. &

( 2004-2005) : . . : .

1

1.2: , :

A Hg 30cm

2.1 20cm 10cm H2O 2.2 ( )

H2O

1.2

1121 ghPP = , 2223 ghPP = , 3334 ghPP = kPa3.14ghghghPP 332211aA =+= , kPa6.115PA =

1.3: , :

F 0,5m 1m

3.1 H2O 2m 3.2 ()

3.3 F A A 1m

1.3 : h=0.5+1=1.5m, Fp=gh=29.43 kN

:

=

y

x 'y'x' ,

=

y

y 'x'x'

m0x0 ''y'x == , m222.0ym667.012bh '43

'x'x ===

x=1.5+0.222=1.722m,

kN25.27FlFlF pp == (lp=2-1.722=0.277m, l=3m)

2

2.1 3.55 ( Bernoulli) 2.1 (3.55) ( . )

3 30.00130 30 0.03sec sec secl l mQ

l= = =

m,

2

0.03 1.6980.15 sec( )2

Q mVA

= = =

hf: 2 210 10(1.698) 1.469

2 2(9.81)fVh m g

= = =

s: 1 1 2 21 22 2 s fP V P Vz z Hg g g g

h+ + = + + + +

(P1=P2=Pa, V1=V2=0) => 1 2 16 1.469 17.469s f s fH z z h H H h m= = = =

: ( n = 80% = 0.8) theoriticalactual

PnP

= =>

1000(9.81)(0.03)(17.469) 16426.408 6426.408 8.6140.8 746

sgQH HPP Wn W

W HP= = = = =

2.2 3.57 ( Bernoulli) 2.2 (3.57) ( . )

3 3 1120000 120000 33.333600sec sec

m m hQh h

= = =3m

s: 1 1 2 2

1 22 2 s fP V P Vz z Hg g g g

h+ + = + + + + ,

(P1= P2 = Pa, V1 = V2 = 0, hf = 0) =>

1 2 60s sH z z H H m= = =

n = 80% = 0.8) actualPntheoriticalP

= => (

11000(9.81)(33.33)(60)(0.8) 15694430.4 15694430.4 21038.11746s

HPP n gQH W W HPW

= = = = =

2

2.3 3.88 ( )

2.3 (3.88)

) ( . s/m0555.0Q 31 = , s/m3333.0Q

31 = , s/m2222.0Q

31 = ,

kPa6.68P1 = s/m49.3V1 = , s/m7. 24V2 = , s/m8

5.12V1 = 2 3. Bernouli (1)-(2): (z1 = z2 = 0)

+=+VPVP 222

211

g2gg2gP2=-63,66kPa

. Bernouli (1)-(3): (z = 0) 3

+=+VPVP 233

211 P =-4,13kPA

g2gg2g 3

x: x3

032

02 Q60cosVQ45cosV =+

(F2x = P2A2cos45 , F3x = P3A3cos60) => Fx = 2.9 kN ( )

y:

3sin 60oV Q+

(F1y = P1A1, F2y = P2A2sin45 , F3y = P3A3 sin60)

( ) ( ) x3x2 FFF ++ 3

1 2 3 1 1 2 sin 45o

y y y yF F F F V Q V Q + + + = + 2 3

=> Fy = 6.21 kN ( ) 2.4 3.114 ( ) 2.4 (3.114)

) x:

u = (V0 u) A u

u

:

1 0

( . Fx = (V0 u)2 A => Fx = (V0 u)2 A H W : W = Fx 2 H W u W(u) = u (V0 u)2, W' = (V0 u)(V3u), W'' = 2 (3V0 2u)

u2 = 03. H V

V u = V 0

2 V 0 > 0, 03V

2 V0 < 0.

03

V .

3

3

3.1 Vo=8m/s SAE 10. W=0.5m L=1.0m. , :

1.1 (L=1m) 1.2 () 1.3 1.4 ,

3.1

3.1.1 =

= 40 10x9LV

Re

m0183.0Re

L5.5

L

== , 0022.0Re664.0c

L

f == , 0044.0c2c fD ==

3.1.2 N129LWV21c2F 20DD ==

3.1.3 W1033FVP D0 ==3.1.4 , N183FD = , W1465FVP D0 == 2 Navier-Stokes :

( U + V ) = - [ ( ) + ( )]t x y x x x y

U U U p U Uy

+ + (1)

( U + V ) = - [ ( ) + ( )]t x y x x y

V V V p V Vy y

+ + (2)

2.1 (=C) . 2.2 , ;

3.2 3.2.1 (=C) :

d dU dp ( ) = dy dy dx

p = 0y

3.2.2 : U U p(U + V ) = - ( )x y x y

+ Uy

p = 0y

: V ~ 0