Mehanika Fluida KV

7/24/2019 Mehanika Fluida KV

1/199

, 2005.


2/199

. ,

. ,

:

, .

, .

.

:

.

.

:

ISBN

: 250

: ,


3/199

. .


4/199

1. 1-

1

1.1

1

1.1.1 1

1.1.2 3

1.1.3 3

1.2

4

1.2.1 4

1.2.2 . 4

1.3. 6

1.3.1 6

1.3.2 . 9

1.3.3 . -

9

1.3.4 12

1.3.5

15

1.3.5.1

18

1.3.5.2

20

1.3.5.3 .

21

1.3.6 23

1.3.6.1 24

1.3.6.2 25

2. 2 28

2.1 . 28

2.2. - 33

2.3 42

2.4 . 68

2.5 92

2.5.1 92

2.5.2 104


5/199

3. 3

114

3.1 114

3.2 1203.3 - 144

3.4 158

3.4.1 158

3.4.2 166

3.5 182

4. 191


6/199

,

-o

*.

,

,

.

1,

,

,

- -

.

,

.

,

.

,

,

,

.

2 3 ,

,

,

.

2,

, , . ,

.,

,

.

3,

, ,


7/199

, . ,

,,

. ,

-.

1.

,

,

, 3+3 .

,

.

,

,

.

,

.

, .

. ,

. . ,

,

.

,

,

,

.

, 2005. .


8/199

1

.

.

, . .

-

, .

1.1

1.1.1

, (, )

,

. , ,

,

.

.

:

1)

,

,

.

EvdivSpEP )3

1(2

(1.1)

: P , - ,

S - , . vdiv

- .


9/199

1 2

ijpP ijsS

.

(1.1)

,

3

)(

3

kk

k

k

zzyyxxii

sx

vvdiv

ppppp

(1.2)

ijs

1,2,3.ji,,)(2

1

i

j

j

ijiij

x

v

x

vss

(1.1)

),3

1(2 vdivspp ijijijij

(1.3)

ij -

ji

jiij

0

1 .

(1.3)

. ,

,

).(

i3

22

x

v

y

vpp

vdivx

vpp

yxyxxy

xxx

(1.4)

2) ,

,


10/199

3

A

AdqQ ),(

q

dAnAd

- .

1.1.2

. :

,

.

.

,

,Re

vDvD (1.5)

.

.

1.1.3

,

.

:

, ,

, .


11/199

1 4

, ,

.

,1

d

dpdp

dS

(1.6)

1.2

.

1.2.1

:

1)

2)

.

,

.

.

.

.

,ppppzyx

: .

1.2.2 .

V

.

: .


12/199

5

,

V A ApddVF .0

, .

A V

gradpdVApd .

V

dVgradpF .0)(

V ,

,

,

,01

gradpF

.1

gradpF

V

dVF

A

Apd


13/199

1 6

.

1.3

, , .

:

,

.

, .

1.3.1

m m mV V A

kjkijiji dAdVdVfDtD ,......... (1.7)

: hij hkij, h=f, ,, , .

, .

(1.7). Vm,

, Dt

D .

(1.7)

,

(1.7). f, . (1.7)

ij , , Vm, kij ,

, Am,.


14/199

7

(1.7)

.

k

jik

jiji

xfv

tf

DtDf

......... (1.8)

fij, vk(xi,t)

, (1.9)

m m mV V A

kkji

ji

ji dAvfdVt

fdVf

Dt

D,...

...

... (1.9)

,

(1.7). -

(1.9)

m mV V k

kjiji

ji dVx

vf

t

fdVf

Dt

D)(

......

... (1.10)

(1.8)

m mV V k

kji

ji

ji dVx

vf

Dt

DfdVf

Dt

D.)( ...

...

... (1.11)

V , , t

Vm . ,

A=Am.

,

V V

ji

ji dVt

fdVf

dt

d.

...

... (1.12)

(1.9) (1.12)

V AA

kkjiji

V

ji

mm

dAvfdVf

dt

ddVf

Dt

D

,

......... , (1.13)


15/199

1 8

:

V,

. .

,

m s ssmV V tAA

kkskjiji

s

ji dAvvfdVfdt

ddVf

Dt

D

)( )( )(

)(......

)(

... .)( (1.14)

(1.7)

(1.10)

mV k

jki

ji

k

kjijidV

xx

vf

t

f.0)(

...

...

...... (1.15)

,

. (1.16)

....

...

......

k

jki

ji

k

kjiji

xx

vf

t

f

(1.16)

(1.7) ,

, , . (1.16)

(1.12)

.)(...

...

...

... dVxx

vfdVf

dt

d

V V k

jki

j

k

kji

ji

(1.17)

,

, . (1.17)


16/199

9

V A V A

kjkijikkjiji dAdVdAvfdVfdt

d............. (1.18)

(1.18) .

,

(1.17).

1.3.2 .

,

, .

mV

dVDt

D.0 (1.19)

(1.19) (1.7) :

,0

,

......

...

jkiji

jif

(1.16)

,0Dt

D0

i

i

k

k

x

v

x

v

t

(1.20)

(1.8).

(1.19),

(1.20) (1.18)

V

V A

iidAvdVdt

d, (1.21)

.

1.3.3 . -

, , :


17/199

1 10

. ,

(1.7),

m m mV V A

jjiii dApdVFdVvDtD , (1.22)

Fi F

pji

,

(1.22) .

(1.22) (1.7)

,...

...

...

,

,

kijki

iji

iji

p

F

vf

(1.22), (1.16)

.j

ji

i

j

jii

x

pF

x

vv

t

v

(1.20) (1.8)

:

.)(j

ij

i

j

ij

i

x

pF

x

vv

t

v

(1.23)

.

:

,)(t

v

k

k

x

pFvvDivPF

Dt

vD

(1.24)

p

,

),,(zyx

nnnn


18/199

11

.p

,

ji jjij

zzyyxxjjiijjn

dApdAn

npnpnpnpepnnPp

(1.25)

(1.18) (1.22)

V A V A

jijijjii dAnpdVFdAnvvdVvdt

d. (1.26)

,

.3

1)(

2

12 ijij

k

kij

j

i

i

j

ijij px

v

x

v

x

vpp

(1.27)

(1.27) (1.23),

, ,

,

),(3

1)(

2

2

k

k

ik

i

ii

k

i

k

i

x

v

xx

v

x

pF

x

vv

t

v

(1.28)

.vdiv3

1

gradvpFDt

vD (1.29)

- ,

(1.26),

A A

k

i

k

k

ii

V A V

ikkii dAx

v

x

vpdAdVFdAvvdVv

dt

d.)(

1

(1.30)

(1.30), ,

,

, . .


19/199

1 12

1.3.4

,

, . , (

2

2v)

,

m m m m mV V A V Aiijijiii dAqQdVdAvpdVvFdV

v

eDt

D

,)2(

2

(1.31)

Q , qi

i-.

, (1.31)

(, )

( ) .

(1.31)

f, (1.7).

,

,)(

),2

(

ki...j

i...j

2

...

kiki

ii

ji

qvp

QvF

vef

(1.16) (1.20)

.)()2

(2

i

i

j

iji

iix

q

x

vpQvF

ve

Dt

D

(1.32)

(2.23) vi


20/199

13

.)2(Dt

D

)

2(

2

2

DivPvvFv

x

pvvF

Dt

vD

j

ji

iii

(1.33)

(1.33)

(1.32).

j

iji

x

vpvP

,

)(z

p

y

p

x

pv

x

pvDivPv z

yx

j

ji

i

.

, . , (1.33)

.

,)(2

1

,

jiji

j

i

i

j

ji

i

j

ji

j

iji

j

iji

j

jii

j

ji

i

spx

v

x

vp

x

vp

x

vp

x

vp

x

pv

x

pv

(1.34)

. (1.34)

m m mm V A V

jijijijiii

V

dVspdAvpdVvFdVv

Dt

D.

2

2

(1.35)

(1.35)

. , Fi

U(x,t),

,F,i t

U

Dt

DU

x

Uvv

x

UF

iiiii

(1.36)


21/199

1 14

(1.33)

j

ji

ix

pv

t

UU

v

Dt

D

)2

(2

(1.37)

(1.34) (1.35)

, .

V (1.13), (1.35) (1.37),

A V

jijijiji

V A V

ii

dVspdAvp

dVt

UdAvU

vdVU

v

dt

d

.

)2()2(

22

(1.38)

(1.27)

.

n ,

, (1.27) :

.,

,pT-pEP n

iizzyyxxnn

nijijij

nnnnnT

nppp

(1.39)

,

- (1.30),

(1.35).

(1.27)

)0x

v(

k

k

(1.35)

(1.13)

V A V A A V

j

i

j

j

iiiiiiii

22

,dVdA)x

v

x

v(vdAv

pdVvFdAv

2

vdV

2

v

dt

d

(1.40)


22/199

15

ijijs

(1.27)

.)(2

1

22

1 222

i

j

j

i

ijijjiji x

v

x

v

ss

(1.41)

Fi(1.36) (1.38) (1.40)

.

1.3.5

,,

.

, ,

,

, ,

.

,

,

.

,

.

,

v(x,t), p(x,t) (x,t).

. ,

,

R

s rdrtrxvRA

Vtxv0

2,),,(21),(

(1.42)

: R , r . A

V

v(x,t)

vs(x,t).


23/199

1 16

R

s rdrtrxpR

txp0

2,),,(2

1),(

(1.43)

R

s rdrtrxR

tx0

2.),,(2

1),(

(1.44)

,

.

, .

.

,'fff (1.45)

: f -

f - f.

, (1.45),

).,('),(),( txvtxvtxv (1.46)

,

T

dttxvT

txv

0

.),(1

),( (1.47)

T

dttxpT

txp0

,),(1

),(


24/199

17

T

dttxT

tx0

.),(1

),(

,

(1.44) (1.47)

, , ,

.

A

2 .dAv

.

, , :

As

dAvAv

.1 22

(1.48)

A A

T dAvdAvAv

).(1 2'22

(1.49)

A

3dAv

.

,

vs3A,

, , :

As

dAvAv

.1 33

(1.50)

+2. ,


25/199

1 18

,

.

,

,)32)(3(4

)12()1(4

33

ttttt

Tnnn

nn (1.51)

nt .

, ,

,

A

sAppdAP . (1.52)

(1.52)

.

,

,

,

, .

.

1.3.5.1.

,

.

,

.

x (1).

1.

1

x1=x

2

x

V

v(x,t)

ydx

x1=x+dx

n

1n

2n


26/199

19

dx.

(1.21)

2

1

.)( 222111

x

x

AvAvdxAt

(1.53)

(1.53) dx.

dxxx 12 (1.54)

,)(,,

dxvAx

vAvAtxtdxx

(1.55)

, (1.54) (1.55),

:

.0)()(

x

vA

t

A (1.56)

(1.8), (1.56)

:

,011

Dt

DA

Ax

v

Dt

D

(1.57)

, (1.8)

Df/Dt= ,x/fvt/f f,A (1.58)

, .


27/199

1 20

1.3.5.2

(1.26) (1.27)

.

(1.26)

V A V

ijijijjii dVFdAnpvvdVvdt

d )( (1.59)

V A V

dVFdAnTnpnvvdVvt

)( (1.60)

(1.60) (1.39).

, 1,

(1.59), (1.60) . .

dx x(i=1, v1=vx=v) (1.59) (1.60):

A

wnxx

V

x

Atdxxtx

x

V

x

dxdxx

ApdxpA

xdApn

Adxdx

dy

gdVF

dxAvx

AvAvAvAvdAnvv

vAdxdVv

,)()(

;

;)(

;

2

,

2

,

2

2

2

221

2

11

(1.61)

: y ,

O=D - , v = v(x,t) w .

(1.61) (1.60), (1.59),


28/199

21

.)()( 2 Ddx

dygA

dx

dApAvp

xvA

tw

(1.62)

(1.56)

vvv

fw

82

2

(1.63)

(1.62)

02

1

vvDdx

dy

gx

p

x

v

vt

v

(1.64)

= (Re, /D) : Re=vD/- - . (1.64)

( 0t/v ) (=const.) (dy/dx=0) .

1.3.5.3 .

(1.38) (1.40) (1.36) (1.39)

:

V A A A V V j

iij dV

x

vdVFdAvnTdAnvpdAnv

vdV

v

t.)(

22

22

(1.65)

, 1,

.

1,(1.65) :

.2

()2

(22

dx

dygvA

vpvA

x

vA

t

(1.66)


29/199

1 22

(1.56) gy

(1.66)

, ,

.0)2

()2

(22

gypv

vAx

gyv

At

(1.67)

(1.67) ,

(1.56)

.2

2

xCgypv

, , (1.65).

(1.64). , (1.64) dx 1-1 2-2

:

2

1

2

1

.222

22

2

221

1

2

11

x

x

x

x

dxt

vdxvv

Dgy

pvgy

pv

(1.68)

(1.53).

2

12

x

xg dxvvDY

(1.69)

, . .

(1.68)

2

1

f(x). vza)(Y12in

x

xin dt

dvL

dt

dvxxdx

t

vY (1.70)


30/199

23

1.3.6

(1.68) (1.69).

,

.

. ,

, , , , .

.

, ,

., , :

Y Y.

Yg= Y+ Y. (1.71)

.

2

2v

Y (1.72)

- v .

,24

2v

R

lY

h

(1.73)

: - , l , Rh

Rh= A/O.


31/199

1 24

1.3.6.1

.

.

,

.

.

. , ,

,

, ,

, .

. :

1.

2.

.

. ,

.

, .

.

. .

. .

.

-


32/199

25

,)1( 2

1

2 A

A (1.74)

: 1 2

. ,

.

, , ,

. ,

, , ,

.

1.3.6.2

(1.73)

.

(, , ),

.

),(Re,D

(1.75)

: - D .

.

.

,

(1.73)

.

Re

64 (1.76)


33/199

1 26

,

. .,

,

.

.

. 4000

.

.8,0)log(Re21

(1.77)

4000 < Re < 40 000

.Re

316,04

(1.78)

40000

).7,3log(21

D (1.79)

, (1.79) ,

.

,


34/199

27

.)Re

68(11,0 4

1

D

(1.80)

(1.80)

.


35/199

2

, :

,

.

, ,

.

2.1 .

,

:

1.

2. .

.

:

pm ()

pv ()

P.

, ,

. ,

.

,

(),

:

p = pa+ pm

:

p = pa pv


36/199

29

pA,

Psti{ljivog fluida= pA.

(

),

,

.

Pnesti{ljivog fluida=pcA,

pc

.

.

,

pa

. 1, . 2. :

,

. pm,

.

pa+ pm.

pv,

.

pa pv.

2.

pm

Pv


37/199

2 30

,

,

.

().

1. h=?

p1p2. : hA, hB, , m. (3)

3.

,

. m .

m .

(I-I). , ,

. :

pA+ ghA+ mgh = pB+ ghB. (1.1)

.)(

g

hhgpph

m

ABAB

(1.2)

pA

pB

hAhB

I I

m

h=?


38/199

31

.

.

4.

4. II II.

II-II :

pA+ ghA= pB+ ghB - mgh. (1.3)

(1.1) (1.3) mgh (1.3). '''' '' '' .

(1.3)

,)(

g

hhgpph

m

ABAB

(1.2) .

.

pA

pB

hAhB

II II

m

h=?


39/199

2 32

2. h2=?

12. : 1, 2, , H1, H2, H3, h, h1.(5.)

5.

, .

I-I 5.

:

pa+pm+1gH1+2gH2+mgh2= pa+ pm+1g(H1+H3)-mgh1+1gh.(2.1)

(2.1)

'''' (1.3).

(2.1)

.)( 122

31

2 hHhHhmm

I I

pa+ pm


40/199

33

3.

1 2

h1h2. : pv, h1, h2, H1, H2, m. (

6)

6.I-I :

pa-pv+g(H1+h1) = pa+gH2+mgh2-g(H2+h2-H1)+ mgh1.

g(H1+h1-h2+H1) =pv+mg(h1+h2),

.)(2

121

211

hh

g

p

hhHm

v

,

, .

2.2

().

Pv

H1

H2

h1h2

I I

m m


41/199

2 34

( ) .

,

. , ,

: p, .

F(p,,T) = 0

.

pv = RT,

: v R-

R= 287 J/kgK.

p1V1= p2V2,

: p1 p2

V1V2 .

:

1.

( )

2.

.

.


42/199

35

4. F=?

h,

. : pa, a, b, h, d, D. (7)

7.

F, h.

. , p1

p2(7).

p0V0= p1V1:

.4

))()((4

)(22

1

22 dDhappdDap aa (4.1)

.

(4.1)

,1ha

appp aa

).1(1

ha

app a (4.2)

p1< 0,

.

, , ,

p2>0.

F

h

d D

a b

F

h

d D

a b

) )

pa

pa

p1

p2


43/199

2 36

p0V0= p2V2:

.

4

))((

4

2

2

2 DhbppbDp aa (4.3)

(4.3)

,2hb

bppp aa

).1(2

hbbpp a (4.4)

. 8. .

8.

, , 8. P1

P2.

, :

,4

))(1(4

)(2222

11

dD

ha

apdDpP a

(4.5)

.4

)1(4

22

22

D

hb

bpDpP a

(4.6)

F + P1= P2. (4.7)

F

P1P2


44/199

37

(4.5) (4.6) (4.7)

h:

4))(1(

4)1( 222

dD

ha

apD

hb

bpF aa

.

5. -

. F, .

,

. : F,G, D, pa, H. (9.)

9.

9, F

,

x.

, y. x y= ?

, 9) 9)

.

4

,4

2

1

2

0

DpFG

DpG

m

m

F

x

G

H

y

D

pm0

F

GGPm0 Pm1

)

) )


45/199

2 38

:

.)(4

,4

21

20

D

FGp

D

Gp

m

m

, ,

,1100 VpVp

).(4

)(4

)(2

1

2

0 yxHD

ppHD

pp mama

.

,)())(( 011 Hppppyx mmma

,)(

1

01 Hpp

ppyx

ma

mm

,

:

.)(4

42 FGDp

Fyx

a

6. h=?

, D, H

m. , pa


46/199

39

. : pa,D,H, m,.

(10)

10.

9).

.

( ) p.

h. ,

10)

,21 hhh

.

z

,

,pzHpa (6.1)

p . (6.1)

.Hp

pz a (6.2)

, 10)

:

,mgPP a

H

D

pa

z

h2

h1h

P

Pa

mg

II

) ))

p


47/199

2 40

,44

22

mgD

pD

p a

.4

2D

mgpp a (6.3)

(6.3) (6.2),

.42

H

D

mgp

p

za

a

(6.4)

z,

,1 zHh

, (6.4)

).4

1(

2

1

D

mgp

pHh

a

a

(6.5)

h2

I-I.

:

,2 pghpa

.2g

pph a

(6.3)


48/199

41

,

42

2g

pD

mgp

haa

.4

22D

mh (6.6)

(6.5) (6.6)

).4

1(4

2

2

D

mgp

pH

D

mh

a

a

.

7. D

H d pv

. H=?

. : D,

d, , pv.(11)

11.

11.

Pv G.

G

Pv


49/199

2 42

.GPv

,

4)( 22

dDpP vv ,

.4

2

HD

ggVG

d

.

.44

)(2

22

DgHdDpv

.)(

2

22

gd

dDpH v

,

2.3

,

. 2.1

.

, .

. 12.


50/199

43

12.

12.

,

.

.

P

.

A

Pm

pm c

APv

pv c

Pm= pmA

Pv= pvA

PC

D

pm

zc

zc

AgzP c

Px CD

pm

zcx

zcx

xxcxAgzP ,

.22 zx

zz

PPP

gVP

Vz


51/199

2 44

,

.

.

,

.

.

8. FC

, H.

a b; . (

13)

13.

;gH0yp .aHgaypB

A=ab:

.222

Hagab

abpp

ApP BAC

C() :

;0xC

.H2a3

H3a2ay

3

a

pp

p2py C

BA

BAC

yC.


52/199

45

9. AB

O, .

A. A O b.

. H (

O) .

. (14)

14.

ghpgHpA ; .

:

;ba

a

p

p

A

0

;p

ba

ap A0

;ap2

1P 01 .bpp

2

1P A02


53/199

2 46

:

.3

b

pp

p2pa

A0

A0C

M0 0 ; F b Pa

P aA C 1 230; F b P

aP aA C 1 23

.

( A) ,

FA=0, :

;aP3

aP C21 ;

3

b

pp

p2pbpp

2

1p

6

a

A0

AOA00

2

AA2

A

2

p2pba

a

6

bp

ba

a

6

a 323A b2ab3ap: . (9.1)

:

sin

sinbHasinbaH

. (9.2)

(9.1) (9.2) :

.b2sin

sinbHb3

sin

sinbsinHb3sinbH3H 323

332223

:

.sinb3H0sinbH3H 23

:

H3bsin.

,

.


54/199

47

.

10. e

- . L. : pv, H, L, , 1, 2.

(15)

15.

- : - pv,

1 2. Pv, P1, P2, .

Cv, .

, ,

pv.

,vvv ApP

Av .

,

sin

H, ,

L

,

sin

LH

Av

H

H

2H

pv

1

2

A

A

H

H

2H

pv

1

2

A

A

Pv

P1

P2

zc1

zc2

C1D1

C2D2

Cv

1

2


55/199

2 48

.sin

HLpP vv (10.1)

1 P1

,1111 AgzP c (10.2)

: zc1 C1

1 ( 1), 1 1. zc

C1, 16.

16.

,

. I-I.

C1

D1.

zc1, vc1. zc1.

, pa pv,

pa.

I-I :

pv

zc1H/2

1

I IC1D1

pa-pvpa1

P1

zc1vc1

vc1


56/199

49

1112

cava gzpH

gpp (10.3)

(10.3)

.211

H

g

p

zv

c (10.4)

1

.sin

1 LH

A

(10.5)

(10.4) (10.5) (10.2)

.sin

)2

(1

11 LHH

g

pgP v

(10.6)

P1 zc1 1. ,

11

11

c

cc

zA

Iz ,

Ic1 1.

,12

)sin

(3

1

LH

Ic

:

pa-pv

1H/2!

:

pa

1zc1!

!


57/199

2 50

.sin12

sin12

sin

1

2

2

1

3

3

1

cc

cz

LH

zH

LH

z

P2. , P2

, D2.

,2222 AgzP c (10.7)

: zc2 C2

2 ( 2), 2 2. zc

C2, 17.

17.

zc2. ,

II-II

C2. ,

,

1.II-II

pv

H

1

II II

C1

D1

pa-pvpa1

P1

C2

D22

H

P2

2

zc2

2


58/199

51

22212

cava gzpH

ggHpp (10.8)

(10.7)

.2

2

2

1

2

2

HH

g

pz vc

(10.9)

1zc22

1

.

, 1


59/199

2 52

2(17 2/).

(10.9) (10.7)

,2)2

( 22

1

2

22 HLH

Hg

pgP v

(10.10)

.22 HLA

-.

x z ,

15.

x-

,coscos 21 xv PPPP

z

.sinsin 1 zv PPP

.)sinsin()coscos( 212

21

22 PPPPPPPP vvzxu

. ,

.

.

11. L

. 1 2.

. . : h1, h2, 1, 2, , L.(18)


60/199

53

18.

, :

F, 1 P1, 2 P2.

1

,1111 AgzP c (11.1)

.sin

11 L

hA

(11.2)

10, zc1

1.

,2

111

1 caa gzph

gp

.21

1

hzc (11.3)

(11.2) (11.3) (11.1)

O

K

1

2

h1

h2

A

O

K

1

2

h1

h2

A

2

1

F

zc1

zc2

P1

P2

vc1

vc1

vc2

vc1

C1

C2

D2


61/199

2 54

.sin2

1 2111 L

hgP

(11.4)

2

,2222 AgzP c (11.5)

.sin

22 L

hA

(11.6)

zc2

2.

,2

222

211 caa gzph

gghp

.22

1

2

12 hhzc

(11.7)

(11.6) (11.7) (11.5)

.sin

)2

( 222112

Lhh

gghP (11.8)

. ( ),

,

vc1, vc2, vc1, vc2.

,11

11

c

cc

vA

Iv


62/199

55

.sin1212

)sin

(

3

3

1

31

1

LhL

h

Ic

vc1,

.sin2sin

111

hzv cc

.sin6

11

hvc

,22

22

c

cc

vA

Iv

.sin1212

)sin

(

3

3

2

32

2

LhLh

Ic

vc1,

.sin2sin

222

hzv cc

.sin6

22

hvc

,

.0O

M


63/199

2 56

18

,0)sin2

()sin2sin

(sin

)(2

221

121

21

cc vh

Pvhh

Phh

F

.)sin2

()sin2sin

(sin

22

2112

1

21

cc vh

Pvhh

Phh

F

. , .

12. -

Pu.

: R, 1, 2, Pu, pm. (19)

19.

, ,

x

z . - x-

: 1-2

, 2 3

1 3 4 2. ,

R

2R

R

pm

1

2

A

A

R

2R

R

pm

1

2

A

A

Pmx

P1xzc1x

z

x

A1

A2

A3

A4


64/199

57

,

.

pm. , , x ,

.mxm PP

,mmm ApP

RLAm ,

.RLpP mm (12.1)

, 1

.1111 AgzP c (12.2)

RLA 21 .zc1

1

,111 caam gzpgRpp

.1

1 Rg

pz mc

(12.3)

(12.2) (12.3) (12.1)

.2)(1

111 RLRg

pgPP mx

(12.4)


65/199

2 58

dPx dPx

dPz dPz

dP dP

R

dPxdPx

dPz dP dPR

, x

, R.

2. 20.

20.

dA, dP.

. , ,

,

dPx,

. 2 z , ,

20 .

21.

. ,

.

:

1. z ,

x .2.

,

()


66/199

59

,

().

, x

.x

,1PPP mx

, (12.1) (12.4) :

.232

1 LgRRLpP mx (12.5)

z . 1-22-3,

z- .

.

,2 zz gVP (12.6)

Vz

.

2 .

22.

22.

H

RL

2

I I


67/199

2 60

Vz,

,kvadrarapolucilindz VVV

.2

1 2 LRHRLVz

H.

I-I,

.2 21 gHpRgpp ama

.22

1

2

Rg

pH m

H Vz

).

2

12(

2

1

2

RR

g

pRLV mz (12.7)

(12.7) (12.6)

.2

12

2

2

2

1 LgRLgRRLpP mz (12.8)

,

1.

2.


68/199

61

,22 zx PPP

, (12.5) (12.8)

,)2

12()23(

22

2

2

1

22

1 gRgRRpgRRpLP mmu

.

)2

12()23( 222

2

1

22

1 gRgRRpgRRp

PL

mm

u

13. -

.

-. L.

: 1, 2, R, L. (23).

23.

. x-

z- .

,

z ,

x .

R L,

.RLAx

R

RA

A1

2

R

RA

A1

2

2

1

z

x

zc

PxPz

R


69/199

2 62

,2 xcx AgzP

zc.

,

. :

.2

221 caa gzpR

ggRp

.

,22

1 RRzc

.)

2

(2

12 RL

RRgPx

z

,2 zz gVP

, , Vz

,

2., :

24.

y


70/199

63

, ,

.

24,

. ,

. 25.

25.

kvadracilindraz VVV 4/3 ,

,4

3 2 RLyLRVz

y

, .

,221 gypgRgRp aa


71/199

2 64

.2

1 RRy

),(4

3

2

12 RRRLLRVz

).14

3(

2

12

2

LgRPz

.22 zx PPP

14.

, L.

h. : h, R, L, , . (26)

26.

.

,

.

,xcx AgzP

x

Px

C

D

zc

Vz


72/199

65

.hLAx zc

,

,2

caa gzph

gp

.2

hzc

,

.2

1 2LghPx

.

.zz gVP

, Vz.

:

.2

1kvadracilindrasec manjegkaikvadraz VVVV

(26)

,Rcos xcos R

x

.cos

2

1

360

2

hLRLR

RhLVz


73/199

2 66

).cos

2

1

360

(

hR

hgRLPz

,22 zx PPP

.)cos21

360(

41 24 hRhhgLP

15.

, L, R, h.

: R, h, , L.(27)

27.

,

.22 zx PPP

,xcx AgzP

.hLAx

Px

zc

R-h

x


74/199


75/199

2 68

.2)( 222 hRhhRRx

:

),arccos(360360

22

cilindrasecR

hRL

RL

RV kai

.2)(2

1)(

2

1 22/1 hRhhRLhRxLV kvadra

,2)(21)arccos(

360

22

hRhhRLR

hRLRVz

.2)(2

1)arccos(

360

22

hRhhRL

R

hRLRgPz

2.4 .

'' ''. , ,

, , .

.

, 28?

28.

pm

R

Vz

Pn

G


76/199


77/199

2 70

30.

.

30.

, .

G (

G ,

0G ) 0P

:

00 PG ,

00 PG

00 PG .

,00 gVP

V0 .

,00 gVG

V0 .

.

G

P0

V0


78/199


79/199

2 72

G01

P02.

, ,

.

().

Pn1, ,

,1111 AgzP cn

1()

.21 RA

zc1

,

,111 caam

gzpghpp

.21

1

h

g

pz mc

.)2

(2

1

11

Rh

g

pgP mn

Pn2, ,

,2222 AgzP cn

2

.22 RA


80/199

73

zc2

,

,222 caam gzpgHpp

.2

2

Hzc

.2

2

22 R

H

gPn

G0je

0110 gVG .

1

,21 301 RV

.2

1 310 gRG

0je

0220 gVP .

2

,2

1 302 RV


81/199

2 74

.2

1 320 gRP

(

.

32.

l?

,

. ,

,

.2

1 30 RV

, ,

,

,31 2|

0 lRV

. .

, ).

-

. -

, .

P0

G0

R

l


82/199

75

,

2.

33.

33. x .

:

.0coscos 0201 PPGP nn

.0cos2

1cos

2

1

2

1

2

1 22

2

1

2

2

2

1

2 gRRgRRgHRghRRpm

2R2

,0)(cos2 2121 gRgHghpm

.cos)(2

2

211

g

gRghpH m

17. d 2H, m

.

D D0.

,

b.

.

P0

G0

RPn1

Pn2

x

y


83/199


84/199

77

,2

43

1 2

0 Hd

V

.6

1 20 HgdP (17.1)

,mmm gVG

,6

1 20 HdVVm

.

.6

1 2HgdG mm (17.2)

,111 AgzP cn

,164

)2(2

2

1

d

d

A

.2

d x

2

:2:

H

dHx

HxHd


85/199

2 78

11 caam gzpghpp

.11 hg

pz mc

.16

)(2

11

dh

g

pgP mn (17.3)

Pn2.

,222 AgzP cn

.164

)2

( 22

2

dd

A

22 caa gzpghp

.22 hzc

.16

2

22

dghPn (17.4)

,

pm,


86/199

79

.4

)( 202

DDpP mm (17.5)

.

.cbFc (17.6)

.

,

.

zc1 Pn1.

,11

11

c

cc

zA

Iz

.102464

)2

( 44

1

dd

Ic

.

)(64)(16

1024

1

2

1

2

4

1

hg

p

d

hg

pd

d

zmm

c

,

.64 2

2

2h

dzc

,0 OM


87/199

2 80

.0)()(33

22110 lFlPFlzlPzlPH

GH

P cmcncnm

Fc

.)()(3

)( 22110 lPFlzlPzlPH

GPlF mcncnmc

(17.1), (17.2), (17.3), (17.4), (17.5) (17.6)

,

,4

)()64

(16

)

)(64

(16

)()(18

1

2

0

2

2

22

2

1

22

1

22

lDDpFlh

dl

dgh

hg

p

dl

dghpHgdcb

m

mmm

.4

)()64

(16

)

)(64

(16

)()(18

11

2

0

2

2

22

2

1

22

1

22

lDDpFlh

dl

dgh

hg

p

dl

dghpHgd

bc

m

mmm

18. : A-A,

B-B .

a.

= 13,6, 8,6

ba .

A-A B-B, H=2b h=b/3. : , b, d.

(35)


88/199


89/199

2 82

PNA, .

,

,AcANA AgzP

.4

2dAA

zcA ,

-(), ,

p0,

.

,0 cAaa gzpgHpp

.HbzcA

H=2b,

.3bzcA

.4

3 2gbdPNA

,

,00 AA

gVP


90/199

83

.16

1)

2(

2

1 330 d

dVA

.16

1 30 gdPA

- ,

.43 2gbdPP NAAistezanja

,

, , , .

.16

1 30 gdPP AAsmicanja

-:

Gz, PNB,

.

,BcBNB AgzP

.4

2dAB

zc,

-,


91/199

2 84

,0 cBaa gzpghpp

.hbzcB

h=b/3,

.3

4bzcB

.3

1 2gbdPNB

,

,zz gVG

.2

7

4

7

)4)4((12

1

22

22

bdHdV

ddddHV

z

z

.2

7 2gbdGz

-

,

.6

19

3

1

2

7

2

22

gbdP

gbdgbdPGP

Bistezanja

NBzBistezanja


92/199

85

,

, ,

.0BsmicanjaP

19. , ,

L.

=0,5D.

. : L, D, , . (36)

36.

36.

,

P0,

.00

gVP

.

,4

)2(

2

0

2

0

LDV

LDV

D

F F

P0


93/199


94/199


95/199

2 88

20. G

2 d1.

1 1 2

. : G, d, D, d, d1, l.(38)

38.

. ,

p2 D p3

d


96/199


97/199


98/199


99/199


100/199


101/199


102/199

95

22.

. b.

, h.

.

, b=h .3

41.

, . :

.

,

gF

aF

z

x

),( gdzadxdp

,

,

,)( cgzaxp

. ,

xz

H

-a

g


103/199


104/199

97

,

2

1 22Hbhb

.2hH (22.3)

,

,

.

,2

hhHz

bx

(22.2)

),2

(b

g

ah

.2

b

gha

,3hb

.3

32ga

23. , DH,

R , h.

a.

B-B

. :D

,H

,R

,h

,a. (42)


105/199


106/199


107/199


108/199

101

. :

,

,0

Rx

zz

(23.2)

.0 Rg

az

).(4

0

2

zhHD

Vcilindra

,

43.

.)2

(32)(

4

32

DgaRhHDV

.12

1)(

4

32

D

g

aRhH

DgPz

.)3

1(

9

1

4

22222

Dg

aRhHgDa

DP BB

24. , D,

.

pm. .


109/199


110/199

103

,

,1

ma ppp

hz

(24.2)

,)( 111 chgapp ma

.)( 111 hgappc ma

1

).)(( 111 zhgappp ma (24.4)

, 2,

, 2. ,

, , (24.4). ,

,

12.

,)(

,0

11 hgappp

z

ma

(24.3)

,0)()( 2211 cgahgapp ma

.)( 112 hgappc ma

2

2


111/199

2 104

).)(( 22112 hhgappp ma (24.5)

- 2. ,,

,2 AppPc

cxxzz

a (24.6)

: zc, xc

, .

.0

,

,

42

2

c

c

x

hz

DA

(24.6)

(24.5)

.4

))((2

2211

DhhgapP m

,

2.5.2

, .

45

x

z

y

FR

2 rr

g


112/199

105

r

,

,

.2

grFR

:

.

,

,

2

2

gF

yF

xF

z

y

x

),( dzFdyFdxFdp zyx

).(22

gdzydyxdxdp

,)22

(2

22

2 cgzyx

p

,

.

.app

,

0,z0,y,0 x

.apc


113/199

2 106

,)

22

(2

22

2

apgzyx

p

.)(2

222

gzyxpp a

xOy

,222 yxr

).2

( 22

gzrpp a

Oxyz Orz.

,

, ,

.

app .

).2

(0 22

gzr

,0

,02

22

gzr


114/199


115/199

2 108

),( dzFdyFdxFdp zyx

).(22

gdzydyxdxdp

,)

22

(2

22

2 cgzyx

p

,

.

, p=pa,

.apc

,222

yxr

,2

22

gzrpp a

.2

22

g

rz

,

.


116/199


117/199


118/199


119/199


120/199

113

, r

,

,)2

(2

2

2/

0

2/

0

223

2

D D

A

rdrhg

RgdrrP

:

).28

(4

222222

ghRDD

PA


121/199


122/199

3

,

,

.

.

1.

,

.

3.1

.

, .

27. ,

h, .

. : pm, pv, ,

h,L, D, u, v, k, f, . (48)

48.

pm

0 0

pv

B

1 1

v

F

k

k k

k

L,D

u hv

V


123/199

115

(1.68),

0-0 1-1.

0-0 :

,

mp

,gh

,

, .02

2

1 v

1-1 :

,

vp

0, '''',

, .02

2

2

v

.

1.3.5.

. ,

0-0 1-1 :

,2

)14(

2

vDLpghp fkvuvm

:

u ,v- ,- ,f- ,1 - ,

,


124/199

3 116

- 1.3.5.2.

(=1) !

.

)14(

)(2

D

L

ghppv

fkvu

vm

,4

2D

vV

.

)14(

)(2

4

2

D

L

ghppDV

fkvu

vm

,

,

,

.2

)(2v

d

lY ig

,

,

, 0 i .

, .

28. , d,

. ,

16 , :) ,


125/199


126/199

3 118

(28.3) (28.2)

v :

.)(2

42

11

D

dv

D

LYg

,161

g

g

Y

Y

,16

2)(

22

4

1

2

v

D

d

D

L

v

d

L

:

.16)(

5

1 dD

(28.4)

) ,

:

,Re

64

,Re

vd

.64

vd

,


127/199


128/199


129/199

121

. : L, l1, l2, D, d1,

d2, (), h, u, v, v1, v2, u, R1, R2, k. (50)

50.

50 ,

h . ,

,

.

, :

1.

2. .

, .

, ,

.

, :

, .

, ,

.

0-0 1-1 :

v

A

B C

h

v1 v2

0 0

1 1 2 2

k

k

u

k

k

R1 R2

L,D,

l2,d2,l1,d1,

v

v1 v2


130/199

3 122

()

,2

)12(2

)(2

1

1

111

2 v

d

lv

D

Lpgh

pvkRvu

aa

(29.1)

.

0-0 2-2 :

.2

)12(2

)(2

2

2

222

2v

d

lv

D

Lpgh

pvkRvu

aa

(29.2)

.

:

. 50,

51.

51.

,

.21 VVV

,4

2d

vV

.

444

2

22

2

11

2 d

vd

vD

v (29.3)

V

1V 2V


131/199

123

(29.1), (29.2) (29.3)

: v, v1v2.

,

.12

,12

,

2

2222

1

1111

d

lC

d

lC

D

LC

vkR

vkR

vu

, :

,22

2

11

2 vC

vCgh (24.4.)

,22

2

22

2 vC

vCgh (24.5)

.2222

11

2 dvdvvD (24.6)

(29.4) (29.6)

.

(29.4) (29.5)

,22

2

2

2

2

1

1

v

C

v

C

,

.2

112

C

Cvv

(29.6)


132/199


133/199


134/199

3 126

52.

52

, v0. , . ,

.

, ,

,

,2

2

0v

d

LgH

.2

0L

gdHv

, .

, ,

,222

2

2

2

1 v

d

lLv

d

lgH

(30.1)

.22

2

2

2

01 v

d

lLv

d

lLgH

(30.2)

(30.1) (30.2)

H

0 0

1 1

l,d, /2

L,D,

v1v01

v2


135/199


136/199


137/199

129

31.

, h .

.

. :K,h, D, D1, D2, l, l1, l2, l3, u, , , v, v1, , p.

(53)

53.

,

, . ,

.hKVB

v2,

,4

2

22

DvhK

.4

22

2 D

hKv (31.1)

B

0 0

1 1

v1

v3

Yp


138/199


139/199

131

.2

33

D

l

gHv

vu (31.5)

gH, (31.4),

,

I II.

, ,

,

,

. ,

.

I

,3VV

,

.

44

2

3

2 D

vD

v

,3vv

.2

3

D

l

gHv

vu (31.6)

,

,21 VVV

,


140/199


141/199

133

.2

4 3

2

D

l

gHDV

vu

(31.11)

, , .

(31.2)

v2 (v2), (31.3) . (31.6)

(31.9), Yp,

Pp.

32. 4

V (m3/s) .

, , P1

P2 . 5

5V .

a) P1, C4 C5

4V 5V

.

b)5 ,

2 4V (Ci

).: pm, 4V , 5V , C0, C1, C2, C3, p1, d.(54)

54.

54 ,

, . ,

v1

v2

v0

v5v4

v3

C5

0 0

11


142/199

3 134

,

.

) 1:

, ''2''.

,

,

.

, ''4''

,4

)2( 2

44

dvV

.2

44

d

Vv

, ''5''

,4

)2( 2

55

dvV

.2

55

d

Vv

, 4V 5V

3V ,

,4

)2(

4

)2(

4

)2( 2

5

2

4

2

3

dv

dv

dv

,543 vvv


143/199

135

,

).(1

5423 VV

d

v

''0'' ''3'' 2d,

,

,30 vv

).(1

5420 VV

dv

,

''0'' ''1''

,44

)2( 2

1

2

0

dv

dv

).(2

,2

5421

01

VVd

v

vv

.

2:

1. 0-0 1-1, ''4''

2. 0-0 0-0, ''5'''.

.

2222

2

44

2

33

2

11

2

00

1 vCv

Cv

Cv

Cpp m


144/199

3 136

, , ,

1.

24244

2

54243

2

54241

2

542401

1)(

1)(

4)(

1

2V

dCVV

dCVV

dCVV

dCpp m

,

,

.)(

4)(2 254

2

4

4310

2

54241

VV

VCCCCVV

dpp

m

, 4:

).4()()(2

3102

4

2

54

2

4

1

24

4 CCCV

VV

V

ppdC m

,

''5'' ,

.2222

2

55

2

33

2

11

2

00

1 vCv

Cv

Cv

Cpp m

5, , ,

,)(

4)(2

2

54

2

55310

2

54241

VV

VCCCCVV

dpp m

).4()()(2

3102

5

2

54

2

5

1

24

5 CCCV

VV

V

ppdC m


145/199


146/199


147/199


148/199


149/199


150/199


151/199

143

.)111

(2

432

234

KKK

K

, 60.

60.

60

,

,52341 KKKKe

, 234

.)111

( 52

432

1 KKKK

KKe

61.

61.

1

234

5h

h


152/199


153/199

145

-

, ,

.

- ,

, , 63 .

34.

D

D, p,

l, (ppa=pbp)

(pf). F vp.

. : ; v; ; u0; u. (63)

63.

63 , -

. , , : ,

-, .

, (-)

, .

, ,

, . v1

v2 .

v1v20 0

1 2


154/199


155/199


156/199


157/199


158/199

3 150

,

. , ,

.

67.

67 .

:

.4

)(

,4

)(

2

0

2

22

2

0

2

11

DDpP

DDpP

:

,21 FPP

,4

)(

4

)( 202

2

2

0

2

1 FDD

pDD

p

.)(

42

0

221 DD

Fpp

(34.8)

(34.7) (34.8) 1

:

.)(

4

2)

214(

2

0

2

2

211

DD

Fv

d

lgHpp kuBR

(34.9)

(34.9) (34.5)

D0 D

P1 P2F


159/199


160/199


161/199

153

1 :

,44

22

11

Dv

dv p

.)( 2

1

1d

Dvv p (35.1)

1 :

,4

)(4

2

1

22

22 DDvdv p

).(2

2

2

1

2

2d

DDvv p

(35.2)

2 :

,44

2

0

2

22

Dv

dv

,)( 2

1

20d

Dvv

, (35.2), :

).(2

2

1

2

0D

DDvv p

(35.3)

2 :

,44

)(2

33

2

1

2

0 dvDDv


162/199

3 154

,2

1

2

2

303

DD

dvv

, (35.3), :

.)( 233D

dvv p (35.4)

, ,

, . ,

,

,

,64

Re

64

111

1dv

, (35.1)

.64

2

11

Dv

d

p

(35.5)

. ,

,64

Re

64

222

1

dv

, (35.2)

.)(

642

1

2

21

DDv

d

p

(35.6)


163/199


164/199

3 156

, ,

:

.64

4

3

2

33

dv

DlppC

p

fR

(35.10)

,

,

,

,

.

:

, ,

,2

2

11

1 vCp

Yp

(35.11)

,2

2

2

2

32 vCpp

(35.12)

.2

2

33

4 vCp

(35.13)

(35.11), (35.12) (35.13) 4

, 1, 2, 3 4. , , ,

.

. ,

.

, 1

,4

)(4

2

1

2

2

2

1

DDpF

Dp (35.14)


165/199


166/199


167/199


168/199


169/199


170/199


171/199

163

,

,

, .

R

dzzxzgV

2

0

.)(2

x(z) , ,

,)2

()( 222 Rx

zR

,

.22)( 2zRzzx

,

R

dzzRzzgV

2

0

2 .222

R

dzzRzgV

2

0

.222

R

zR

zRdzzRzgV

2

0

,2

2222

R

dzzR

zRzgV

2

0

.2

)2(22


172/199

3 164

,2

,

,

,2

uRz

dzdu

dudz

uzR

.2

,02

,0

,22

Ru

uR

u

uRR

d

d

g

g

.)2(

22

2

0

duu

uuRgV

R

,

.15

642

5

RgV

37.

, .

: R, .(72)

72.

z

dz

x

R

r


173/199

165

R

dzzxzgV0

.)(2

,)( rRzx

r

.)2(,)(

222

zRzrzRRr

.)2()( zRzRzx

R

dzzRzRzgV0

.)2((2

,

).(2

),2(2

21

00

IIgV

dzzRzdzzRgV

RR

.32

,

2

5

1

0

2

1

1

RI

dzzRI

R


174/199

3 166

:

,20

2 dzzRzI

R

,2

,

,2

tRz

dzdt

zRt

.)15

9216( 2

5

2 RI

,

.)15

9216(

3

22 2

5

RgV

3.4.2

,

,

,

.

, .

,)()( dtzVdzzA u

: (z) ,

dz , )(zVu - .

, ,

.


175/199


176/199

3 168

.4

)(2D

zA

2.

74.

,

.

r(z),

,)()( 2 zrzA

.

, 74. ,

,

,

,:)(:)( HhzDzr

).()( hzH

Dzr

, ,

.

,

)(zVu ,

.

D

H

h

r(z)

z

dz

l,d

v(z)

,


177/199


178/199

3 170

38. -

.

(s).

.

. : D,d, ,T,H. (76)

76.

: ,

:

- 1 ,

- 2 .

, , . 76

z1z2.

:

, ,

. :

H

H

D

A(z)

z2

dz2

l,d

v(z)

,

z1

dz1

H


179/199


180/199

3 172

,432

)(22

zd

l

gdzV

.128

)(4

zl

gdzV

(38.3)

, ,

z, ,

.

. , ,

, r(z)

,

,2

:)(:)3( 1D

HzrzH

).3(2

)( 1zHH

Dzr (38.4)

,

,)()(2

zrzA

, (38.4),

).69(4

)( 2112

2

2

1 zHzHH

DzA

(38.5)

,

)(

)(2

3

111

H

H zV

dzzAT


181/199


182/199

3 174

H

HzV

dzzAT

2

222 ,

)(

)(

, ,

H

H

dz

zl

gd

D

T

2

2

2

4

2

2 ,

128

4

,

H

Hz

dz

gd

lDT

2

2

2

4

2

2 ,32

.2ln32

4

2

2gd

lDT

(38.7)

(38.6) (38.7)

).2ln2

7

2

3ln9(

324

2

gd

lDT

,32

843,04

2

gd

lDT

,

,98,264

2

gd

lDT


183/199

175

R

A(z)

z

dz

l,d,

v1(z)

,

l,d, v2 v1k k

u

v(z)

v2(z)

L,D,

Rr(z)

.98,26 2

4

D

Tgdl

. , ,.

39.

.

. : R, D, d, L, l, , u, v1, v2, k, .

(77)

77.

77. D

.

,)(

)(2

R

RzV

dzzAT

,

)(zV ,

D. ,

v(z) A(z).

.

:


184/199


185/199


186/199


187/199


188/199


189/199

181

(40.1)

,

2

)(

2

2

24

1

2

2

2 v

d

dvgz su

.

)(

2

4

1

22

d

d

gzv

su

,

)(

1

4

1

2

2

d

dsu

.222 gzv (40.3)

(40.3)

.24

)(2

222 gzd

zV

v1(z) (40.3)

,22

1

2

221 gzd

dv

,)( 2

1

221d

d


190/199


191/199

183

.

79.

79.

, , , s x-.

,

p

v

c

vM (3.5.1)

: .v

p

c

c

-

,3

1vgraddivvpF

Dt

vD

, ,

dx

1

1

2

2

p2

v2

2T2

p1

v1

1T1

p

v

T

p+dp

v+dv

+dT+dT

Dx

dx

l

+dA=const.

M(x)

Re(x)

=(x)


192/199

3 184

,)(3

1x

ivdivvdx

dp

Dt

Dv

, vdtdx

.0(3

dxivdivv

dpvdv x

(3.5.2)

, ()

.0)2

(2

rdYdpv

d

,2

2v

D

dxdYr

, ,

.2

22

D

dxM

v

dvM

p

dp (3.5.3)

,0v

dvd

(3.5.4)

.0

T

dTd

p

dp

(3.5.5)

dx. dYr.


193/199

185

(3.5.2) (3.5.5)

.

, .

41.

(=const.). ,

1M .

: l,D,R,T, , . (80)

80.

, . ,

,

,

.

, ,

, .

, ,

:

,0v

dvd

(41.1)

,2

22

D

dxM

v

dvM

p

dp (41.2)

D

v

lm1

M1 M=1/

T=const =s


194/199

3 186

.0T

dTd

p

dp

(41.3)

(41.3)

(=const.),

.

d

p

dp

(41.1)

,

v

dvd

.v

dvd

p

dp

(41.4)

(41.4) (41.2),

,2

22

D

dxM

v

dvM

v

dv

, ,

.21 2

2

D

dx

M

M

v

dv

(41.5)

(41.4)

.21 2

2

D

dx

M

M

p

dp

(41.6)

,

, ,

, :


195/199

187

.21 2

2

D

dx

M

M

v

dv

p

dpd

(41.7)

,.MconstcMv

,M

dM

v

dv

.21 2

2

D

dx

M

M

M

dM

(41.8)

(41.8) ,1

2

2

M

M

.2

12

2

D

dx

M

dM

M

M s

,

,

.2

112

1 02

2

D

dx

M

dM

M

M slM

M

m

(41.9)

,

,lnln2

1

2

1

2122

1

2

2

1 MMMMD

lms


196/199

3 188

.ln2

1

2

1

2 2

1

2

1

2

2

1

M

M

MMD

lms

(41.10)

).ln2

1

2

1(

2

2

1

2

1

2

2

1M

M

MM

Dl

s

m

(41.11)

,1

2

M

).ln11(2 2121

1 MM

Dls

m

42.

(const.). ,

=1.

: l,D,R,T, , . (81)

81.

, .:

,0v

dvd

(42.1)

Mk=1Dv

l

M1

Tconst, dq=0 =s


197/199


198/199

3 190

, ,

.

2

1

T

dT

M

dM

v

dv (42.8)

(42.5) (42.7) (42.8)

,

)2

11(

)1(

2 23

2

MM

dMMdx

D

(42.9)

, .

=1,

.

(42.9) x

.2)1(

2)1()(ln

2

1)

11(

12

22

22

M

M

M

M

MMD

l l

ll

s

( Ml)

.

,)1(2

)1(ln

2

1)1

1(

12

2

2M

M

MD

lks

.)1(2

)1(ln

2

1)1

1(

12

2

2 M

M

M

Dl

s

k


199/199

4.

1 ., ., , , ,

, , 1990.

2 ., .,

,, 1997.

3 Roberson I., Crowe R., Engineering Fluid Mechanics, Boston, 1993.

4 ., ,

, 1978.

5 ., - ,, , 2000.

Mehanika Fluida KV

Documents