Курбатов Ю.Л., Шелудченко В.И., Кравцов В.В. Механика жидкости и газа: Учебное пособие
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M<1
(,ll,OKplITJ1qeCKOe HCTeqeHHe), TO 3HaKH
dw
H
df6y,D,yT
npom-
BononmKHbIMH,
T.e.
npH
YMeHbUJeHHH CeqeHH5I
CKOPOCTh
ysenHqHBaer-
C5I,
conno
HMeer
<popMy
KOH<PY30pa;
ecnH
M > 1
(cBepxKpHTHqeCKOe
HC-
TCqeHHC),
TO
3HaKH
dw
H
df
O,ll,HHaKOBbI, T.e.
np"
YBenHqCHHH CeqCHH5I
CKOPOCTb
YBenHqJ1BaerC5I, COruIO
HMeer
<P0PMY ,ll,H<p<pY30pa;
CCJIH
M =
1,
TO
df
=0,
T.e. CeqeHHC
51Bn51erC5I
3KCTpeMaJIbHbIM (MHHHMaJIbHbIM),
HnH
KplITJ1qeCKHM.
TaKHM
06Pa30M,
)J,ll5I nonyqeHH51 ,ll,oKpHTHqeCKOU CKOpO-
CTH
(w<a)
npHMeIDllOT
c)')KHBaIOIl(HeC5I
conna;
)J,ll5I
nonyqeHH5I
cBepx-
KplITHqeCKOU
(cBepX3ByKoBOU)
cKopocm
(w>a)
npHMeH5IIOT KOM6HHH-
pOBaHHoe
conno
(conno
JIaBan5I, H3BeCTHoe H3
Kypca
TepMO,ll,HHaMHKH),
COCT05lll1.ee H3 c)')KaIIJ;euc5I
qaCTH, B KOTOPOU nOTOK YCKOp5lerCSI
,ll,0
CKO-
pocm
3ByKa,
H paCIlIlfp5lIOIIJ;eUC5I, B KOTOPOU
CKOPOCTh
nOTOKa ,ll,OCTHraer
cBepx3ByKoBoro
3HaqeHH5I,
paCCqHTbIBaeMoro
no
<popMyne
(106).
5)
B
npoQecce
HCTeqeHH5I
npH
a,D,Ha6aTHbIX
ycnoBH5IX
YBCJIHQHBaerC5I
y,ll,CnbHblu
06'beM
ra3a
H YMCHbUJaercSi
cro
TeMncpaTYPa.
TIapaMerpbI
ra-
3a
B KpHTHQCCKOM H
nI060M
,ll,pyrOM CeQeHHH, B T.Q. H BblXO,ll,HOM,
pac-
CQHTbIBaIOTCSI
C nOMOIIJ;bIO fa30,ll,HHaMHQeCKHX <PYHKQHu:
- OTHOCHTenbHaSI
CKOPOCTb
.---~--------~
A=~=
~[I_(h)K~ll;
w
Kp
.
K-l
PI
(110)
- OTHOCHTenbHoe ,ll,aBneHHe
K
1t=
~
=(1-::~A2l-1;
(111)
- OTHOCHTenbHaSI nnOTHOCTb
I
£=:1
=(1_::~A2)K-l;.
(112)
- OTHOCHTenbHaSI
TeMnepaTYPa
T
K-1
2
't'=--=I--).;
T)
K+l
(1l3)
87
B
KpHTlflIeCKOM
CeqeHHH
corum
JIaB<lJUI
A=
1 H ra30,lJ,HHaMHqeCKHe
q,y"~HH
(110, 111, 112, 113)
npHHHMaIOT
BH,LI;:
K
It
- .
(
2
)K-1
Kp.
-
K+l
'
(114)
1
E - .
(
2
)K-1
Kp.
- K+ 1 '
(l15)
2
t=--.
K + 1
(116)
6)
KpHTHqeCKOe
H BbIXO,lJ,HOe CeqeHHSI
conJIa
JIaBaJISi onpe,lJ,eJISIIOTCSI
H3
ypaBHeHHSI pacxo,lJ,a
(cnJIOllIHocrn):
G
f
Kp
=---
PKpWKP
G
f
SbIX
::::----
PSblXWSblX
me
G -
MaccoBbIH
paCXO,lJ,
ra3a,
Kr/c.
,1lrIHHa paCllIHpSlIOll\eHCSI qaCTH
conJIa
paCCqHTbIBaeTCSI
no
ymy
pacKpbl-
THSI,
npHHHMaeMoMY
B npe,lJ,eJIax 7
...
11
o.
6.4.
HCme'leHUe
KanenbHoii
}lCUOKOCmU
nod
yposeHb
ECJIH
npocTPaHcTBo,
Ky,lJ,a
BbITeKaeT
JKH)J,KOCTb,
TalOKe 3anOJIHCHO
)l(H,lJ,KOCTblO
(pHc.44),
TO
roBOPSlT,
'ITO
HCTeqeHHC npOHCXO,lJ,HT no,lJ,
ypo-
BeHb
(HHoe
Ha3BaHHe
-
HCTeqeHHe
qepe3
3aTonneHHoe
oTBepcTHe).
CKO-
POCTh HCTeqeHHSI H pacxo,lJ, MO)l(eT
H,
PHCYHOK
44
HCTe'leHHe
H,-
6bITb
paCCQHTaII
no
H3BCCTIIOH
q,op-
MYJIe T
opmemIH
w
=Jl.~2gHO
,M/C
V=f'Il·~2gHO,
M
3
/C,
r,lJ,e
Ho
- npHBe,lJ,eHHblH
Hanop,
M,
11
-
K03q,q,HIIHCHT
paCXO,lJ,a,
3aBHcSlIIIHH
OT
q,OpMbl
HaCa,lJ,OK
3aTOnJlCHHOC
(CM.
E - 4.2).
npH
nOCTOSlHHbIX ypOBHSlX
HI
H
H2
H
88
BHeUlHMX
,naBJIemrnX
PI
H
P2
rrpHBe,neHHbIM
Harrop
orrpe,nemreTCH
rro
IPOpMyJIe
Ho
=H+
P)-P2
pg
6.5.
HCme'leHUe
KanenbHOii
)f(UOKOCmu
npu
nepeMeHHoM
yposHe
TTo,no6HbTe
3a,naqH
BCTPeqalOTCX
rrpH
BbTTeKaHHH
)KH,nKOCTH
(BO,nbl,
HeIPTenpo,nYKTOB
H ,np.)
H3
6acceMHoB,
6aKoB,
pe3epByapoB,
URcTepH.
06bIQHO
TPe6ycrcx
onpe,neJIHTb
BpeMX,
Heo6xo,nHMoe
.nmr
OnOpO)KHe-
HHX
eMKocTH.
F
'/
'//
I
h
i
_ I ,J'Ll
\ f
=§~
f
I
'"
I
PaCCMOTPHM
npocTeMUlHM
CJl)"IaM
HCTeqeHHX
KarreJIbHOH
)KIf,nKOCTH
H3
co-
cy,na
nOCTOXHHoro
CeqeHHX
F
Qepe3
OT-
BepcTHe
B
,nHH~e
llJIO~a.nblO
f
(pHC.4S).
,ll,BH)KeHHe
HeCTaQHoHapHo,
T.K.
Harrop co
BpeMeHeM
YMeHbUlacrcH,
H
KaK
CJIe,nCT-
BHe
YMeHbUlacrcx pacxo,n Q
(M
3
/C).
PHCYHOK
45
- K
BblBOAY
«JIOPMYJlbI
HCTeqeHHH
3a
6eCKOHeQHO
MaJIbTM
rrpOMe*y-
TOK
BpeMeHH
dt
ypOBeHb
onyCTHTCX
Ha
MaJIYIO
BeJIWurny dh, H
TeqeHHe
MO)KHO
CqHTaTb
CTaQHOHapHbIM.
KOJIHqeCTBO
BbITeKUleM
)KH,nKOCTH
paBHO
dV=Q·dt
HJIH
dV =
~
. f
.figh
. dt
C
,npyrOM
CTOPOHbI
dV=-F·dh.
Tor,na
-F·dh=~·f~2gh
·dt
OTKY,na
dt=
F·dh
~.f~2gh
(117)
89