-
,
, 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