1

2

8.1

y

V

x (x)

Re Re >> 1 Re Re Re >> 1Re >> 1

uy

2

Re Re Re

Re Re

y

V

x(x)

( )x

99%99%

1

V

x

, , Rex

2

Ux

x =Re

x x

U=Re

( ) 65 103~103Re =crx( ) 3104Re =cr

2

U

*

= 0 u = U

y U

y

0

u = u(y)dy

3

*0

( )U U u dy = *

0(1 )u dy

U =

U

* = 0 u = U

**

() ()

*

0(1 )u dy

U =

4

y U

y

0

u = u(y)dy

U

= 0 u = U

5

U U

( ) ( ) = 0 dyuUuUU = 0 1 dyU

uUu

U

= 0 u = U

=0

1 dyUu

Uu

8.3

x

y

U A

B

C

Dx

+ d

x+ dx

CVCVCVCV

2

x

y

U A

B

C

Dx

+ d

x+ dx

ppACAC

wwpp p+ p+ dpdp

xx

x wdpF dx dxdx

=

xx

( ) ( )20 0d du dy dx U udy dxdx dx

3

( ) ( )20 0 wd d dpu dy U udydx dx dx =

1

( ) ( )20 0 wd d dpu dy U udydx dx dx =

212

p U C+ = dp dUUdx dx

=

( ) ( )20 0 wd d dUu dy U udy Udx dx dx = + U U x x

( )0dU udydx ( )0d U udydx = 0dU udydx

2( )0 0d dUUudy udydx dx =

( ) ( )20 0 0d d dUu dy Uudy udydx dx dx + w

dUUdx

= +0w

dU Udydx

= + ( )2

0

d Uu u dydx

( )0dU U u dydx w=

0(1 )u u dy

U U = 0 (1 )u dyU =

( )2 wd dUU Udx dx + =

( ) 21 2 wd dUdx U dx U + + =

H =( ) 22 wd dU Hdx U dx U

+ + =

1

( ) 21 2 wd dUdx U dx U + + =

u , , w , u , , w ,

2

0y =

y =

w =0,0 == vu

u U= 0 = 0uy =

3 yy

0n

nu

y = 1, 2, 3n = "

2

2u u dU uu v Ux y dx y

+ = +

NN--S S

yy = 0= 0uu = 0= 0vv = 0= 02

2u U dU

dxy =

42

2u u dU uu v Ux y dx y

+ = + yy

2 2 3

2 3u u v u u uu vy x y x y y y

+ + + =

yy = 0= 0uu = 0= 0vv = 0= 03

3 0u

y =

8.4 y

V

x (x)

LL

p C =V C =

( ) 21 2 wd dUdx U dx U + + =

2

2wd

dx U=

20 1wd u u dy

dx V V V

=

y

V

x (x)

( )u f y=11

32 3u a by cy dy= + + +

yy = 0= 0uu = 0= 0

y

V

x (x)

yy = = uu = = VV0a =

2 3V b c d = + +yy = = = 0= 0 0== dy

du

4

yy = 0 = 0 2

2u U dU

dxy =

y

V

x (x)

032 2 =++ dcb

0dUdx

= 0222

== c

yu

3

30 , ,2 2V Va c b d = = = =

5

201 wd u u dy

dx V V V

=

3

232V yu y =

0w

y

dudy

=

=

2232w

V =

621 140

2 13x C

V = +

xx = 0= 0 = 0= 0

xV

= 641.4

Re x xV = 4.641

Re x

x =

74.641

Re x

x =xV

= 641.4

1 2x

32wV =

8

xV

w

3

3232.0 =

l

b x o dx x

0

l

wD bdx=

x x

9

l

b x o dx x

blVD 36464.0 =

212D

D C V A =

1011.293

ReD LC =

5.0 xV =

1.328ReD L

C =

1ab

aUabUbUa/Ub

aabbaaUUaabbUUbb

UUaa//UUbb

a a

a

b Ua

AVCD D2

21

= 2 aUV = abA =

aUa

l =Re aUC alD328.1

Re328.1 ==

1

bUV = abA =

bUb

l =Re

aUbabUaUD aaaa32 328.1328.1 ==

b b AVCD D

2

21

= 2 a

b

Ub

bUC blD328.1

Re328.1 ==

1 bUabaUbUD bbbb

32 328.1328.1 ==

ba DD =

bUaaUb ba 33 328.1328.1 =

3ba

UU

b

a =

2V

VV

a

2b o x

x

y

dylV

21

2DdD C V dA =

dyldA =dyy

baa

=

2

a

2b o x

x

y

dylV

lV

l=Re

= ybaaV

lDC Re

328.1=

( ) dybayaVdD 664.0 3 =

2

a

2b o x

x

y

dylV

3

0

1.32842

b aD V a y dyb

= baV 771.1 3=

8.5

00

V

x

1 p C =V C =

0dp dUdx dx

= = 2

=Vdx

d w

11

17

max

u yRu

=

2

7Re 10x V x=