,

, 2008.

0. 1 .

1. 2 .

2 1: -

9 .

3 : ;

16 .

4 2: .

23 .

5 3: .

26 .

6 .

31 .

7 4: .

38 .

8 . . 44 .

9 47 .

10 5: .

59 .

11 6:

64 .

12 7: .

66 .

180 1 ATM.

(kg/m3)

. (N/m3)

.106 (Pa s)

.106 (m2/s)

1022 10025.82 481.8 4.715 680705 6670.86916 578620 0.850.88 879 8623 670 0.762 1260 12360.6 1053360 836

790 7749.9 1240 1.57

716 7023.96 247.74 0.346 13551 132935.31 1558.4 0.115

791 7759.71 600.4 0.759

900 8829 399600 444

00 1 ATM.

(kg/m3)

. (N/m3)

.106 (Pa s)

.106 (m2/s)

1.252 12.28 16.7 13.34 0.771 7.56 9.3 12.06 1.783 17.49 21.04 11.8

0.089 0.87 8.4 94.38

1.977 19.39 14 7.08

1.25 12.26 16.7 13.36

1.429 14.02 19.2 13.44 0.716 7.02 10.2 14.2 0.9 8.83 29.7 33 0.178 1.75 18.85 105.88 3.22 31.59 12.91 4.01

1 ATM. t

(0C) (kg/m3)

. (N/m3)

.106 (Pa s)

.106 (m2/s)

0 999.9 9802.02 1797 1.797 4 1000 9810.00 1560 1.560

10 999.7 9807.06 1307 1.307 15 999.1 9800.00 1140 1.140 20 998.2 9792.34 1004 1.006 30 995.7 9767.82 803 0.806 40 992.2 9733.48 655 0.660 50 988.1 9693.26 551 0.558 60 983.2 9645.19 470 0.478 70 977.8 9592.22 407 0.416 80 971.8 9533.36 357 0.367 90 965.3 9469.59 317 0.328 100 958.4 9401.90 284 0.296 150 917.2 8997.73 184 0.201

1 ATM.

t (0C)

(kg/m3)

. (N/m3)

.106 (Pa s)

.106 (m2/s)

-50 1.584 15.54 14.62 9.23 -30 1.453 14.25 15.69 10.80 -20 1.395 13.68 16.18 11.60 -10 1.342 13.16 16.68 12.43 0 1.293 12.68 17.20 13.28

10 1.247 12.23 17.66 14.16 20 1.205 11.82 18.17 15.06 30 1.165 11.43 18.64 16.00 40 1.128 11.06 19.13 16.96 50 1.093 10.72 19.62 17.95 60 1.060 10.40 20.11 18.97 70 1.029 10.09 20.60 20.02 80 1.000 9.81 21.09 21.09 90 0.972 9.53 21.48 22.10 100 0.946 9.28 21.88 23.13 120 0.898 8.81 22.85 25.45 140 0.854 8.38 23.74 27.80 160 0.815 8.00 24.77 30.09 180 0.779 7.64 25.31 32.49 200 0.746 7.32 26.00 34.85

1

2

. :

, (1)

aAfF

AF

afp ===

() (2) g

dzdp = , == dzgpgdzdp ,

( ).,. constCCgzpconst =+== p= p= p pat >0 p= p= pat - p >0

-Pa () = N/m2 - : 1 at = 760 mm =101 030 Pa - : 1 at = 10 m = 98 100 Pa - : 1 = 105 Pa - 1 mm = 9.81Pa - 1 mm = 133.4 Pa 1 . . 850 N . 15 m2, 150 m2. W : ) ; ) - 0.75 m - -. 103 kg/m3. .:) 866 kg; ) 878 kg.

: )

NaAPW

AW

aPpp

AWp

aPp 8500

101510150850,, 4

4

2121 =======

W e: kgg

W 86681.9

8500 == )

2444412 /1044.5710736.0107.5675.081.910001015

850 mNghaPghpp =+=+=+=+=

NApW 8616101501044.57 442 === , W e: kggW 878

81.98616 ==

2 . P, , d = 20 mm. D = 200 mm, G = 200 N. Q = 25 N. (+b)/a = 10.

.: 24800 N

3

3 . p1 , 7850 N. 10% , p1. p2 = 1at. D = 100 mm, d = 30 mm.

.: 12,1 at

4 . 760 mm . Pa? 13.6. :

kPaPahgp A

4.10110139676.098106.1376.081.91000

=====

5 . =640 kg/m3 . 1.2 m , , Pa?

.:7.55 kPa

6 . U- , . 30 cm . 20 cm . , .? 13.6.

:

( )12

1,,,

hhgphgphgpphgpppppp

at

ADC

ABCBatD

++=++=+===

( )( )[ ]

[ ] kPaPaPahhhg

hghhgppp

atAA

8.63637653.05.06.1381.9100011

11

===+

=+==

4

7. . U- .. 13.6 101.3 kPa, . h1=15cm h2=30cm?

.: 59.8 kPa

8 . , 770 mm . .

.: 260 mm Hg

9 . h a , p1 = 0.15 at. 775 mm . H = 1 .

.: 591 mm

10. . U- B. , a=1.5m, b=0.75m h=0.5m. 13.6.

.: 54.4 kPa

11 . U- B. , h1=60cm, h2=180cm h=45cm.

.: 16.2 kPa

5

12 . , U - . . :

( ) kPaggp

ggggppgppp

gppgppgpp

pp

x

atx

x

at

2659.22.26.1381.91000

9.22.26.11.13.11.1

5.2,6.1,9.0,1.1

,0.2,3.1,7.0,1.1

,8.1,

34

23

12

01

0

===

++===

+==+=

=

13 . U - , c 920 g/m3. p = p1-p2 , , a h = 125 mm. .

.: 10mm

14 . , - . : / , = 0.2 m, b = 1.4 m, C e c = 1.2 m. / ,, , p = 10 kPa. . .: a) 0,833.103 kg/m3; ) 0.2 m; 2,6 m; 2,2 m.

II. :

( )zyx aaaa ,,=r ( ) Cdzagdyadxap zyx ++=

6

x z

a = -g ( )

15 . 3m/s2. 3m , 1.5 m. ) , ) , ) .

:

a) o173058.081.93, =======

gatg

gatgtg 0

) kPaghpmtgAChhmh AACAC 2.1996.181.91000,96.13058.05.15.1,5.1 ====+=+== ) kPaghpmtgCBhh BBCB 2.1004.181.91000,04.13058.05.15.1 ====== 16 . 930 kg/m3 4.8m/s2 . 1.5m 1.2m 0.9m, : ) , ) 6m/s .

.: ) 22 kN; ) 14.8 kN Oz

17 . h ( R1 R2 ), p : / a, ; / .

tgga

dxdzdp

Cgzaxpaaconstaa zyx

===+=

====

0

0., ( )00

0.,

==+=

====

dxdzdp

Czagpaaconstaa xyz

.constp =

( )( ) ( ) .

20,

22

0,,22222222

22222

constgrzydyxdx

gdzdpCgzrCgzyxp

yxrayaxa zyx

+=+==+=++=+====

7

: a) ( )

( )( )

( ) ( )gagp

hhagppp

hagpphzppzagpp

pCzppCzagp

at

at

at

atat

======

====+=

1

0,

)

( )( )

( ) ( )g

RRg

phRRghppp

ghRRppRrhzpp

gzRrpp

RpCRrzppCgzrp

at

at

at

atat

22

2

2

20,

2

21

22

222

21

2

22

21

2

1

22

22

22

2

121

22

===

+====

+=

====+=

18 . , , , . , . H , n = 300 /, D = 0.2 m. .

.: 0.503 m

III. : - W , -

G = FA G > FA - G < FA - 19 . 115m3. : ) , 1025kg/m3; ) 1000kg/m3, . : a) tonneskWgFG A 118MN115611581.91025 ===== ) 3118

81.91000115600081.91000 mWWWgFG A =====

Ay FgWF ==

8

20 . 120cm 125cm. , 3m . . 7900kg/m3, - 1000kg/m3.

.: 36450N; 13950N. 21 . (. 0.9) 00 : ) ; ) , , 4m2?

.: 0.1 m3 ; . 22 . 5kg . 2.7kg 7.5 3. . .

.: 2.34kg ; 5.36kg.

- ,

......... ........ ........ .............................................................................................

. N ....................... ............. : ............. : ................

/ / /- . /

1

-

: : . I. : , . .

.1

. df, , - .

df . 2

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

V

V

V

8

. , , , , , ., - , . : ; ( ); ( ). , ( ), , . : , - .

. 3

) )

rV

II.

1.

1- - () 1mm 2- 2 2 - 2b - 3 - ( ) 4 -

. 4 2.

0/

1- 2- 3- 4- ( )

. 5 : (1) ) 2 , 2 - , . ; ) ( ); ) ( ) . : (2) ) . . ( ) . . ) 2. , . ) ( ). , - . III. 1)

. 6 Re

00

. ( dV=Re ),

, , , .

.7

Re .

IV. (CFD) , ( ) ( , .). ( ) : (, ); ( , ); ( , ).

- FlowLab, (CFD) . FlowLab FLUENT GAMBIT .

01

1)

. d - (5d 20d ) , .8), 12000 .

a)

b)

c)

d) . 8 FlowLab: ) ; b) Re=40; c) Re=100; d) Re=400.

, .

02

2) (Clark Y)

. . . 0.4036 m, (Clark Y). .

a)

b)

c)

.9 (Clark Y) :

) =00 ; b) =160; c) =60 .

03

V. : ) , . ) ( R) .6 .7 .8 . ) ( ), . ) .9 .

04

16

: ;

. :

[Q]=m3/s AvQ = , v - [q] = kg/s q = Q : v1, v2

1 . , 450mm . 300mm . , 150mm ., 225mm . D. 1.8m/s D 3.6m/s, D ? :

( ) ( )( )

sm4.053.0

45.08.144

sm8.090.01770.1432

4

sm0.14320.14312863.0

,0.14316.3225.044

0.017715.044

,2863.08.145.044

2222

23

322

322

322

=

=

===

======+=

===

======

B

AAB

BBAABA

C

CCDACDCA

DDD

CCCC

CAA

A

DDvvvDvDQQ

DQvQQQQQQ

smvDQ

smvvvDQsmvDQ

2 . , F1 Q1, Q2. F2 F , cm F1, F2 F .

3 . , p, v z. ( ) 18 m/s, 350 kPa 36 m .

.: 88.2m

4 . 25 mm. , , 4.5 m , 12 m/s.

.: 31.7 mm

2211 vAvAQ ==

17

. (m2/s2 = J/kg) - (m= J/N) - (N/m2 = J/m3) -

v e 5 . D=50mm d=30mm . . h=300mm Hg. - , Hg=13,29.104 N/m3. :

:

: 2

21

==DdvvvAvA IIIIII

III zz = Pa398703.01029,13 4 ==== hghpp HgHgIII

sm0.0067657.94

03.014.34

322

2 ==== IIII vdvAQ

6 . , D=14mm e d=9mm. H=1.5m. Q. H, , .

7 . , f1=0.1m2, f2 =0.05m2 h=0.5m. 400 C

.constEE pk =+

22

22

11

21

2v

2v gzpgzp ++=++

IIIIII gzpgzp ++=++ 2v

2v 2II

2I

( ) smDd

ppvppDdpp

IIIIIIII

III /57.9

0.050.03-11000

398702

1

212

v2v

2v

44

42II

2I

2II =

=

==

=

.2v2 constgzp =++

( ){

( ){ ( )

{ .2v

2

constzgp

g=++

{ { {.

2v

pk

E

E

2

constgzp =++4444 34444 21321

18

8 .. . Q , U- , h . . 9 . :

: =0,82.103 kg/m3 : 125mm : 50mm z2 - z1 =300mm e 27,5.103 Pa.

10 . =9,3.103 N/m3 Q=1.10-2 m3/s :

1/ h1, h2, h3 1, 2, 3, d1=d3=100mm, d2=25mm p1=3.105 N/m2;

2/ p1 1, 2 .

11 . =103 kg/m3 Q=5 l/s. 1, 2 3 p1 . : p1=0.4MPa, d1=d3=0.1m; d2=0.025m. , p2 0.

12 . D/d= 2 p =9,3.103 N/m2. , . 6500m (- =6N/m3). . 100m/s

13 . 75 mm , 1.8 m , 3.6 m . , .

: . ,

: vvvbazbzvpppz CBBAAatCAC ==+====== ,,,0,,0

CCAA gzpgzp ++=++ 2v

2v 2C

2A

sm0.03714

075.014.34.84

4.86.381.9222v

322

2

===

====dvQ

smgbvgb

19

. B,

14 . D = 300 mm. 1atm, t- = 200 C. ( ), , Q = 2.12 m3/s.

15 . , . , p=2,65.104 Pa. H1 e , H2=1.5m, d1=75mm d2=50mm. .

16 . H=10m Q=20T/h. h=1m. - .

17 . , 2cm, 3m . , , 10m 1 cm. pA 2 bar.

1/ , . . 2/ . ,

.

( )

47.06kPa1047.061094.5210100

94.521094.528.181.9100024.81000

2v

2v

2v

2v

333

322

22B

2A

======+==+=

+++=+++=++

Pappp

kPaPapppgbpp

bagpgapgzpgzp

atB

BatBat

BatBBAA

20

18 . , . , H=1.8m, h=4.5m, d1=50mm, d2=30mm.

19 . -, . , H1 . : d1=100mm, d2=150mm, H2=1.15m.

20 . , . , H=4.5m, h=1.8m, d1=d3=60mm, d2=40mm. , , p0 =9,6.104Pa. p . =1,33.105N/m3.

21 . M=3.105 Pa, M=0.5.105 Pa. , 100 s W=0.3m3. d, .

III. () 1 2:

22 . ; d=150mm, H0 =3.3m, H1=6.8m H2=1.5m. p =6.103 Pa. .

: .13. . 1 2, : vvvHzHzvgHppppz atat =====+=== 21110002202 ,,,0,,,0

22

22

11

21

2v

2v pgzpgzp +++=++

( ) ( )48kPa1048105210100

5210525.18.681.910002v

2v

3331

31211

21122

2

11

2

=========

+=+++=++

PapppkPaPapppHHgpp

gHpgHpgzpgzp

at

atat

at

21

. 0 2,

23 . V=0.5m/s. Hs=4m , . d=100mm, - , p =5.103 N/m2 Q .

24 . 300 mm 100 mm 0.98. U- . U- 55 mm . , U- .

.: 0.0285 m3/s

25 . . 4.5 m/s 1.5 m/s . 1.5 m 3 m. 0.3 (v1-v2)2/2g, v1 v2 . ?

.: 5.28 m 26 . 0.9 75 mm. 34.5 m 4, 0.97.

.: 0.0106 m3/s IV. 27 . . ? .

: . ,

BBAA gzpgzp ++=++ 2v

2v 2B

2A

: vvvpphzz BABABA ==== ,,0,, ghv 2= - .

ghAAvQ 2== - , . () QQQ == , < 1

ghAQ

QQ

2==

( )sm0.0853

415.014.383.4

4

83.41000

1062)5.13.3(81.922

22v

322

3

202

2

0

===

===++=

dvQ

smp

HHgvpgHgH

22

23

31 . , , , ( =0.8) h=1m. 2h.

V. 32 . D=200mm . B, . , H2 =0.3m, B - H1=0.2m. 0.84.

33 . D=200mm, L=75mm . =800 kg/m3, sin=0.2. M=40kPa, t=160 C. pat=735mm Hg. , v /v=0.84.

34 . c=15m/s. . , .

35 . , , , , . Q , 0.6m. h=8mm t=3500C. (t0=00C p0 =105Pa) =1.25kg/m3. : t t0C p0 =105Pa

t t= +027315

27315.

..

36 . d=400mm. , D=1m. , h=150mm (-=1.29kg/m3, =800kg/m3).

- ,

......... ........ ........ .............................................................................................

. N ....................... ............. : ............. : ................

/ / /- . /

2

. : 1. : A. :

. 1

. 2

. 3

.

. 4

23

0 ( ) (0) V V p p V

2

002

2 2

+ = + . = 0 = p V0=0 . 5 ( ) ( ) ppV =

2

( )ppp = 2. 2== VPP

( )

ppV

=

== 2.1...9.0

22

2. 4 1 3 z

24

. 6

1. 2. 3. 4. 5. z 6. 7. 3. : 3.1. (3) (2). U- l10, (3) l20. , .., V = V, :

= pp 22

,

7 5

2 6

1= , [ ] mmlgklp == 1010 ; ; [ ] mmllkgp == 2020 ;.. ; ...........;.........................;.................. 2010 == kmmlmml

20

10

ll= =.........

3.2. (3).

. pat= ............... Pa ; R = 287,14 J/kg.K; T=273,15+t 0 = ........K

....== RTpat kg/m3;

(3) z l2, . z=0 . , .., latpp = 2 = 0. 1

N z mm

l2mm

p g k l= . . 2 Pa

= pV 2

m /s 1 0 l20 2 3 4 5 6 7 8 9 10 0

4. V z z. z

25

V

. 7 5. 5.1. 5.2. V = f(z): z

V= const .

- ,

......... ........ ........

............................................................................................. . N ....................... ............. : ............. : ................

/ / /- . /

3

.

1. . :

. 1

PV

PV

112

222

2 2+ = + . .+ gz + gz1 2 -

p1 (1), p2 (2); V1 (1), V2 (2); z1

(1), z2 (2). , z1 = z2.

V1.f1 = V2 .f2 -

fe (1), f2 (2) fd= .

2

4.

Q = V2 . f2 -

26

( ) ( )Q f p

ff

fp

ff

fg h h

ff

k h h=

=

=

= 2

2

1

2 2

2

1

2 21 2

2

1

2 1 2

2

1

2

1

2

1

p1 - p2 = =g(h 1-h2); k f gff

=

2

2

1

2

2

1

Q - Q (1) (2) . , .., Q = Q . . = Q, - , - =

Re, ,

ff

2

1 Re

.= V d2 2 . 1.1. 1.2.

1.3. 1.4. : , , , . 2.

. 2

27

3. : (i) . (ii) . (iii) .

(iv) .

(v) (1) (2).

(vi) (1) (2) (35 ) .

(vii) , (1) (2) ( - 10 ).

(viii) - , , - 60 sec.

(ix) . 4. :

. 3

, D1=26.mm , D2=16.mm

, f2=4

22D = 0.201.10-3 m2

28

, f2/f1 = 21

22

DD = 0.379

, Q=W/t

h1 (mm)

h2 (mm)

h1 - h2 (mm)

, W (l)

, t

(s)

5.

k fg

ff

=

2

2

1

2

2

1

= m5/2/s

h1 - h2 (m)

,

21 hhkQ = (m3/s) Q=W/t (m3/s)

29

30

6. :

Q Q, () . 7.

: ; ; , .., ?; ?; - ?; .

. . :

22221111 nApDnApD rrrr == -

1 2. 21 nnrr

- .

1n

r 2n

r ( ) GDDqR rrrrrr +++= 2121 vv

Gr

- ; Rr

- , FRrr = -

:

1. 2. 3. 4. 5.

1 . , . , 50 mm 6.3 m/s. X

Y1

21: ( ) ( ) ( vvvvvv === ,0,,0,0, 22211 )rrr atpppp === 22211 - ; qq =1 ,

qvvqvqvqR xxxx == 2222212111 0222222212111 =+== qvqvvqvqvqR yyyy

NAvRR x 78405,0..3,6.1000

222 ====

2221 2 qqq ==

22

2 . 0.225 m , 0.6 m/s . 0.14 m3/s, .

: 1 . v, w = v u,

smdQv 52,3

225,0.14,34.14,04

22 === , smu 6.0= smw 92,2=

NAwR 3394225,0..92,2.1000

222 ===

WuRW 2036,0.339. ===

31

3 . . Q1 , . V=30m/s Q=0.036m3/s. Q1=0.012m3/s. . . . .

211

22

: ( ) ( ) ( )vvvvvvv === ,0,sin,cos,0, 22211 rrr , ( ) 1221211 ,, QqQQqQq === ( ) cos1 vQQQvRx = ( ) vQvQQRy 11 sin0 += , Ry = 0:

( ) ( ) 011

11 3021

012,0036,0012,0sin0sin =====+ QQ

QvQvQQ

( ) NRx 45630cos.30.012,0036,0.100030.036.0.1000 == 4 . 30 cm . , 300 . 25 mm 6 m/s. , .

.: 15.25 N, 17.3 cm 5 . G=500N l=1m , . l1=0.8m , c=10m/s d=0.04m. .

32

6 . G=0.12208N, d=36mm. , z, .

7 . V=70m/s. d=50mm, a =100. u=40m/s.

21

1

22 : ( ) ( ) ( ) sin,cos,sin,cos,0, 22211 vvvvvvvv === rrr ,

2,2, 22211 qqqqqq === ( ) ( ) cos1cos1

2cos

2cos 2 +=+=++= AvqvqvqvqvRx

02sin

2sin0 =+= qvqvRy

( ) kNRR x 1910cos1405,0..70.1000

22 =+== -

( ) ( ) ( ) kNAuvRR x 5,310cos1405,0..30.1000cos1

222 =+=+== -

8 . 15 m/s 1200. , 0.45 kg/s. 6 m/s.

.: 11.7 N, 300, 21.9 W

33

9 . d=38mm D=75mm. , p=0.4MPa, Q=0.01m3/s.

.: R=1700N

10 . h=4m Q=0.4 m3/s. , , d1=250mm d2=500mm. , , . .: R=4827kN, p=32.9kPa

11 . 900, . V=33m/s, D=2m. , p=0.5MPa. .

:

( ) ( )

=

=== 0,

4,

4,0,0,,,0

2

2

2

121DpDDpDvvvv

rrrr

( ) MNDpDvDpqvR x 54 2.14,310.5,033.1000444002

6222

22

=+==+=

MNRRRMNRDpqvR yxxy 06,75040 22

2

=+==== 12 . D1=1.5m D2=1m. , . p=4.105Pa, Q=1.8 m3/s. .

:

( ) ( )

=

=== 0,

4,0,

4,0,,0,

22

22

21

112211DpDDpDvvvv

rrrr

44,0

22

2

21

121DpDpqvqvRR xy

+==

34

smDQvsm

DQvskgQq 29,2

1.14,38,1.44,019,1

5,1.14,38,1.44,18008,1.1000 22

2222

11 =========

p2 (1) (2), z1 = z2:

( ) ( ) Papvvpppvppv atat 5522122212222121 10.98,310.429,2019,121000222 =+=+=++=++ ( ) ( ) NRx 55252 10.93,310.98,3.110.4.5,1414,329,2019,11800 =+=

13 . . , x Q=0.1m3/s. 1-1 2-2 . h=0.5m, F2/F1=n=1/2. , w1 w2 x, 1=600 2=1700. , .

14 . aXb, 600 . , , .

15 . 600 mm 30 m 3m/s. 750. .

.: 104 kN, 52030

16 . c1=200m/s. c =550m/s, q=35kg/s, q q k=q/q =1.04. , ,

35

.. p2 .

II. .

22112211 DrDrvrqvrqMrrrrrrrrr ++=

( zMM ,0,0= )r ( )0,, yx

O

Rr1

Rr2

1 . 0.6 m . 6 m/s 12.5 mm. ) , ) u, ) u .

:

) 0,0,0,2

,0,0,2

,0,0,0 22211222221211 ===

=

== DDDvLvrvLvrv rrrrrrrr

NmqvLM z 65,26,0.6.40125,0.14,3.1000 2

2

=== ) w=v-u. ( )uvAvR = W1 ( 1- ) = ( )uuvAvRu = W ( 1- ) = ( )uuvAvRu = 22 1- = ( ) kEuvAv = 22

1.2

1- : ( ) ( ) ( )222212 uvAvuuvuvAvEW k =

+=+=

(...) = ( )( ) uv uuvAv uuvAvEW +== 22 22

) W

( ) smvuuvdudWuWW

uu

32

020max 0000

====

==

( ) ( ) sJuuvavuW 25,133.3.6.40125,0.14,3.1000.22

2

000 ===

... = 0

02uv

u+ =66,7%

36

2 . , , . d=6.5m, l=7.2m . p=3.105Pa Q=180m3/s, N=50MW, =9.2s-1. , . : M=N/ e . .:R=10950kN, M=73300kNm

3 . d1=0.7m, p1=2.104Pa. d2=0.5m, p2=88.104Pa. =100s-1 Q=1.3m3/s, N=1250kW. : k=0.6m, l=0.75m m=1.1m. . : M=N/, . .:R=185kN, M=126kNm

4 . , d=20mm. r=400mm. H=2m. : ) ; ) , .

.:M=9.8Nm, =15.7rad/s

37

- ,

......... ........ ........

............................................................................................. . N ....................... ............. : ............. : ................

/ / /- . /

4

.

:

:

( )r r rR q v v= 1 2 ,

rR , rv1

rv2 , , . : . )

rv1 =(V, 0), r r rv v v2 21 22= + , rv21 =(0, V), rv22 =(0, -V) Rx=qV Ry=0.

)

rv1 =(V, 0), r r rv v v2 21 22= + , rv21 =(- V, 0), rv22 =(- V, 0) Rx=2qV Ry=0.

38

) q V

(0) (1) V U g= 2 2 s

q , W t , q= W /t.. e Q=q/. U=Q/A, . )

T - F - M - ( ) m -

F = 0, . :

Mg mg Tl l l1 2 3 0+ = (1) F 0, x . :

( )Mg mg x T Fl l l l1 2 3 0+ + = (2) (1) (2), :

39

Fmg

x=l

:

:

(i) . (ii) . (iii) .

(iv) . (v) ; , , .

(vi) .

40

(vii) , .

(viii) .

(ix) 35 .

(x) (viii) (ix) . - , , - 60 sec.

(xi) .

(xii) .

(xiii) (iii) (vi) (x). (xiv) . (xv) : ; ; .

:

, =1000 kg/m3 , m=..kg , d=..m , l = m , s = m , =m2

)

, x

, Q=W/t

(mm)

, W (l)

, t (s)

)

41

, x

, Q=W/t

(mm)

, W (l)

, t (s)

)

, x,

(m)

.

Fmg

x=l

,

(N)

, Q=W/t (m3/s)

, q=W/t (kg/s)

U=Q/A (m/s)

V U g= 2 2 s

(m/s)

qV (N)

Rx=2qV (N)

)

, x,

(m)

.

Fmg

x=l

,

(N)

, Q=W/t (m3/s)

, q=W/t (kg/s)

U=Q/A (m/s)

V U g= 2 2 s

(m/s)

qV (N)

Rx=qV (N)

42

:

F qV , Rx=2qV Rx=qV . F/qV.

F F R x R x qV qV

: ; - ;

;

.

43

. . 1. . * : - ( )

: M ( F ), L, T 3 (M, L, T) (F, L, T)

(): V, a, F, p, ... V ~ / ~ LT-1, a ~ / ~ LT-2, F ~ . ~ MLT-2, p ~ / ~ ML-1T-2, ( ), x : (1) , x, .

() 3 , ; : a, g,

M, L, T a, g, : , , ( ) : * ( , 1914): n n m ( ), m . 1 . , P D, N, . ,

=

253 NDfDNP .

: , n = 5; , m = 3 n m =2 ( ) ,,, DNP = , D, N

1=f(2)

( )Re35 fNDP =

(1)

M, L, T (2)

, D, N

(3)

(1) / (3)

M/L3 1 D L D 1

N T-1 N 1

M D3 L D

T N-1

ML-1T-1 D3D-1N=D2N 2=/ ND2

2= ND2/ =ReP ML2T-3 D3D2N3=D5N3 1=P/D5N3

3x 21 TLMx = x321 ,,

213013201001 ~,~,~~,~,~

gaTaMaLTMLTMLgTMLa

213,,

gaaa

44

2 . , F D, V, N, . ,

=

VDNVDfVDF ,22

. : , n = 6; , m = 3 n m =3 ( ) ,,,, DNVF =

(1)

M, L, T (2)

, D, V

(3)

(1) / (3)

M/L3 1 D L D 1

V LT-1 V 1

M D3 L D

T DV-1

N T-1 VD-1 2=ND/V

ML-1T-1 D3D-1 VD-1=DV 3=/ ND2

3= ND2/ =ReF MLT-2 D3DV2D-2=D2V2 1=F/D2V2

, D, V 1=f(2, 3)

= Re,22 VNDf

VDF

3 . . , T D, N, p . ,

=

pNfNDT 3 .

4 . . , Q D, N, H, g . ,

= 22

23 ,

DNgHNDfNDQ

, , gH

. 2. () (, ) , , . , . 5 . 1.83 m/s, 8.9 N. - . . 103 kg/m3 1.2 kg/m3, 1.01x10-3 Pa s 1.86x10-5 Pa s. : (1) , (2) .

45

: ( )

( ) ( ) ( )

==

21ReRe

21

21

xx cc

(1) :

smddvvdvdv 36,9

31.83,1.

10.01,110.86,1.

2.11000... 3

5

2

11

1

2

2

12

2

222

1

111 ====

(2) :

( ) ( ) ( ) ( ) NFdd

vvF

dv

Fdv

Fxx

xx 515,29,8.3.83,1.1000

36,9.2,1..

421

421

22

2

1

2

1

2211

222

2222

22

22

1211

1 ==

==

6 . 0.051 m 0.61 m/s 0.244 m 30.5 m . 122 m, 0.204 m . , . 103 kg/m3 1.2 kg/m3, 1.01x10-3 Pa s 1.86x10-5 Pa s.

.: 3.59 m 7 . 225 mm 25 / 1.1 Nm. 675 mm . 103 kg/m3 1.2 kg/m3, 1.01x10-3 Pa s 1.86x10-5 Pa s. ( . 1) : 1 , P 1 . :

ML2T-2 D3D2N2=D5N2 1= /D 5N3

1=f(2), 2 = ND2/ =Re ( )Re25 fND =

. (1) , (2) .

:

( )( )

=

=

2

1ReRe

225

125

21

NDND

(1) :

NDDNDNDN 63,4225.

675225.

10.01,110.86,1.

2.11000...

2

3

5

1

2

2

1

1

2

2

12

2

5222

1

5111 =

=

==

(2) :

NmDD

NN 933,01,1.

225675.

2563,42.

10002,1..

52

1

5

1

2

2

1

2

1

22 =

=

=

46

- ,

......... ........ ........ .............................................................................................

. N ....................... ............. : ............. : ................

/ / /- . /

N 5

: . : 1. : 1.1. ( )

=y , u (y) = 0,99 U (1) 1.2. * =

10

uU

dy (2)

1.3. ** =

uU uU dy10 (3) y U 0,99U dy u(y) 1 - * 1 1 2 ** 2- x O

. 1 2. Ox e :

: Re, .xU x=

Re, Xkp 3,2.105 U y U u(y) (x) (x) * (x) **

. 2 3. e : 3.1. - RexRex,kp

(5) ( ) x xx

0 3715

,

Re; ( ) * , .

Rex x

x

0 04615

; ( ) ** , .Re

x x

x

0 03615

4.

. 3

- 1- 2 - 3 - 4 - 5 - 6 - U- , 300

5. : (x), *(x), **(x) 1, 2, 3 u(y) U:

u p=

2

ms

; p g lC= . . .sin 30

0 [ ]Pa ;

= pR T

AT

. kg

m3

pAT = .................. Pa

R- = ............... J/kg.K; T- = ................. ; =.......... ms2

C =.............

1 x No y y p g lC= . . .sin 300

u 1-u/U u/U(1-u/U)

mm mm mm l , mm p , Pa m/s 1 0 0 0 0 0 1 0 2 0,2 0,2 10 n U(x) 0 0 1 0 0 0 0 0 1 0 40 2 0,2 0,2 n U(x) 0 0 1 0 0 0 0 0 1 0 70 2 0,2 0,2 n U(x) 0 0 1 0 0 0 0 0 1 0 100 n U(x) 1 0 (x) ( 1 ), . *(x), **(x) 2 3 ( 1 ). 2:

2 x mm 10 40 70 100 (x) . *(x). **(x) . 6. 4 5 3 Rex,k = 3,2.105

3 x, mm 10 40 70 100

RexUx=

(- , .)

() . *(x) . **(x) .

7. 7.1. u(y) 7.2. :

.(), .(), *.(x), *.(), **.(x), **.(x) y y

x,mm x,mm

. 4 . 5

8. , .

I. 2

.2

...v

Dlp =

1) : (Re3000):

0 - ; 0

48

1 . 300 m 150 mm, 2.73 m3/min 0.04. :

smmQ 33 0.04556073,2min73,2 === , sm

dQv 2.57

3,14.0,150,0455.44

22 ===

mg

vdl

gp

hvdlp 27

81,9.2.15,057,2.300.04,0

2.

2.

22...

...

2

... =====

2 . , 6 m , 720m 3 m 240 m . 1.2 m 0.04, - ?

: . B,

..

2B

2A

2v

2v

BBAA pgzpgzp +++=++

vvvHhzHzvpppz CBCAAatA ==+====== ,,,0,,0 , 2.2

...v

dlp = , 21 LLl +=

sm45,24

2,1.14,3.17,24

17,2

2,1720.04,01

6.81,9.2

1

22

.2v

322

21

22

===

=+

=++=+=

dvQ

sm

dLL

gHvvdlgH

. B C,

( )BCCCBB pgzpgzp ..2C

2B

2v

2v +++=++

( )2

.2

2...

vdLp BC

= , ( )

( ) PaHhgvdLpp

vdLpHhgp

atC

atC

506209.81,9.10002.2,1

17,2.1000.480.04,02

.

2.

222

22

==+=

+=++

p = pat - pc = 50,6 kPa. 3 . 75 mm 900 m 0.85 0.33x10-3 m2/s 40 t/h. , . :

skghtq 11,113600

1000.4040 === , smqqQ 30,0131000.85,011,11

1000.==== ,

smdQ 2,94

3,14.0,0750,013.44v 22 === , 200066810.33,0

075,0.94,2vRe 3

4 . 300 m 150 mm 50 l/s. 103 kg/m3, 1.14 mm2/s. :

smdQsmslQ 2,83

3,14.0,1510.05.44v10.5050 2

3

233 =====

, smsmm262 10.14,114,1 ==

20003,7.1037236810.14,1

15,0.83,2vRe 56 >==== d - e .

k = 0,15 mm.

001,0150

15,0 ==dk 0208,00052,0

4== .

Padlp 166585

0,15.283,2.1000.300.0208,0

2v.

22

... === mgp

h 98,1681,9.1000

166585...... ===

5 . 10 mm2/s 100 mm 120 m 5 m.

.:12.6 l/s II. 1.

,2

21vp = ..

2

2

1

AA

-1=

,2

22vp = ..

2

1

2 1AA=

6 . 0.5 m 1 m. U , - . , 35 mm, .

:

h =0.035 m, = 13,6 .103 kg/m3 , 45,0

1,4

,4

22

1

2

1

222

2

21

1 =

=

===

dd

aad

ad

a

( . 4, 10., ) : ( ) ( ) Paghpp 3312 10.33,4035,0.81,9.100010.6,13 ===

,2

22vp = .. 91a

a=

2

1

2 =

2

1

221 v.4.vv == a

a

50

. 1 2, z1 = z2

( ) ( )( )

.943,04

1.14,3.2,1

4v2,1

1000.310.33,4

3v

2v

61162

v2

v2

v

322

22

3

2

22

12

22

..2

22

1

21

smd

Qsmgh

ghppppp

======

==++=+

2.

p v.. = 22

2 , :

D2/D1 0 0.2 0.4 0.6 0.8 1 0.5 0.45 0.38 0.28 0.14 0 3.

p v.. = 22

2

)

=0.5

)

=0.1 0.05

)

30o

)

7 . . h=1.2m. d=200mm. , : ) ; ) ; ) . ) - t=20mm, =4mm.

.: ) Q=0.124m3/s; ) Q=0.145m3/s

a

:

) 2

22vp = .. , 1,02,0

02,0 ==dt

, 02,02,0

004,0 ==ds

, 62,0= . 1 2, z1 = h, z2 = 0, p1 = p2 = pat, v1 = 0:

.12,04

2,0.14,3.81,3

4v

81,362,1

2,1.81,9.212v

2v

2v

2v

2v

322

22

2

22

22

..22

22

11

21

smd

Q

smghghpgzpgzp

===

==+=+=+++=++

5)

( )p v v.. = 1 22

2 ,

52

6.

p v.. =

22 2

22

, = 1-FF 8sin

1

2

( 0.06 0.005) 7.

x/d 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Fx/F 0.948 0.856 0.74 0.609 0.466 0.315 0.159

0.07 0.26 0.81 2.06 5.52 17 97.8

8.

( )p p p ddat..

=

1

12

1 11.

9. 900

(R- )

R/d 1 2 3 4 5 6 7 8 10 0.25 0.15 0.115 0.098 0.089 0.083 0.076 0.073 0.065

10.

53

200 400 600 800 1000 1200 1400 1600 1800 0.04 0.14 0.364 0.74 0.984 1.26 1.86 2.43 2.85

11.

50 100 200 300 400 500 600 650 820 0.05 0.29 1.56 5.47 17.3 52.6 206 485

8 . d=60mm . . h=3m ( ). , : ) ; ) , d1=80mm, ) =150 d1=80mm. .: ) Q=17.7 l/s; ) Q=21.4 l/s; ) Q=23.2 l/s

9 . , x=30mm d=80mm, . =0.024.

.: l=2.7m 10 - d=15mm, Q=0.68 l/s ? p=1.4 at. .

.:=400

11 . ( . .) , D=100mm Q=15 l/s. (d=50mm) (=0.06), =60. . .: h=1.87m, h =0.406m

III.

+=+=+= 452222

.8

22 d

dlQv

vdlppp ....

( ) ( )

= == =

+=

+=N

i

M

j i

ij

i

iiN

i

M

jj..i..

ii

ddlQppp

1 1452

2

1 1.

8

= =

+=

N

i

M

j i

ij

i

ii.

i

ddl

gQh

1 1452

28

54

11

12 21 31 321 2 3

11

12 21 31 321 2 3

2;1;2;3 321 ==== MMMN

12 . , : d1=10mm, d2=20mm d3=15mm. , H=4m. , , .

0 0 3

3: . 0 3, z 3 = 0, p0 = pat , p3 = pat + g (z0 H), v0 = 0:

3 4 : ( ) ( ) ( ) ( )4..3..2..1.... o ppppp +++= ..

23

..33

23

00

20

2v

2v

2v

oo pgHpgzpgzp +=+++=++

1) ( )2v21

11.. = p , 5,01 =

2) ( )2v22

22.. = p , 9101,002,011

2222

1

2

2

1

22 =

=

=

=

dd

AA

3) ( )2v23

33.. = p , 3 25,075,002,0015,0

32

3 == dd

4) ( )2v23

44.. = p , 14 =

3

22

1

331 .v5,1.vv =

=

dd ,

32

2

2

332 v75,0.vv =

=

dd

++++=2

v.1

2v

.25,0275,0.v

.92

5,1.v.5,0

2v 23

23

423

423

23 gH

smgH 21,363,7

4.81,9.2125,075,0.95,1.5,01

2v 443 ==++++=

smdd

smdd

22,7.3,215,1.vv,8,1.3,2175,0.vv 22

1

331

22

2

332 ==

===

=

13 . d1=50mm d2=100mm . Q H=1.5m. ( t/d =0,3 s/d=0,012), (R/d=1), ( ), (4=4) . .

.: Q=3.68 l/s

0 0

5 1 1

6

55

14 . d1=100mm d2=60mm. H=3m koe =5. . ?

.: Q=8.6 l/s, =24.2 15 . , , d1=20mm , d2=25mm. H=900mm, h=400mm . , , . - , - (.. ) . .

.: Q=2 06

515.

. + l/s, min=3.1.

16 . d2=50mm, h=400mm =0.25. d1=30mm , =8.5 0.8. H . .

.: H=26.6m, Q=4.9 l/s 17 . , , H=16m. d1=50 d2=70mm. =4. , .

.: Q=14.1 l/s 18 . 100mm 450m. 12 m . , 0.04.

: . A B, z A = 0, pA = pB = pat , zA = H, vA = 0, vA =:

..

2

..

2B

2A

2v

2v

2v

ooBBAA pgHpgzpgzp +=+++=++ 1 ( ) 2 :

56

( ) ( )2..1...... o pppp ++= 1)

2

2

..

vdLp

= , 04,0= 2) ( )

2v2

11.. = p , 5,01 =

3) ( )2v 2

22.. = p , 12 =

2

v2

v2

v2

2

21

2

2

2

1

2

..

++=++=dLv

dLp o

sm

dL

gHdLgH 14,1

15,01,0

450.04,01

12.81,9.2

1

2v2v

121

2

21 =+++

=+++

=

+++=

.95,800895,04

1,0.14,3.14,1

4v 3

22

slsmd

Q ==== 19 . 39 m. 50 mm 15 m . 75 mm . , , 2.8x10-3 m3/s. 0.0192 50 mm 0.0232 75 mm

.:0.852 m

20 . d1=10mm, d1=20mm l=20m. p=1.5 at., H=6m. (1=0.5), (2=3.5), (=0.03) (3=0.1).

.: 11.3 m/s

21 . d=25mm l=10m. , p1=2 at., H1=1m, H1=5m. : 1=0.5, 2=4, 3=0.2, =0.025.

.:Q=2.17 l/s

22 . e d=80mm L=2l=10m. d1=80mm ( =0.82). =0.3 =4; =0.03. H , h=1.5m.

.: H=9.6m

23 . d=40mm. =0.04.

57

1. Q p h l;

2. h .

.:1) ( )Q g hd

= ++

d4

2 2

1

ll

, p=

gl l

hd

d

+

1

1

;

2) h=d/=1m, p=0, Q g= d4

2

2 h

24 . L D=65mm, , , d=30mm, Q=1.2m3/min, , M=0.8MPa ( )? h=10m; =0.1 ( ). . (=0.054) (=0.025).

.: L=17; L=37m..

25 . Q , M=0.4MPa h=5m. =4 =0.06 ( ). k=1 mm ( ). Q, d1=200mm?

.: Q=68.4 l/s, Q=129 l/s.

26 . l1=5m, d1=20mm; l2=5m, d2=40mm (=765kg/m3, =0,5.10-6m2/s) M=90kPa - , V=30kPa; h=6m. k=0.1mm, =4. , .

.: Q=1.2 l/s, =45

58

- ,

......... ........ ........ .............................................................................................

. N ....................... ............. : ............. : ................

/ / /- . /

6

: . :

1. : 1.1. - , . 1.2. 1.3. - , , , .

2. :

Re = Vd , , d - , V - , - , V Q

d= 4 2 .

Re. - , , .

Re . = V d ; VQdKPKP= 4 2 .

Re.= 2320 ( ) . 2000 4000 ReKP - , .

: - ( 1842 - 1912 .) , . d =0.022m 1 4 3 5 2 5 2 7 6

1- 2 - 3 - 4 - 5 - / 6 - 7 - : t 0 = ............. 0 (t 0) = ........... Q V Q

d= 4 2 . Re

.= V d

m.l/s m3/s m/s : ) Re. ) . ) Re. 2320. ? ) .

- ,

......... ........ ........

............................................................................................. . N ....................... ............. : ............. : ................

/ / /- . /

7

1. :

. :

(1) ( )Eu f= Re, Fr, Sh Eu :

(2) Eup= V

2

2 ,

- , - , V - , :

(3) ( )p f= Re, Fr, Sh V2

2.

, , (3) :

(4) ( )p f= Re V2

2

.

( )f Re , (4) . . , .

:

(5) d2V Re,

2

= l

kdp... ,

Re, dk

-

kd

-

l, d - .

VQ=

4 d2 - , (Q - ).

(, , , .), . (5) :

(6) ( )2V Re

2

..= p ,

( ) Re - .

2.

1. - 2. - d = 92 ; l =4,7 3. . 4. . 5. . 6. U - . 7. . 1 - 2 (p,) (p, ) (p,) . (7) ...- ppp += .. . :

(8) . ..ppp = 21 (5),

( p p ) (

1 2, = 0) (7) (8).

(6), ( p p1 2 ) , (7) (8)

( )9 p p p , , ,= , (9) . (.. ).

(10) ( ) = f1 Re ( )Re. 2f = , 4.

d

k

1

.

3.

( )

=

==sm

p

pf

ffQV ,

2

2

111

- (. BS 848) =.. ( ) [ ]12 p k g l g l Pa= = ................ ,

pa

R T

g

m=

3

m

s =............ ( ) [ ]13 1 2 08p p p g h g h Pa= = = .

( ) [ ] [ ]=

==

2

2....

. ,

2

2

.. ,Re14V

pp

lV

dpdV

,,,

1 p

V

2

2 V,

p , p , p p p , , ,=

Re

lm

p

m

P h

a h

a

P

m /s a mm P mm P a - - -

1 2 3 . . . .

4.

( ) = f1 Re ( )Re. 2f =

.

. R e R e

6. ( ) = f

1Re

( ). .

AcrBCF.tmpAcrB7F.tmpAcrB2F.tmpAcrAD9.tmpAcrA85.tmpAcrA21.tmpAcr9BD.tmpAcr975.tmpAcr6C5.tmpTITLE.pdf

LAB_EX_3.pdf 3. 1 . 2. 3

LAB_EX_3.pdf 3. 1 . 2. 3