rotcaf noitazilitU
otcaf noitazilitu neewteb noitaleR noitcaer fo eerged dna r
yb nevig si rotcaf noitazilitU
yb nevig si noitcaer fo eerged ehT
dna rotcaf noitazilitu rof noisserpxe eht ni X fo eulav eht gnitutitsbuS gniyfilpmis
enibrut sreluE erehw snoitidnoc eht rednu rotor elgnis rof dilav si noitauqe evoba ehT
ni dilav si noitauqe evoba ehT .1 = R nehw dilavni si noitauqe evoba ehT .dilav era snoitauqe
fo egnar gniwollof eht R = 0 R < 1.
rotcaf noitazilitU mumixaM
caf noitazilitU yb nevig si rot
ixe eht fi mumixam rotcaf noitazilitU .muminim si yticolev etulosba t si sihT nehw elbissop
noitcerid laixa ni si yticolev etulosba tixe eht
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ENIHCAMOBRUT ]65EM01[
egaP 14
yb nevig si rotcaf noitazilitu mumixaM
eslupmi rof rotcaf noitazilitU mumixaM enibrut
,0 = R enibrut eslupmi na roF suht = 2 1
era DBO dna BAO selgnairt yticolev eht morF .ralimis
U = BA suhT
1 elbissop sa llams sa edam si ( 51 0 02 0)
senibrut noitcaer %05 rof rotcaf noitazilitU mumixaM
senibrut noitcaer %05 ;evah 1 = 2 2 = 1; 1 = 2; 2 = 1 mumixam rof dna
noitazilitu 2 gnidnopserroc ehT .noitcerid laixa ni eb tsum era selgnairt yticolev
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ENIHCAMOBRUT ]65EM01[
egaP 24
enibrut noitcaer%05 dna eslupmI neewteb nosirapmoC noitazilitu mumixam
)a( edalb emas evah htob nehW deeps
rof selgnairt yticolev ehT .senibrut noitcaer %05 dna eslupmi fo sdeeps edalb eht eb RU dna IU teL
era noitazilitu mumixam
brut eslupmi taht raelc si ti ,2 dna 1 .qe gnirapmoC eni %05 naht ssam tinu rep ygrene fo
nibrut noitcaer e .mumixam si noitazilitu x senibrut eslupmi naht tneiciffe erom era senibrut noitcaer %05 ,revewoH x .senibrut ne eht flah refsnart senibrut noitcaer %05 tuB x eslupmi ylno fi ro deriuqer era segats erom desu era senibrut noitcaer %05 ylno fIts desu era senibrut wol si ycneiciffe tub ssel era sega x ro eno esu ot nommoc si ti elbaliava si oitar erusserp egral erehw senibrut maets nI
segats noitcaer yb dewollof segats eslupmi owt
noitazilitu mumixam ta enibrut noitcaer %05 dna eslupmI neewteb nosirapmoC
)b( ah htob nehW refsnart ygrene emas ev
)c( dna 1V nehW 1 sMT htob ni emas era
noitazilitu mumixam rof egats noitcaer %05 dna eslupmi rof oitar deepS
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ENIHCAMOBRUT ]65EM01[
egaP 34
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ENIHCAMOBRUT ]65EM01[
egaP 44
5 :TINU
SENIBRUT MAETS
:noitcudortnI
hgih ,senibrut maets nI .diulf gnikrow a sa maets eht esu senibrut maetS erusserp
detrevnoc gnieb maets fo yplahtne eht hcihw ni ,elzzon ni dednapxe si reliob eht morf maets
eht revo segnipmi elzzon fo tixe eht ta yticolev hgih ta maets eht ,suhT .ygrene citenik otni
oitcerid wolf eht egnahc ot esuac hcihw )rotor( sedalb gnivom a esuac suht dna maets fo n
eht dna rotor eht neewteb noitca cimanyd siht ot euD .sedalb rotor eht no ecrof laitnegnat
epyt wolf laidar ro laixa fo eb yam senihcam esehT .depoleved si krow eht suht ,maets
secived .
eman ,sdnik owt fo eb yam senibrut maetS .enibrut noitcaeR )ii( dna enibrut eslupmi )i( ,yl
elzzon eht ni srucco )pord erusserp( pord yplahtne elohw eht ,enibrut eslupmI nI
1.giF .sedalb rotor eht revo ssap sdiulf eht nehw tnatsnoc sniamer erusserp ecneH .flesti
pmI fo margaid citamehcs eht swohs .enibrut eslu
eb osla lliw ereht elzzon eht ni pord erusserp eht ot noitidda ni ,senibrut noitcaeR nI
.sedalb rotor eht revo sessap diulf eht nehw rucco pord erusserp
enibrut maets eht fo tsoM si i hcihw enibrut mortsgnujL tpecxe secived epyt wolf laixa fo a s
.epyt laidar
:senibruT maetS fo gnidnuopmoC
,sedalb gnivom fo wor elgnis dna elzzon elgnis fo gnisirpmoc ,egats eno ylno fI
i ta elbaliava ygrene citenik ro ygrene wolf eht neht ,desusi debrosba ton si enihcam fo teln
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ENIHCAMOBRUT ]65EM01[
egaP 54
sedalb gnivom fo wor eno yb ylluf o yticolev etulosba fo flah ta gninnur eht gniretne maets f
neve ,esuaceb( egats = V/U ,noitazilitu mumixam rof 2/1 = ot eud ,taht yas ot snaem tI .)
hcam fo telni ta ygrene elbaliava eht lla deeps lanoitator hgih gnieb hcihw dezilitu ton si eni
tsaw ylpmis taht wonk ew oslA .enihcam fo tixe ta de tixe ,noitazilitu mumixam rof yticolev
rof ,ecneH .elbigilgen ro muminim eb dluohs maets fo ot sah eno ,noitazilitu retteb a evah
eihca ot redro nI .rotor fo deeps laitnegnat elbanosaer o owt ,esu ot evah ew ,siht ev r erom
alb yranoitats fo wor a htiw sedalb gnivom fo swor .meht fo riap yreve neewteb sed eht ,woN
enihcam fo telni ta elbaliava maets fo ygrene latot swor eht lla yb debrosba eb nac ni
wor tsal eht fo dne eht ta maets fo ygrene citenik eht litnu noisseccus .elbigilgensemoceb
ecneH nac gnidnuopmoC elbanosaer gniniatbo fo dohtem eht sa" denifed eb
eno naht erom gnisu yb pord erusserp llarevo nevig a rof rotor fo deeps laitnegnat egats "
laitnegnat eht fi esuaceb senibrut maets rof yrassecen si gnidnuopmoC alb pit sed
,siht euD .sserts lagufirtnec ot detcejbus era spit edalb eht neht ,s/m 004 naht retaerg yticolev
yb enod eb nac gnidnuopmoC .wol osla si egats eht fo ycneiciffe eht ecneh wol si noitazilitu
,gnidnuopmoc yticoleV )i( ,yleman ,sdohtem gniwollof eht ro gnidnuopmoc erusserP )ii(
erusserP )iii( egats uaetaR - eslupmI )vi( dna gnidnuopmoc yticoleV - .gnigats noitcaeR
.1 : enibruT eslupmI fo )egatS sitruC( gnidnuopmoC yticoleV
& )rotor( sedalb gnivom fo swor ,selzzon fo tes fo stsisnoc sihT wor a yranoitats fo
.enibruT eslupmI gnidnuopmoc yticolev gnidnopserroc eht swohs 3.giF .)rotats( sedalb
ot wor gnivom tsrif eht morf gnimoc maets eht tcerid ot si sedalb yranoitats fo noitcnuf ehT
llA .yticolev ni egnahc elbaicerppa tuohtiw wor gnivom txen eht ygrene citenik eht elbaliava
eht ta si maets eht&swor gnivom eht lla yb debrosba ylevisseccus si tixe elzzon eht morf tnes
wor gnivom tsal veihca ot yticolev wol htiw enibrut ehT .noitazilitu hgih e siht rednu skrow
colev dellac si egats gnidnuopmoc fo epyt .g.E.enibrut dednuopmoc yti maets egats sitruC
enibrut
.2 : enibruT eslupmI ) egatS uaetaR( dednuopmoC erusserP
.gnidnuopmoc erusserp sa dellac si seires ni degnarra segats eslupmi elpmis fo rebmun A
lb dexif fo swor htiw dedivorp si enibrut eht ,esac siht nI hcihw seda elzzon a satca eht ta
ni ecalp ekat ton seod maets fo pord erusserp latot ehT .sedalb gnivom fo swor hcae fo yrtne
eht rof elzzon sa tca hcihw sedalb dexif fo swor eht lla gnoma dedivid tub elzzon elgnis a
erroc eht swohs 4.giF .swor gnivom txen .enibrut eslupmI gnidnuopmoc erusserp gnidnops
era seiticolev wolf hgih yrev esuaceb seicneiciffe rehgih ot sdael gnidnuopmoc erusserP
etulosba eht ,noitazilitu mumixam roF .selzzon tnegrevnoc ylerup fo esu eht hguorht dediova
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ENIHCAMOBRUT ]65EM01[
egaP 64
ltuo eht ta maets fo yticolev egral ni lausu si tI .detcerid yllaixa eb tsum rotor tsal eht fo te
dednuopmoc yticolev eht retfa segats noitcaer ro dednuopmoc erusserp evah ot senibrut
.egats
.3 erusserP - :gnidnuopmoC yticoleV
tuohtiw decuder era sdeeps rotor hgih ,dohtem siht nI .tuptuo eht ro ycneiciffe eht gnicifircas
sihT .segats owt ta srucco erusserp resnednoc eht ot erusserp tsehc eht morf pord erusserP
erusserp ot derapmoc sa noitcurtsnoc elpmis ot eud ralupop yrev si tnemegnarra fo epyt
.enibrut maets gnidnuopmoc
erusserP - dna tsriF .5.giF ni nwohs sa si segats owt rof tnemegnarra gnidnuopmoc yticoleV
fo tes a fo stsisnoc gnidnuopmoc yticolev a ot lacitnedi era yletarapes nekat egats dnoces
isac ot sedalb dexif fo swor dna tfahs eht ot dexif sedalb gnivom fo swor dna selzzon ehT .gn
fo noitrop ylno htiw strap maets yticolev hgih ehT .selzzon eht ni ecalp sekat noisnapxe eritne
sedalb dexif ot no dessap neht dna sedalb gnivom eht fo tes tsrif eht ni ygrene citenik eht
pa tuohtiw ecalp sekat tej fo noitcerid ni egnahc ylno erehw tej sihT .yticolev ni ssol elbaicerp
.srucco ygrene citenik ni pord rehtruf erehw senav gnivom fo tes rehtona ot no sessap neht
sitruC dellac osla si enibrut fo epyt sihT .enibruT
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ENIHCAMOBRUT ]65EM01[
egaP 74
.4 eslupmI - :enibruT noitcaeR
si ereht enibrut fo epyt siht nI .noitcaer dna eslupmi yleman selpicnirp htob fo noitacilppa
ot gnidnopserroc tnemegnarra siht ni sedalb dexif ehT .6.giF ni nwohs si enibrut fo epyt sihT
rof dettimda si maets ,selzzon fo tes a fo daetsnI .enibrut eslupmi eht ni derrefer selzzon eht
elohw maets eht ,sedalb dexif fo wor tsrif eht hguorht gnissap nI .ecnerefmucric eht fo
wor tsrif eht sretne neht maetS .sesaercni yticolev sti dna erusserp ni pord llams a seogrednu
oitcerid ni egnahc a sreffus ti enibrut eslupmi ni esac eht sa sedalb gnivom fo erofereht dna n
ot esir sevig siht gnirud pord erusserp ehT .sedalb eht ot eslupmi na sevig sihT .mutnemom
rotcev si ecrof gnivird eht suhT .yticolev dedda fo taht ot etisoppo noitcerid eht ni noitcaer
.noitcaer dna eslupmi fo noitammus
ibrut siht yllamroN foepyt siht ni yticolev maets ehT .enibrut noitcaeR sa nwonk si en
uoba gnieb mumixam eht ,wol ylevitarapmoc si enibrut sihT .yticolev edalb ot lauqe t fo epyt
.enibrut noitcaeR s'nosraP sa dellac osla si tI .ecitcarp ni lufsseccus yrev si enibrut
noitidnoC sedalB ralugnaiuqE htiw ycneiciffe edalB ro rotcaF noitazilitU mumixaM rof
:enibruT eslupmI rof
rof sedalb ralugnaiuqe htiw ycneiciffe edalb ro rotcaf noitazilitu mumixam rof noitidnoC
eps maets eht no ycneiciffe edalb fo ecneulfni eht dna enibrut eslupmI egats elgnis a ni de
ni nwohs sa smargaid yticolev gnidnopserroc gniredisnoc yb deniatbo eb nac enibrut eslupmI
eht naht decuder si teltuo ta yticolev evitaler eht ,ssol noitcirf edalb fo tceffe eht ot euD .9.giF
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ENIHCAMOBRUT ]65EM01[
egaP 84
.telni ta yticolev evitaler V,eroferehT 2r = C b V 1r yticolev ,noitidnoc siht ot gnidnopserroc ,
nwohs sa nward era )ylno evitatilauq( selgnairt .erugif ni
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ENIHCAMOBRUT ]65EM01[
egaP 94
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ENIHCAMOBRUT ]65EM01[
egaP 05
:segatS owT no sisylanA
sitruC( enibruT eslupmI dednuopmoC yticoleV rof ycneiciffE mumixaM fo noitidnoC
enibruT )
nwohs sa era enibrut sitruC a fo egats dnoces dna egats tsrif rof selgnairt yticolev ehT
etulosba lanif eht taht detceles os eb dluohs selgna eht dna deeps ehT .erugif evoba nI
iffe mumixam niatbo ot sa os ,laixa si wor dnoces eht gnivael maets fo yticolev ehT .ycneic
detnuom era sedalb gnivom eht lla ecnis emas si swor eht htob rof edalb fo deeps laitnegnat
.tfahs emas eht no
,si maets fo gk rep enod krow eht ,sedalb gnivom fo wor tsrif eht nI
W 1 V( U= 1u V+ 2u g/) c VU= 1u g/ c
ew ,elgnairt yticolev egats I morF ,teg
W1 V( U= 1r soc V+ 2r g/)soc
fI 1= 2 dna V 1r = V 2r W ,neht , 1 ( U2= V 1r soc 1 g/ )
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ENIHCAMOBRUT ]65EM01[
egaP 15
W1 V( U2= 1 soc 1 - g/ )U
yticolev eht sa emas si wor tsrif eht gnivael maets fo yticolev etulosba eht fo edutingam ehT
,sedalb gnivom fo wor dnoces eht gniretne maets fo V,.e.i( ssol lanoitcirf on si ereht fi 2 V= 3 )
.degnahc eb ot gniog si noitcerid eht ylno tub
,si maets fo gk rep enod krow ,wor gnivom dnoces eht nI
W2 V U= 2u = g/ ( U V 3r soc 3 V + 4r g/ ) soc
fi niagA 3 = 4 V dna 3r V = 4r
W2 V( U2= 3r soc 3 g/ )
W2= ( U2 V 3 soc 3 - g/ )U
V neht ,rotor II eht ot rotor I morf gniretne maets fo yticolev etulosba ni ssol on fI 3 V = 2 & 3
= 2
W2= ( U2 V 2 soc 2 - g/ )U
V ,oslA 2 soc 2 V = 2r soc 2- V =U 1r soc 1 - V( .U 1r V = 2r & 1 = )2
V 2 soc 2 V( = 1 soc 2 - )U U V( 1r soc 1 V = 1 soc 1 - )U
V 2 soc 2 V = 1 soc 1 - U2
W2 V( U2 = 1 soc 1 - g/ )U3
yb nevig si segats eht htob morf maets fo gk rep enod kroW latoT
WT W= 1 W+ 2 = [ U2 V 1 soc 1 - V +U3 1 soc 1 - g/]U
WT = [ U2 V2 1 soc 1- g/]U4
WT = [ U4 V 1 soc 1- g/]U2
evoba eht ,mrof lareneg nI ,sa desserpxe eb nac noitauqe
V[ U n 2 = W 1 soc 1 - g/]Un
.segats fo rebmun = n ,erehW
,yb nevig si ycneiciffe edalb eht nehT
=
12
2
= 4(1 soc 1 2U)
12
2
=8
1soc 1
2
1= 8[ soc 1 2]
,ycneiciffe edalb mumixam roF
= 0
dnA 2/1= wor tsal eht ni enod krow n krow latot fo
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ENIHCAMOBRUT ]65EM01[
egaP 25
V1 eht ta yticolev maets ro rotor tsrif eht gniretne maets fo yticolev etulosbA=
.s/m ,elzzon eht fo tixe
1 telni ta deeps edalb laitnegnat ro enalp leehw ot tcepser htiw elgna elzzoN =
,rotor tsrif eht ot .seerged
V 1r .s/m ,egats I fo telni ta diulf fo yticolev evitaleR =
1 eerged ,Vyb edam rotor 1 fo telni ta elgna edalb ro rotoR =
V 2r egats I fo teltuo ta diulf fo yticolev evitaleR = .
2 elgna edalb ro rotoR = edam rotor I fo teltuo ta eerged
V2 s/m ,egats ro rotor I eht gnivael maets fo yticolev etulosbA=
2 V yb edam maets fo elgna tixE = 2 eerged ,
V3 eht morf maets eht fo yticolev tixe ro rotor 2 eht gniretne maets fo yticolev etulosbA =
.s/m ) V C( = rotats
3 2 rof rotats fo elgna tixE = ,rotor eerged
.egats dnoces eht ni seulav gnidnopserroc era , V, ,) V C= ( V
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ENIHCAMOBRUT ]65EM01[
egaP 35
:TINU 6
SENIBRUT CILUARDYH
:noitcudortnI
ordyH( ygrene retaw eht trevnoc hcihw senihcam eht era senibrut )retaw( ciluardyH
eb yam ygrene retaw ehT .ygrene lacinahceM otni )rewop laitnetop fo mrof eht ni rehtie
ehT .retaw gniwolf ni ygrene citenik fo mrof eht ni ro ,sriovreser ,smad ni dnif ew sa ygrene
lacinahcem strevnoc hcihw rotareneg cirtcele eht ot delpuoc yltcerid enibrut eht fo tfahs
si sihT .ygrene lacirtcele ot ni ygrene ordyH sa nwonk - ."rewop cirtcelE
:senibruT ciluardyH fo noitacifissalC
no retaw fo noitca eht )i ot gnidrocca sdnik suoirav otni deifissalc era senibrut retaW
deeps cificeps eht )iii dna rennur eht hguorht wolf diulf fo noitcerid eht no desab )ii ,sedalb fo
enihcam eht .
(i) :sedalB no retaW fo noitcA enibrut sicnarF a no desaB
epyt noitcaeR )2 dna epyt eslupmI )1:otni deifissalc eb yam esehT
tnatsnoc si rennur eht revo diulf gniwolf eht fo erusserp eht ,enibrut eslupmi nI
na ot lauqe yllarenegdna telni ta ygrene laitnetop elbaliava eht llA .erusserp cirehpsomta
ot tceffe eslupmi ylerupa hguorht dezilitu nrut ni hcihw otni detrevnoc yletelpmoc eblliw
si enibrut a fo telni eht taygrene elbaliava eht ,enibrut eslupmi ni ,eroferehT .krow ecudorp
t ylno .ygrene citenik eh
segnahcerusserp retaw eht dna retaw htiw dellif si gnisac enibrut eht ,enibrut noitcaer nI
a sA.)sedalbdexif( elzzon morf ygrene citenik ot noitidda ni rotor eht hguorht wolf gnirud
telni eht ta elbaliava era dna erusserp eht htob ,elohw gnicudorp rof senibrut noitcaerfo
.rewop
:rennuR hguorht diulF fo wolF fo noitcerid eht no desaB )ii(
:otni deifissalc era senihcam ciluardyH
wolf larehpirep ro laitnegnaT)a
wolf drawtuo ro drawni laidaR)b
wolf lanogaid ro dexiM)c
.sepyt wolf laixA)d
:senihcaM wolF laitnegnaT)a
fonoitator fo htap eht ot tnegnat eht gnola swolf retaw eht ,senibrut wolf laitnegnat nI
:elpmaxE .rennur eht leehw notleP
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ENIHCAMOBRUT ]65EM01[
egaP 45
:senihcaM wolF laidaR)b
amer wolf dna noitcerid laidar eht gnola swolf retaw eht ,enihcam wolf laidar nI sni
ro wolf drawni eb yam tI .rennur eht hguorht sessap ti sa noitator fo sixa eht ot lamron
.wolf drawtuo
eht hguorht sessap dna yrehpirep retuo eht ta sretne retaw eht ,senibrut wolf drawnI nI
yllanif dna noitator fo sixa eht sdrawot yldrawni rennur .yrehpirep renni ta sevael
:elpmaxE enibrut sicnarF lf eht senihcam wolf drawtuo nI . eht ot etisoppo si noitcerid wo
.senihcam wolf drawni
:wolF lanogaiD ro dexiM)c
revo sessap ,yrehpirep retuo eht ta retne yam diulf fo wolf eht ,enibrut fo epyt siht nI
eciv dna noitator fo sixa eht ot lellarap ro yllaixa sevael dna yldrawni rennur eht - asrev
:selpmaxE enibrut zaireD ,enibrut sicnarF nredoM
:seciveD wolF laixA)d
.noitator fo sixa eht ot lellarap noitcerid eht gnola retaw eht ,enibrut fo epyt siht nI
pmaxE .cte enibrut relleporp ,enibrut nalpaK :sel
:deepS cificepS no desaB )iii(
:otni deifissalc era senibrut ciluardyH
)a( :deepS cificepS woL m 0071 ot pu m002 fo egnar eht ni daeh hgih syolpme hcihW
N .leehw notleP :selpmaxE .egrahcsid wol seriuqer enihcam sihT S elgnis 03 ot 01 =
.leehw notleP tej elbuod rof 05 ot 03 dna tej
)b( :deepS cificepS muideM 002 ot m05 fo egnar eht ni sdaeh etaredom syolpme hcihW
N ,enibrut sicnarF :elpmaxE.m S .004 ot 06 =
)c( :deepS cificepS hgiH 2 fo egnar eht ni sdaeh wol yrev syolpme hcihW m 05 otm5.
0001 ot 003 = N ,.cte relleporP ,nalpaK :selpmaxE .egrahcsid hgih eriuqer esehT
notleP leehW :
)ii( elzzoN )i( :sessop ylniam tI .enibrut ciluardyh wolf laitnegnat fo epyt eslupmi a si sihT
gnisac )iii( stekcub dna rennur )vi( .giF .elzzon ekarB ordyh fo tuoyal lareneg swohs 1 -
.leehw notlep htiw tnalp rewop cirtcele
,kcotsnep eht fo dne eht tA .kcotsnep eht hguorht wolf ot edam si mad eht morf retaw ehT
eht fo deeps ehT .ygrene citenik hgih otni ygrene laitnetop eht trevnoc hcihw dettif si elzzon
wolf eht gniyrav yb daeh raeps eht gnitarepo yb detaluger eb nac elzzon eht morf gniussi tej
strats rennur eht hcihw ot eud stekcub eht revo gnignipmi tej fo yticolev hgih ehT .aera
oc si ygrene ciluardyh ybereht dna stceffe eslupmi eht fo esuaceb gnitator otni detrevn
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ENIHCAMOBRUT ]65EM01[
egaP 55
eht edivorp lliw gnisaC .ecar liat otni sllaf retaw eht ,rennur eht retfA .ygrene lacinahcem
rennur eht gnirb ot desu era selzzon ekarB .erehpsomta ot nepo si dna rennur rof gnisuoh
eppots eb ot si ti revenehw noitidnoc tser ot deeps hgih morf retaw siht eveihca ot redro nI .d
.rennur fo taht ot noitcerid etisoppo ni wolf ot edam si
:senibruT ciluardyH fo seicneiciffE dna sdaeH
:sdaeH ciluardyH
)a( :daeh ssorG ereht nehw level ecar liat dna ecar daeh eht neewteb ecnereffid eht si tI
H sa detoned si dna daeh citats sa demret si ti hcus sA .wolf on si S H ro g.
)b( :daeh evitceffE deniatbo si tI .enibrut eht fo telni eht ta elbaliava daeh eht si tI eht neht ,ssol latot eht si h fI .kcotsnep ni sessol daeh lla gniredisnocyb
=H si enibrut eht evobadaehevitceffe Hg - hf
:seicneiciffE
a senibrut ciluardyh fo seicneiciffe suoiraV :er
I ( ycneiciffe ciluardyH) H) )ii cirtemulov ( ycneiciffe loV )
( ycneiciffe lacinahceM)iii hcem ) VI ( ycneiciffe llarevO) O)
)i ( ycneiciffe ciluardyH H :) retaw eht ot rennur eht yb depoleved rewop fo oitar eht si tI
.enibrut eht fo telni eht ta elbaliava rewop
=( )(11 22)
( )
= (11 22)
=
=
fo telni eht ta daeh evitceffe si H erehW .enibrut
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ENIHCAMOBRUT ]65EM01[
egaP 65
( ycneiciffe cirtemuloV)ii loV :) eht gnikirts yllautca retaw fo ytitnauq eht fo oitar eht si tI
.rennur eht ot deilppus retaw fo ytitnauq eht ot rennur
=
lacinahceM)iii ycneiciffe ( :) leved rewop fo oitar eht si tI eht ot rennur eht yb depo
retaw .enibrut eht fo telni eht ta elbaliava rewop
=
=
(11 22)
)vi ( ycneiciffe llarevO ): eht si tI op tuptuo tfahs fo oitar retaw eht ot enibrut eht yb rew
enibrut eht fo telni ta elbaliava rewop
=
=
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ENIHCAMOBRUT ]65EM01[
egaP 75
:leehW notleP eht yb enoD kroW
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ENIHCAMOBRUT ]65EM01[
egaP 85
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ENIHCAMOBRUT ]65EM01[
egaP 95
:enibruT noitcaeR
daeh yticolevotni detrevnoc si telni ta retaw fo daeh latot fo trap ylno ,senibrut noitcaer nI
rap gniniamer eht dna rennur eht sretne ti erofeb ni detrevnoc si daeh latot fo t sa rennur eht
enihcam eseht nI .ti revo swolf retaw eht aw eht ,s lla ni dellif yletelpmoc si ret fo segassap eht
laudarg retaw fo erusserp eht ,suhT .rennur hguorht sessap ti sa segnahc yl ,ecneH .rennur eht
russerp htob senihcam fo dnik siht rof .g.E .telni ta elbaliava era ygrene citenik dna ygrene e
ut sicnarF ,enibr .enibrut zaireD ,senibrut nalpaK
s sa si epyt wolf dexim fo si hcihw enibrut sicnarF drawni fo si tI .4 .giF ni nwoh wolfidar rennur eht sretne retaw eht hcihw ni enibrut fo epyt dna yrehpirep retuo eht ta ylla sevael
sti ta yllaixa .retnec
i( :fo stsisnoc enibrut sihT llorcS ) ( gnisac ii yatS ) ( gnir iii ediuG ) ( senav rennuR )vi
.ebut tfarD )v(
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ENIHCAMOBRUT ]65EM01[
egaP 06
:gnisaC llorcS )i( )gnisac larips dellac( gnisac llorcs eht sretne kcotsnep morf retaw ehT
f niam ehT .rennur eht sdnuorrus yletelpmoc hcihw na edivorp ot si gnisac larips fo noitcnu
nI .yticolev tnatsnoc edivorp ot ecneh dna rennur eht dnuora retaw fo noitubirtsid mrofinu
sa seserced yllaudarg gnisac eht fo aera lanoitces ssorc eht ,yticolev tnatsnoc edivorp ot redro
rennur gnihcaer retaw eht
gnir yatS )ii( : era esehT .gnir yats ro enav deeps eht sretne gnisac llorcs morf retaw ehT
eht tcerid)a( ot si noitcnuf riehT .senav ediug eht fo rebmun ni flah yllausu dna sedalb dexif
eht tsiser )b( ,senav ediug eht revo retaw tni ot eud enibrut no daol lanre dna retaw fo erusserp
.noitadnuof eht ot dettimsnart si sdaol eseht
:senaV ediuG )iii( eht ot revo sessap gnir yats eht retfa retaW dexif ro senav ediug fo seires
nibrut eht dnuora yletelpmoc sdnuorrus yehT .senav snoitcnuf senav ediuG .rennur e t era )a( o
nur eht gniretne retaw fo ytitnauq eht etaluger no retaw eht tcerid )b( dna ren .rennur eht ot
)vi( :rennuR ehT eht ot retaw eht dael ot si stnenopmoc rehto eht fo esoprup niam rennur
htiw enibrut fo rennur ehT .ygrene fo ssol muminim s fo stsisnoc si devruc fo seire 61( sedalb
fmucric eht dnuora degnarra ylneve )42 ot eht neewteb ecaps eht ni ecnere ehT .etalp owt
etne retaw taht depahs os era senav retuo ta yllaidar rennur eht sr ti sevael dna yrehpirep
i egnahc ehT .retnec sti ta yllaixa fo noitcerid n laidar morf wolf eht revo sessap nehw laixa ot
cerppa eht sesuac rennur laitnerefmucric ni egnahc elbai ot elbisnopser nrut ni hcihw ecrof
.rewop poleved
:ebuT tfarD )v( at eht ot swolf rennur eht morf retaw ehT .ebut tfard eht hguorht ecar li A
p a si tfard cennoc hcihw aera gnisaercni yllaudarg fo egassap ro epi eht fo tixe eht t ot rennur
ets etalp ro tsac fo edam eb yam tI .ecar liat eht fo dne tixe ehT .etercnoc ro le si ebut tfard eht
taw fo level eht woleb degrembus syawla eb tsum dna ecar liat eht ni re ria - .thgit
sesoprup owt sah ebut tfard ehT :
ta dehsilbatse daeh noitcus ro evitagen a stimrep tI )a( ti gnikam suht ,tixe rennur eht elbissop
.daeh fo ssol tuohtiw level ecar liat eht evoba enibrut eht llatsni ot
fo noitroporp egral strevnoc tI )b( cejer ygrene yticolev lufesu otni rennur eht morf det
.ygrene erusserp
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ENIHCAMOBRUT ]65EM01[
egaP 16
:sebuT tfarD
ni esoprup eht evres ot deyolpme era hcihw sebut tfard fo sepyt tnereffid era erehT eht
giarts rof taht devresbo neeb sah tI .5.giF ni nwohs sa era enibrut fo noitallatsni th tnegrevid
naht erom eb ton dluohs elgna enoc lartnec eht ,ebut tfard epyt .8 si sihT elgna siht fi ,esuaceb
tuohtiw ebut tfard eht hguorht gniwolf retaw eht 8 naht erom si gnitcatnoc ecafrus renni sti
stluser hcihw t fo ycneiciffe eht ecneh dna seidde ni tfard eh .decuder si ebut
ebut lacinoc tnegrevid thgiartS )a(
ro( ebut gnidaerps ydooM )b( enoc ardyH )
ebut woble elpmiS )c(
.teltuo ta noitces ssorc ralugnatcer dna telni ta noitces ssorc ralucric gnivah ebut woblE )d(
seicneiciffE dna enoD kroW sicnarF fo :enibruT
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ENIHCAMOBRUT ]65EM01[
egaP 26
tixe ta lrihw on si ereht taht hcus rennur eht sevael tixe ta yticolev etulosba ehT
i. .e V 2u ni nwohs sa snoitidnoc tnereffid rof nward era elgnairt yticolev telnI ehT .0 =
)a( 6 giF & .)b(
/enod kroW )i( retaw fo gk , = (11 22)
2= )yticolev teltuo laixa( enibrut sicnarF ni 0
= 11
ycneiciffe ciluardyH )ii( :
=
( ycneiciffe cirtemuloV )iii( ): tI eht hguorht retaw fo ytitnauq fo oitar eht si ( rennur Q2 )
retaw fo ytitnauq eht ot deilppus Q( 1)
=2
1
( ycneiciffe lacinahceM )vi( :)
=
( ycneiciffe llarevO )v( :)
=
=
senibruT nalpaK & relleporP :
rennur wolf laixa na fo stsisnoc enibrut relleporp ehT lioforea fo sedalb 6 ot 4 htiw
taht ot ralimis era sedalb ediug dna gnisac larips ehT .epahs eht nI .senibrut sicnarF eht fo
relleporp f era rennur eht no detnuom sedalb eht ,senibrut non dna dexi - ni tuB .elbatsujda
tator nac dna detsujda eb nac sedalb eht enibrut nalpaK eht ot dexif stovip eht tuoba e fo ssob
itacifidom eht ylno si sihT .rennur eht alb ehT .enibrut relleporp ni no detsujda era sed
la ta taht os msinahcemovres a yb yllacitamotua tuohtiw sretne wolf eht sdaol l .kcohs
ot lellarap si wolf eht hcihw ni enibrut noitcaer wolf laixa na si enibrut nalpaK ehT
ht fo sixa eht ni nwohs sa tfahs e .giF eht u ylniam si sihT retaw fo ytitnauq egral rof des dna
4( sdaeh wol yrev rof - s cificeps eht hcihw rof )m 07 eht fo rennur ehT .hgih si deep nalpaK
eroferehT .pihs a fo relleporp a ekil skool enibrut sa dellac osla si ti semitemos relleporp
tA .enibrut tfard eht enibrut nalpaK eht fo tixe eht egrahcsid ot detcennoc si ebut eht ot retaw
.ecar liat
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ENIHCAMOBRUT ]65EM01[
egaP 36
yticolev eht ,telni tA)1 el giF woleb ni nwohs sa si
)2 teltuo ,.e.i tnenopmoc yticolev lrihw on htiw laixa syawla si egrahcsid eht ,teltuo eht tAgir a tsuj elgnairt yticolev .giF woleb nwohs sa elgnairt elgna th
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ENIHCAMOBRUT ]65EM01[
egaP 46
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