Курбатов Ю.Л., Шелудченко В.И., Кравцов В.В. Механика жидкости и газа: Учебное пособие
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IIpH
YMeHhllIeHHH
,l1.HaMeTpa
Ha
20%:
APTP
= 15· (
_\0
]5
=
45,78MM.B.CT.
1 100
3allaqa
N!~6.
KaK
M3MeHMTCH
nponycKHaH cnoco6HoCTh
llhIMOBoro
KamlJla
(pacxoll
llhIMOBhIX ra30B),
eCJIH
npH YBeJIlflleHHH
llHaMeTpa
Ha
20%
pa3HHlJ,a
PI
-
P2
OCTaHeTCH
HeH3MeHHOH
(CM.
3a,l1.aQH
N!!4 H
N!!5)?
PellIeHHe.
Pacxo,l1.
llhIMOBhIX ra30B onpe,l1.emlM C
(II
7.15):
1t 5
2·~p
·_·d
Tp 4
V=
').,.
£. p
(II
7.19)
CJIe,l1.0BaTeJIhHO:
v
~.fci
.
(II
7.20)
CooTHollIeHHe pacxollOB
llm!
llByx
pa3Hhlx llHaMeTpoB (npH npOqHX
paBHhlx
YCJIOBHRX):
(II
7.21)
HJIM
(II
7.22)
IIpH
YBeJmqeHHH
llHaMeTpa
Ha
20%:
(
1
+
20
)5
V 2 =
35409·
~
= 35409 ·1,58 = 55860 M'/q
IIpH
YMeHhllIeHHH
Ha
,l1.HaMeTpa
Ha
20%:
V,
~
35409·
J(
l-ll~~
r
~
35409· 0,57
~
20269 M'/q
200
3allaqa
N
o
7.
)J;aBJIeHMe
B KaMepe npOMTenJI03HepreTMqeCKOH
YCTaHOBKM
(I1TY)
PI=
1 MM.B.CT., pa3pX)I(eHlle
nepell
TxrOBbIM
CpellCTBOM
P2
=
20
MM.B.CT.. fMllPOCTaTMqeCKMe nOTepM npM
3TOM
COCTaBJIXIOT
10%
OT
06IIJ.ero conpOTMBJIeHMX llbIMOBOro TPaKTa;
pa3HMQa
Me)l(llY
llMHaMMqeCKMMM
llaBJIeHMXMM B HaqaJIe M
KOHQe
TPaKTa npeHe6pe)l(MMO MaJIa.
KaK
M3MeHMTCX
llaBJIeHMe B KaMepe
I1TY PI npM
HeM3MeHHOM
pa3pX)I(eHMM
P2,
eCJIM
TenJIOBaX
MOIIJ.HOCTb
YBeJIMqMTCX
Ha
5%?
3allaqy
pernaTb llJIX llBYX BapMaHToB:
1)
KaMepa
M llbIMOBOH
TPaKT
ra30nJIOTHbI;
2)
llbIMOBOH
TPaKT
ra30nJIOTHbIH, a
KaMepa
Hera30nJIOTHa, npMqeM
YTeqKM
llbIMOBbIX ra30B
nponoPQMOHaJIbHbI
~
M
COCTaBJIXlOT
B
MCXOllHOM
BapMaHTe
2%
OT
06IIJ.ero
pacxolla?
PerneHMe.
)J;aBJIeHMe
B KaMepe
nTY
MO)l(eT 6bITb OnpelleJIeHO
M3
ypaBHeHMx
nepHYJIJIM:
PI+PIIHHI=P2+PIIHH2
+dPTJl+dPMc+dPr.
110
YCJIOBMlO:
PIlHIl
I
=PIIHH2
06IIJ.Me nOTepM (dPI=dPTJl+dPMc+dPr):
dPI=
PI-P2
dPI
=
1-
(-20)
=
21
MM.B.CT.
(n
7.23)
CYMMY nOTepb Ha TpeHMe B
MeCTHblX
conpOTMBJIeHM5IX
OnpelleJIMM
qepe3
dp:
dp
=
dprp
+
dpMC
fMllPOCTaTMqeCKMe nOTepM
no
YCJIOBMlO:
dpr=
0.1 .
dPI
dpr
=0,
I . 21 = 2,1
MM.B.CT.
CYMMa nOTepb B 6a30BoM BapMaHTe:
dp
=
dPI
-
dpr,
dp
= 21 - 2,1 = 18,9
MM.B.CT.
I)
B cJIyqae ra30nJIOTHOH KaMepbI I1TY
pacxoll
llblMOBblX ra30B
nponoPQMOHaJIeH
TenJIOBOH
MOIIJ.HOCTM,
a
TaK
KaK
CYMMa
nOTepb
dp
nponOpnMOHaJIhHa
KBallpary
paCXOlla,
TO
OTHOllJeHMe
nOTeph
nponopn:MOHaJIbHO
KBallpary
OTHorneHMH
paCXOllOB:
201
~PII
=(VII
)2
~p,
V,
'
n
7.24)
OTKY,l1,a:
1,05· VI
( )
2
~PII
=
18,9·
VI
= 20.8MM.B.cr.
113
(II
7.23):
PI.n =
P2.n
+
(ilpn
+
ilpr)
(n
7.25)
PI.n = -
20
+
(20,84
+
2,1)
=
2,94
MM.B.CT.
2)
B
cnyqae
Hera30nnoTHoH KaMephl
nTY.
YTeqKM
,l1,hIMOBhIX
ra30B B
6a30BoM
BapMaHTe
COCTaBmUOT:
2
il
VI
=
_.
VI
= °
02·
VI
100 ' ,
pacxo,l1,
ra30B, KOTophle
npOXO,l1,flT
qepe3
,l1,bIMOBOH
TpaKT:
VI'=Vr-ilV
r
,
V
r
=
(1-
0.02)·VI=
0.98·Vr.
YTeqKM ra30B
no
ycnOBMIO
nponoPQMOHaJIhHhI
~,
3HaQMT,
npM
nOBhlllleHMM TennoBoH
HarpY3KM
MX
MO)l(HO
paCCqMTaTb
no
!J>0pMyne:
MnM
PI,I!
ilVI!
=
0,02·
VI'
--
PI,I
Pacxo,l1,
ra30B
Qepe3
,l1,hIMOBOH
TpaKT
COCTaBnfleT:
Vn'=V
n
-
il
Vu
,
MnM
(II 7.26)
, PI,II (
~)
VII=1,05·Y
I
-O,02·Y
I
·
--=Y
I
·
1,OS-O,02·
VI
-
I
-
.
Pl,1
CYMMa IIoTeph:
YII
(
')2
L\PII
=
L\PI'
V'I
'
MnM
202
\2
1 05 - 0 02 .
~
PI, II V
, ,
l'
I
dPIl
= 18,9·
0,98·
VI
YpaBHCHHC
ECPHYJIJIH
(11
7.25)
,nmr
:noro
cJIyqasr npHMcT
BH,n:
[
1
05
_ 0 02.
{PI,
II
2
, ,
V-I
PI
II
=-20+
18,9· +2,1
,
0,98
Pcwasr
3TO
ypaBHcHHc, nOJIyqHM:
PI,II
= 2,5
MM.B.CT.
TaKHM o6pa30M, B cJIyqac
HCra30nJIOTHOCTH
,naBJICHHC
B KaMcpc
I1TY
nOBbIIuacTcsr B MCHbllICif
CTcnCHH,
qCM
B
cnyqac
ra30nJIOTHOCTH.
3a,naqa )(08. HaifTH
CKOPOCTb
HCTCqCHHsr
npHpo,nHoro ra3a
H3
ropCJIKH npH H.<l>.Y. H ,ll,.<l>.Y. ,nml
YCJIOBHif:
,naBJICHHC
ncpc,n
ropcJIKoif
Pr=300
MM.B.CT.,
nJIOTHOCTb
ra3a npH H.<l>.Y. pro=O.72
Kr/M
3
;
TCMncpaTypa ra3a
tr=30
°C,
,naBJIeHHe
B KaMepe
I1TY
PK=35
I1a,
aTMOClPepHOe
,naBJIeHHe
B=730
MM.pT.CT.,
K03IPIPHU:HCHT
HCTeqCHHsr
<p=0.95.
PeIlICHHe.
CKOPOCTb
HCTCqCHH5I
npH ,ll,.<l>.Y.:
w =
q>'
J2.
(pI'p -
PK),
11
7.27)
I1JIOTHOCTb
ra3a
npH
,ll,.<l>.Y.
Ha
Bblxo,ne
H3
roPCJIKH:
273
B+PK
PI'
=PI'o'
273+t
'101300'
I'
=072.
273 .
730·133+35
=0
622
Kr
/
PI' ,
273+30
101300 ' / M
3
'
(11
7.28)
w = 0
98.
2·
(300.
9,8-35)
=
94
5MI
,
0622
'
Ic
.
,
203
CKOPOCTb
MCTeqeHHJI
npM H.ct>.y.:
w
w
--------
o - 273 +
tr
101300'
273
B+PK
94,5 = 81,6
M
/
c
.
W 0 = -2-73-+-30--1-0-13-0-0- / C
273
730·133+35
(II
7.29)
3allaqa No9. OrrpellenMTb Heo6xollMMoe
llaBJIeHMe
B0311yxa
rrepell ropenKoH, qTo6hI
o6eCrreQMTb
MCTeQeHMe
C
CKOPOCThlO
w=55
M/C
rrpM
,Ll.ct>.y.,
ecnM
TCMrrcparypa
B0311yxa
350
DC,
llaBnCHMC
B
KaMepC
IlTY
PK=3
MM.B.CT.,
aTMOC<pCPHOC
llaBneHMC
B=745
MM.pT.CT.,
K03<p<pMIJ.MeHT
MCTCqeHM5I
<p=0,92.
PellIeHMe.
Heo6xOllMMOe llaBneHMe
Orrpellen5lCM
M3
ypaBHeHH5I
(II
7.27):
W
2
.p
PB
=
--2
+
Pk·
(II
7.30)
2·
<p
IInoTHocTh
B0311yxa
npM
,Ll.ct>.Y.
(II
7.28):
=1293.
273 .
745·133+3·9,8
=0554
Kr
/
PrI
, 273 + 350 101300 ' / M
3
,
55
2
.0,554
PB
= 2 +
3·9,8
=
1020Ila
=
104MM.B.cT.
2·0,92
3allaqa
No
1
O.
PaCCQMTaTb
pa3MepbI
KOnbIJ.eBOH
llJ,enM
M5I
BhIXOlla
B0311yxa
M3
ropenKM
lln51
ycnoBMH:
pacxoll
B0311yxa
rrpM
H.<D.Y. Vo=10000 M
3
/C,
CKOPOCTb
B0311yxa
rrpH
,Ll.ct>.Y.
w =
60
M/C,
TeMrrepaTypa t =
250
DC,
llaBneHHe
Ha
BbIXOlle
H3
rOpCnKH
p = 2
MM.B.CT.,
aTMOc<pepHoe
llaBneHHC B = 735
MM.B.CT.;
BHyrpeHH5I5I
rroBepxHocTh
KonbIJ.eBOH
llJ,enM
o6pa30BaHa ra30BoH
rpy60H
C
HapY)KHhIM
llHaMcrpOM d
r
= 1 08
MM.
PellIeHMe.
DonbllIMH llMaMeTp
KOnhIJ.eBOH
llJ,CnH
DB
HaXOllMM
M3
6anaHCa
rrn
° llJ,all C
H:
1t.D
II
=F
+1t.d
2
,
4
II
4'
204
(II
7.31)
D -
!4.P
s
+d
2
r
A-V
11:
BbTXO.L\HOe
Ceqemle
.L\nn
S03.L\yxa:
R =
Vao
B ,
Wo
SbTXO.L\Han
CKOPOCTb
S03.L\yxa
npH
H.<l>.Y.
(n
7.29):
W RO = 273 + 250 60 101300 = 30,2
%,
273
735·133+2·9,8
P = 10000 = 0 092M
2
R 3600. 30
2'
,
,
DR
=
4·0,092
+ 0,108
2
= 0,359M =
359MM.
11:
(n
7.32)
(n
7.33)
TaKHM
o6pa30M, Konbilesan
rn;enb
.L\nn
SbTXO.L\a
S03.L\yxa
HMeeT
pa3MepbI:
60nbllIHu
.L\HaMeTp
D
B
=359
MM.,
MeHbllIHU
- d,=108
MM.
3allaqa
No
11.
PaCqeT
conna JIasann.
PaCCqHTaTb
conno
.L\mI
nO.L\aqH
KHCnOp0.L\a
H3
ycnosHu:
-
pacxo.L\
npH
H.<l>.Y.
Vo=900 M
3
/q;
-
H36bTTOqHOe
.L\aSneHHe
nepe.L\
connOM
PI=5
Kr/cM2;
-
H36blTOQHOe
.L\aSneHHe
Ha
SbIXO.L\e
H3
conna P2=200
MM.S.CT.;
- TeMnepaTypa
nepe.L\
connOM
t
l
=20
dc.
PellIeHHe.
1)
HaXO.L\HM
KpHTHQecKYIO
H
SbIXO.L\HYIO
CKOPOCTH
KHCnOp0.L\a
C
IlenblO
onpe.L\eneHH~
<i>OPMbI
conna.
KpHTHqeCKa~
CKOPOCTb:
a6c
2.k
PI
w
Kp
=
--.--
(n
7.34)
k+
1 PI
k = 1,4 -
nOKa3aTenb
a.L\Ha6aTbI
.L\nn
.L\BOaTOMHbIX
ra30S;
PI
a6c=PI
H36+
B
=5·98000+ 100000=598000
na;
B=100000
na
(npHHHMaeM);
205
PI
=
IIJIOTHOCTh
KMCJIOpO,D,a
IIepe,D,
COIIJIOM
(n
7.28):
= 1
43
. 273 . 598000 = 7
86
Kr
/
PI
,
273
+ 20 101300 ' /
M3
W
Kp
= 2 ·1,4 . 598000 =
297,9%
.
1,4+1 7,86 C
BhIXO,D,Ha»
CKOPOCTh:
W BblX =
<po
2'TI._k_.
PI
k-l
(IT
7.35)
<p
= 0,97
(IIpMHMMaeM),
P2a6c=P2H36+100000
= 200·9,8+100000=101960
ITa.
W = 0
97·
2·
598000
'~'[1-(
101960
)I':~I
1 = 445 9
M1
BblX'
7
86
1 4
-1
598000 ' 7 C
, ,
TaK
KaK
W
BblX
> W
Kp
MCTeqeHMe
KMCJIOpO,D,a
,D,OJI)l(HO
IIPOMCXO,D,MTh
qepe3
KOM6MHMpoBaHHoe
COIIJIO
(COIIJIO
JIaBan»),
COCTO»llI,ee
M3
cY)l(aJOllI,eHc»
M
paclliMp»JOllI,eHc»
qaCTeH.
2)
OlIpe,D,eJI»eM
KpMTMqeCKOe
CeqeHMe
M
,D,MaMeTp
COIIJIa
JIaBan».
CeqeHMc:
f = VO'Po
Kp
(IT
7.36)
w
Kp
'P
Kp
nJIOTHOCTh
B
KpMTMqeCKOM
CeqeHMM
HaXO,D,MM
M3
ra30,D,MHaMMqeCKOH
cl>YHKI..\MM:
I
PKP
=
=(_2_)k-1
-E
Kp
,
PI
k+
1
I
=786.(_2_)1,4-1
=4
98
Kr
l
P
Kp
, 1,4+1 '
1M
3
'
f = 900·1,43
=241.1O-
4
M
2
.
Kp
3600. 2
97
. 4
98
'
, ,
206
(ll
7.37)
d
Kp
=
4·2,41·10
= 0,0175M =
17,5MM
.
3,14
3)
Onpe.l1:eJUleM
BbIXO.l1:HOe
Ceqemfe
II
.l1:lIaMe1'p
conJIa
JlaBaJUI:
YO'Po
f BbTX =
-----".~-'=---
W
BblX
• P
BblX
(IT
7.38)
(IT
7.39)
ITJIOTHOCTb B lICX0.l1:HOM
CeqeHlIlI
HaX0.l1:lIM C
ra30.l1:lIHaMlIqeCKOH
CPYHKQlIlI:
(IT.40)
r.l1:e
A = W
BblX
• A = 445,9 = 1 497' A = 2 24
W
KP'
297,9 ' , "
1
= 7
86.(1_
1
,4-1.
224
)1,4-1
= 2 443
Kr
/
PBbIX'
1,4+1'
, / M3 '
f = 900 ·1,43 =
328
.1O-
4
M
2
BblX
3600.445
9·2
443 '
, ,
lICXO,l(HbIH .l1:lIaMeTP:
d =
~4'
F
BbTX
BblX
,
1t
(IT
7.41)
-4
d
4·3,28
·10 = 0,0204M =
20,4MM.
BbTX =
It
4) HaXO.l1:lIM
.l1:JIlIHY
paCllIJt:pSnorn:eHC$I
qaCTlI
COTIJIa,
npHHlIMa$l
yroJI
paCKpbITlI$I
a = 9°:
dB,"x
-d
KP
f=---.:....
2· tg"i '
f = 20,4-17,5 =
20,5MM.
2·tg1
207
(IT
7.42)
5)
Onpe~enfleM
~aBneHHe
H TeMneparypy B
KpHTHqeCKOM
CeqeHHH
KHcnopo~a,
Hcnonh3Yfl
ra30~HHaMHqeCKHe
IPYHKl\HH.
}l,aBneHHe:
a6c
-~
PKP
( 2
)k-I
pf6c
=1t
Kp
:::
k+l
1,4
pa6c
:::
598000
.(_2_)1,4-1
:::
315912TIa
Kp
14+1
'
,
p~~c
:::
315912
-10000:::
215912TIa
:::
3,22
K%2
.
TeMneparypa:
T
Kp
2
--='t
:::
T
1
-
KP
k+l'
T
Kp
::: 293·
_2
-:::
244K
=
-29
D
C.
1,4+ 1
(II 7.43)
(TI 7.44)
6)
Onpe~enfleM
TeMneparypy H
~aBneHHe
KHcnopo~a
Ha
Bblxo~e
H3
conna, Hcnonh3Yfl
ra30~HHaMHqeCKHe
IPYHKl\HH:
T BbIX
==
't
= 1 _ k - 1 .
')...2
TI
k+l'
T = 293 .
(1-
1,4
-1
. 2 24
2
) = 184 K =
-89
D
C.
BblX
1,4
+ 1 '
(II.46)
TaKHM
o6pa30M,
conno
JIaBanfl
~nfl
3a~aHHblX
ycnoBHll
HMeeT
napaMeTphI:
KpHTHqeCKHll
~HaMeTP
d
Kp
= 17,5
MM.;
BhIXO~HOll
~HaMeTP
d
Bb'X
=20,4
MM.;
AJIHHa
paCllIHpflIOllI.ellCflqaCTH f
=20,5
MM.;
H36
22
I
~aBneHHe
B
KpHTHqeCKOM
CeqeHHH
PKP
=3,
Krc M2;
TeMnepaTypa B
KpHTHqeCKOM
CeqeHHH
t
Kp
= - 29
DC;
TeMnepaTypa B
HCXO~HOM
CeqeHHH
t
BblX
= - 89
DC.
3a~aqa
NO
12.
PaCCqHTaTh
nonHoe
~aBneHlfe,
KOTopoe
~omKeH
pa3BHBaTh
BeHTHJTSlTOP,
nO~aIOllI.Hn
B03~yx
no
~ByM
napanJTeJThHblM
TpaKTaM.
COnpOTHBJIeHHe
o6men
qaCTH
ceTH
(~o
pa3BeTBJTeHHSl)
~Po6u\
= 200
na,
cyMMapHoe
conpOTHBJTeHHe
nepBoro
TpaKTa
~PI
=
208
soo
na,
BTOpOrO
-
~PII
= 300
na,
CKOPOCTb
B03,lJ,yxa
Ha
BbIXO,lJ,e
H3
nepBoro
TPaKTa
npH
H.<I>.Y.
W',o
= 30
M/C,
H3
BToporo WH,
o=SO
M/C,
TeMnepaTypa
B03,lJ,yxa
t=
200°C,
,lJ,aBJIeHHe
Ha
BbIXO,lJ,e
H3
nepBoro
TPaKTa
PBb1x.I
= 5
MM.B.CT.,
H3
BToporo -
PBblx.lI=
3
MM.B.CT.,
K031PIPHIIHeHT
HCTeqeHHH
«>,=
«>,,=0,98.
PellIeHHe.
nOJIHOe
,lJ,aBJIeHHe
BeHTHJIHTOpa
PnOBH=PCT
+Pi\HH
onpe,lJ,eJIHeTCH
,lJ,JIH
,lJ,Byx
CeqeHHH:
Ha
BhIXO,lJ,e
H3
BeHTHJIHTOpa
H
Ha
BXO,lJ,e
H3
ceTH:
PCT1,
j+Pi\1I111,
j=
PCT2,
j+
Pi\IIH1,
j+(~Po61l\+~Pj)
.
,ll;HHaMHqeCKOe
,lJ,aBJIeHHe
Ha
BbIXO,lJ,e:
W20i'PO
273+ti
101300
P1VfH2,i
=
2.'
273
. B .
2·«>
,
+p,
,ll;JIH
nepBOrO
TPaKTa:
=
5.9
8 +
30
2
·1,293
273
+ 200
10
1300 + (200 + 500) = 1 786I1a.
Pllomd
'
2·0
98
2
273
740 ·133 + 5
·9
8
, ,
,ll;JIH
BToporo
TPaKTa:
=
3.98
+
50
2
·1,293
273
+ 200 101300 + (200 + 300) = 3424I1a.
Prront,II
'
2.098
2
273
740.133+3.98
, ,
TaK
KaK
,lJ,JUI
o6eCneqeHHH
pa60TbI BToporo
TPaKTa
nOTPe6JIHeTCH
60JIbllIee
,lJ,aBJIeHHe,
BeHTHJIHTOP
BbI6HpaeM
H3
YCJIOBHH:
H
BeIlT
?:
3424
na.
209