Васильев Ю.С., Виссарионов В.И., Кубышкин Л.И. Решение гидроэнергетических задач на ЭВМ (Элементы САПР и АСНИ)
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ossi
0a
=
xdldus*
Eq+Erdi
*q
=
xqlror+
Erqi
*r
=
Hgx6I
dns
*
Eq
+ grErd;
{
rd
=
lt'dxalaay
+
Eq.gz
t
Erd.,
0 rq
=
ltq'qlqA"
*
ErQ'
B
Qopr'rynax
(38)
-
(51)
p
-
cHMBon
gu$QepeHrs{poBannn;
9r, 9rd,
Lrq
-
noToKocIIeFIeHI'Ie
o6uororc cTaTopa,
poropa
u
llg
HoMrlHilrlbHafl
qacrora
BpaqeHl{n;
Mg"
=-9alqav+{qIdus
MeHr
Hacoca,
ornece"irrrfi
x 6aancHotry
MoMeHry;
M+
=
MrlMa
-
MoMeHr
Tpelmff,
orHeceHHrtft
rc 6arncxovry
MoMeHTy'
ypanueHnn
(40),
(41) xapaKrepH3ylor
nepexoEHble
npoueccbt
B cra'
-prln
uenu,
(42i
-
s
o6N,Ioire
nosbyxgeHnn,
(43)
'
(44)
-
s
geNIn$eP
rrbrx
KoHTypax,
(45)
ypaBHeHI{e
Epnxetx1f
cI4cTeMbI
llBgraren6-Hacoc,
(46)
-
ypaBHeHI{e
Yma
HaTPY3KI{.
'
YpaUueUUe
nepexo$Iblx
npoUeCcoB,
npoTeKarcug{x
B
aBToMaTHqecKOM
perynnrope
nos6yxgeHl,tff
(APB)
EBl{rarenff'
3aIIrIueM
B BI{ge
Kos
KsPs
E;(l+PTs)=Ero
t:-a-+--,
'
-r
w
l+
pTs
l+
pTz
\
r4e
7",
TtrTz
-
nocTofiHHD-te
BpeMeHH
VOZ6yg'nenn,
611orcoe
t{3Mepe'
nUor
ot*nbnennfi
qacToTbl
BpaIqeHHfr.
il ee
nponraognofi;
Ks,
Ko
-
rooQ-
onrrueurtr
ycHneHHfl;
Ero
HaqanbHoe
HanpffxeHHe
uoa6yxAeHHfl
Ma'
IIMHbI.
YparHerule
npoqeccoB
B
perynflrope
noabyxgeman
AonxHo
oblrb
Ao'
noJrHeHo
ycIIoBHffMI{,
xapaKTepI'I3yIou-U{MI{
pa6ory
ycrpofrcrr
aBToMarH'
Kr{.
TarcosrINol
ffBnflrcTcfi'
Er
=
0
rIpH
BKnIoqeHrIH
racnTeJlbnoro
conpo-
TnBneHI{ff
npH
rrycKe
H,
noglcnrcqeHl{I{
o6uorru
noe6yxgenug
K
Hanptxe-
rr1aro
Bo3fiyru{renfl,
ynpaBnffeMoMy
no
3atrauHoMy
3aKoHy
npu
noEcI{H'
xponHofi
qacrore
BpauleHllfl
EBl{rarerlfl
'
ypanuennn
(38)
(51) Moryr
6ltrr
npeo6paaoBaHbl
crle[yrcIrl't't
oG
pa3oM:
(40)
(41)
(42)
(43)
(44)
(4s)
(46)
(47)
(48)
(4e)
(s0)
(s
1)
0a,0q,
npelerrb-
d0a
>
Lr
dt
ur
q
-rAt-r
pyeuan
n
Qarax
craropa roKaMI,I o6prorru
poropa,
npetrerrbHoro
n norepeq-
Horo
UervrnQepHbrx
KoHrypoB coorBercrBeHHo;
Eq
-
9.[C o6ilrorrcu
eos-
6yxgerurx
B
Qa.rax
crarop€;
Er
Hanpflxerme sa
oduorrce
noe6yxtre-
poB
ABl{raTenff;
Xd, Xq
CHHxpoHHbIe
I{H,qyKTI{BHbIe
ConpoTI{BJIeH}Ifl no
npoAonbHoit u nonepe,mofi ocfiM MzrrrruHbr;
Ida",
Ioor, Id"r, Iqsn
-
npotronbHar.
u
flonepeqHaf, cocraBJlfirory{e roKoB
craropa H BHerrrHeft
ce-
M cooTBeTcTBeHHo;
8r,
8z
MaTHHTHbIe
napaMeTpbl;
Pd,
Pq,
Prt.
Prd,
Prq,
Psn
-
AeKpeMeHTbI
3aTyXaHHfl
ToKa B cTaTopHblx
H
poTopHblx
KoH'
Typax
ABnrarerrff
r{
BHeurHefi cern coorBercrBeHHo;
6
-
yron
Mer4[y tro-
82
a0q
=
os(1
+s)
{a-
r,srrlqnn-
@sUtqi
dtlr
rr
-"
=
@sPr(Er-
n);
dt
d*rd
dt
(s3)
r;
pd,
p{,
Ird
-
Kogdouu.reHrrr
MarruTHofi cBmn orAErbnrrx Korry.
dt
d
(s4)
(ss)
83
ds
_
t_
dt TJ
!!_,n
dt
d6
=
dt
dldsn
@ssi
as
grnlirn:
/
-
M'. Mr\
l-
*atu
rp*
{qlaup-
-,
n;
)
;
(s6)
(s7)
(s
8)
3recr
xr',
xrd,
xrQ
peaKTHBHoe
COnpOTHBnelMe
xr
=
Xad
*
.Xrr'i
Xrd
=
Xad
t
Xsrdi Xrq
=
XaQ
xs7,
x57f,,
xsrQ
-
peaKTIIBHOCTb
paccefr'J,llA
o6ruorxn
SepHrtx
KoHrypoB:
poropHbrx r(oHryPoB:
t
Xsr
q',
aosoyxge'Ilufr.I{
AeMn'
I
1
xsr
=
-(
I
-1
\i
xsrd
=
\"r-;-
-*)
(r
I 1\
\
"-;
.*
-
-*,,
)
asU
asUtd
xsn
dlqsn
=
t'u
tq
-
asu
cosD
-
gsru,rlqsrr
*
(rs
(l +s
)lrrnu.
(60)
dt
Xns
xBH
B
Sopr"ryn
ax
r
-
aKrHBHoe
conporr,rBreHr,re
craropHofr
uenu
I
dBH
=
=
Bs*a-
BrQr-Cr*rdi
Ino"
-
Lr@q-{rq);
Ei,t
=
Dr*a
+
r
Et*,
+
Frgrrti
E,
=
Erot KsPS
+K6sl
Ertt
=
Gtld
+Hc{,
+
+Kt|ra;
Erq=
BrQrq-NtQqi
Ura
=
Bo(l
+s)9n+
A3I4o"+
+
Dz0d
+
Ez0,
+
Fz*ra
-
BzE,
*
AqUsin 6
-
AsIdrn
-
46
(1
+
s)/q
nH
i
(Jrq
=
Lr(l
+
s)lta
-
Lilq
oo
+
Lq{
rcl
-
Lsgq
+
L6
Ucos6
+
I
llqvn-
Ie
(1
+s)/4sH.
KoaSQnruaeHrbl
Bblql{cnffIorcfl
no
SopvrynaM
Bs
=
(l
-
S
6z)lwxa;
Bt
=
0
-
q)lwxai Cr
=
(1
-g
r)lwxai
Dt
Et
=
o'al*i
Fr
=
@a-sr)lw;
K3
=
oalw;
Gs=
Qtagr-p'a)lw;
-H4
=
Qt'a-g)lw;
ru=
o4+ltagz-ltd+
+
lt'd8r
-
Srgzi
Bo
=-BslsH
l(Bsxsn
+
1);
82
--
Brxsuprl(Bsx""
+
1);
C2
-
CrxsnPrdl(Bsxsn
+
l);
L1
=
llxnooi
Bt
=
llon.;
Nr
=
Unlor;
04
=
|
-lta;
oq
=
'-tto;
o'd
=
l-P'di
Dz
=
BzDr*
CzGti
E2
=
BzEr
*
CzHcl
Fz
=
BzF'r
+
C2K3i
At
=
Bor)
A4
=
BolBsxsHi
As
=
BoPsnl
Bsi
As
=
Bol
Bsi
xsr
q
xad,
xaq
xad
=
I
t, tl
x'4,
xj,
x'n
-
nepexollHaff
LI
CBepxnepexoggafl
peaKTHBHocTb;
xs
-
peaK'
rr,rBHocTb
pacceflHl{fi
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rr
aKTHBHoe
conpoTHBneHHe
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nOe6yXgeilHfr;
l,ss,
Iss
-
aKTHBHOe
H IIHg,yKTHBHOe
COnpOTHBneHHff
BHelII'
uefi cern,
npI{BeAeHHbIe
K basllcHrtN'I
ycnoBnffM.
Beln.mHu
Prd
H
PrQ
paBHbl:
grd
=
rrdl*ra'
1re
=
rrQlxrqi
fqe
rrd,
fre
-
aKTI,IBlIbIe
COnpoTHBJIerMff
npoAonbHoro
H
[OnepeqHOro
AeMII-
QepHux
KoHrypoB.
flpn
peruenwr
Aanuofr
3aAaqil
npI'IMeM
cncreMy
porop
nLu,poMar[HHbI-
poTop
3neKTpoMaIrIlIHbI
xecTKofi,
T.e. 6ygeu
npeHe6peraTb
ynpyrllMu
Ee'
@pr.aary.rnnfl{
Bilna
arperaTa
npn
nepexoAHblx
npoUeccax. B :rou slyqae
MoxHo
3angcarb
ypaBHeHHfi
AsHxeHHff
poropa
arperara
6ee
ytera
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lrbrx
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dt
(
4--
t-\
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rs
xaq!
peaKTHBHocrb
peaKrlnfi
craroPa:
Xd-
Xsi
XaQ
=
Xq
-
xsi
nln
orpeAeneHufl
Hbr
lll,
Hcnonb3yeM
3HaqeHHfl
rHApaBnHqecKoro
MoMeHTa
ruApoMa[IH'
qerbrpexKBagpaHrHble
(rcpyronue)
3HeprerHqecKHe
Lt
=
Lrxrrl(LlxsH
+
1);
L?
=
Lzri
L4
=
LzBtPrsi
Ls
=
LzNrPrQi
Lo
=
LrlLtxsui
Lt
=
Pr,^LzlLr;
L'8
=
KoeoSnrg{eHTbr
naanlHrHofr
cBfl3r't,,
MarHI{THbIe
napaMerpbl,
[eKpeMeH'
161
o6naorrH
sor6yx.q,ennfl
t{ BnerrrHefr
Uema
onpeg,enflrcTcfl
BbIpaxeHI{flMH
xapaKTepHcTHKlt,
n cTaBJreHHbIe
B BHAe
3aBHCHMOCTeH
MeX[y
npHBe'
mApatsnHqecKnM
(puc,23):
i
=
f
,tr
(0)
I
MoMeHTou
M
npn
yrne
noBopora
nonactefr
I
=
const
7,,4
=
f
,Wr(Q);
(61)
*ad
pd
=
-.-'
xrxd
xad
8t
=
;
Xy
a
-
,*;
xad
t
xrd
I
Itd
8z
n
=
fnz(Q);
M
=
I'M2(Q),
r4HAeKc
I
0
coorBercrByer
ycrloBlrrc
II
nD'
M,
:
rl=___:.
V
=______.i
Dr
_Ar{aMerppafu.
t/
sla
I
psla
loi
(62
x
rqx
Q
rr
-
tsu
Pr
= --
i Pnu
=
-
xv
xsn
rAe
0=
84
DirM
n
)
/
/
/
,/
f
fra1il0
/r2
KoTopble
He BrcnrcqaloTcff
B onpetrenernie
MriioBeHlioro
peiKHMa. Oiruio'
r{e}lue Me)Krrv naDaMeTDaMI{ THIIDOMaUMHbI,
OnpetreneHHbtMH
Ha oCHOBa-
-''-"-ry
----E
r
rprg
crarlnoHapHoft
xapaKTepucrl{Kr{
H 3aMepeHHblMI{
rlpH
nepexoA]tblx nPo'
ueccax,
3aBr,rcHT
oT
Bo3geficrBufl
Ha
pafuqee
Koneco raK
Ha3blBaeMoro
npHcoeAHHeHHoro
MoMeHTa
HHepLU4H
BoAbl.
Eonluux
ruaqeHr'1fi 3TH
oT'
icloHennn
Moryr
Aocrr{rarb
npn
MarIbIx
Hanopax m[poMauuurt,
oco6eu'
Ho B
KancynbHbrx
rngpoarpefaTax,
c
ue6onr[MM
MoMeHToM
HHeptgan
3neKTpoMa[IHHbI.
HCXOAn
H3
3Toro,
npeg,tlaraeTcfl
BBoEJ'lTb
B
pacqeTbl MOMeHT HHeP
ww
J
[6]
:
J
=
Jo*
Jn
f
/n.*,
.
rge
,[o,
f
^,
J
n.M
-
MoMeHT
HHepU{H
coorBercrBenHo
poropa,
SxeKTPoMa-
lrruHbr
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pa6ouero
Koneca
rnApoMaurlrHbl
(uacoca)
tr
npnco'
etrHHeHHbIx
Macc
BoEbI.
Moueur
HHeplU{u
npucoeru{HeHHblx
Macc
npHMeM
KaK
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KonbIIa
xg{,qKocTll
B
KaMepe
pa6ouero
Koneca
B npegenax
no'
nacrHofi
cl{creMbl
Ila]
:
,In.*
=
p
!
I
zzdrds,
TS
ttre
z
-
paccrofiHr{e
or
nporonruofi
ocu
Hacoca
ro
ueHTpa
r{xecrn
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>ra4KocTH;
dr,
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H
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o6tenaa
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P
-
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C
yuerona ocpe$IeHl{fl
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ot-a4
,In.*
=
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37
rAe
Ix
EITHHa
xopgbr
npoQnnn
B
cpeAHeM
ceqeHI{H
nonacrl{
paEouero
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Hacoca;
p
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npoQnnn
cpe4{ero
ceqeHHfl
;1O'
nacm
n
nnocKocrbro,
nepneHgl{KynfipHofi
ocu
arperara;
Dt,
d
-
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prr
pa6ouero
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I{
BrynKH
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_
^
MoueHT
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B
Haqiue
nycKa,
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fi
=
0,
paBeH:
0,It.
n/no
-
4,0
htc.
23,
XapaxrepucrHKH
ocnoBHoro o6opygonaanx:
a
-
nonHafl
yHHBepcaJrbHafl
sHeprETH'{ecKa.E xapaKTepncr[Ka
ocesoft rufpoMaunr-
usry, 6
-
nycKoBir-n
crarucrurrecKar
xapaKTep{ crr{Ka sne KTpol{Burarenfl
npn
Mo
1
M7lM6;
npn
Ms
2 T7fM6,
rge
M,
=
kr.nMo
-
Ms
HoMl{Hanrrnfi
r$eHT
TpeIII{ff
noKofl.
MoMeHT
Tpermfl
noKoff;
M6
-
6asucHltfr
MoMeHT;
Bpauarcu.ufi
MoMeHr
EBllrarenfl;
kr.n
rcorSQH'
Mouenr
rpeHl{fl
cKonbxeHl4ff
MoxHo
npu6nnxeHHo
npHHHMarb
nocTo-
qero
Korleca rldApoMilrlmnbr;
p
-
DrorHocrb BoAbr;
QnH
-pacxornHa-
IIop ruApoMarrlr{Hbr.
Kpyrorrre
xapaKrepllcrnKn
(61),
(62)
orpegenflrorcff
B crauroHapnbrx
ycrroBnffx.
OgHaro npn HeycraHoBr.rBrrruxcfl
pexuMax
Ha
pa6o.mfi
npoqecc
oKa3brBarcT
BJrHflHlre KoMnoHeHTbr
ycKopeHr{ff
noToKa
B r}IApoMa[rHHe,
86
frIHblM,
paBHbtM.
Mr
=
sign
(n)kr.rMs,
rge
kr..
-
xoeQSuIS4eHr
rpeHHff
cKonbxeHl{fl;
t4
-
qacrora
BpaIqeHHfi
po'
TOpa
rH,qpoarperaTa.
8',|
flepexog rpeHH.E noKofl
B
TpeHIae
cKonbxexr{fl
HMeer
Mecro npn
qacrore
Bpa[IeHHff
nr.c.
Ha
caMoM
nepexogHoM yqacrKe,
T.e. npn
0
1
n 1nr.r,
MOMeHT
CHII TpeHLITI
BbIrIHCnrIeM
TaK:
Mr
=
sign
Ecnu nplt
repexoAnoM
npouecce
nponcxo4{r
HanonHeHr{e
r4nv onopox-
HeHI,Ie BoAoBoAoB, To
yqnrblBaerctr
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l/
n nporou-
1,)
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.
*
(k,n
-
kr.J
(t-
;")'l*,
htn
yrrera
ynpyrnx
csoftcrs
BoAonpoBofffIuefi
cHcreMbl
rntrpaBflHqec-
rcuu
ytrap
B
f3O
MoxHo
onncarb
gt{QQepeHLu{iInbHbtMH
ypaBHeHHffMH
nanep6onnqecKoro
THna
nepBoro
nopftrKa
B
qacTHbIX
npoH3BoA,lIbIx.
YpanHenne
lDHXeHI,tfl
xHAKocrH
dn
I
-+
Dx
fe
9*
r
-q^l
=o;
0r
zDf2s
(6s)
ypaBHeHHe Hepa3pblBHocrH
dW
=
edt,
rAe
O-
pacxoABotrbr.
fiagpaenHqecrnfi nepexogHufr rpoqecc
B r(oporr(oM
Bo[onpoBo[fliueM
TpaKTe f3O Mo)KHo 3anucarb
ypaBHeHHeM
HeycTaHoBnBrrrerocfl
Apr{xe-
rur Hecxuuaeruoft
xffAKocrr,I
B BoAoBoAe
c
xecrKl{Mr{
creHKaMr{
H=Hrr+
h*+h2*h^,
f
0x
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0r
3ru
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BbIpaxeHHeM cKopocru
c
pacnpocrpaHeHn,ff
yaapHofi
BoJIHbI
qepe3
ynpyrne
csofrcrsa BoAonpono!,fl'
rqeft cncreMbl
lt Bog,bl.
Dlts,
Mo[enupoBa]Iuff
rl{ApaBnnqecKoro
yAapa
pa3AenHM
BoEoBor Ha
fracrKn
ErmHoft
Ax,
npI,tHffB
EJtff
Kax.u,oro H3
HHx
),
=
const.
Pacqer
rntr-
paBnnqecKoro
yaapa
B BoroBotrax
f3O
cBor$ren
K
petueHulo
ypaBHernfi
(65),
(66)
orHocnrenbHo
rlepeMeHHwx
H(x,
t)
u
Q(x,
t) npu
3aAaHHbIx
HaqanbHbrx
ycnoBuflx.
nln
HHTerpHpoBaHHff
ypaBHeHHfi
rHupaaJrnqecKoro
yaapaHcnonb3ylorcfl
pa3tnqHble npubnnxeHHble Mero,qbl.'\
Vparueuua
(65)
u
(66)
MoxcHo
3am{carb
B
KoHeqHo-pa3Hocrnofr
Qoprrae:
(63)
(64)
rtre
H
-
A,eficrsyroqr.rii
Hanop;
Hr,
-
crarrqecKnfr nanopi
hr"r
u
ht
-
no-
TepH Harropa
MecrHbre H no
SIIHHei
hn
-
HHepu{ornrnrfi
Hanop.
florepu Hanopa
ft,
n rogoBo[e
rrpH
nepexoAlroM
rpoqecce
npHMeM
c
Ao-
[yueHHeM
KaK
Arrff
ycTaHoBr,rBrxerocf
pexHMa:
,.
=
ug
(;
Ei_
*
i
tr),
Tts
\
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