水力学习题解析12章

则

Qdth h

2g4D2

h)dt 4d22d22g(ha h)a

DT1d2D

2gha hhhha a (hha hhhh

h h h) H

h) ah[(h 1a h)dh1 3/ 23/2a2[(Ha)3/2h[(h a a a 2 [(1.50.5)3/21.53/20.53/2]h hhha h)

3

T1d2ha时，

2g

(0.644752)2 D2 d2d2 D02D0T2d2

2g

0hh2d2 hh2

ad220.0120.62ad220.0120.622LDbhLD，油槽LDbhAc，流速为vc

12.74

vc式中，为流速系数。流量为式中AcA称为收缩系数。

QvcAc

2ghA油罐内，任一油层深处的液面宽度为b

ΩbLdtQdt

2ghdt

Dhh2

dt

D

A

32/

T

hdh

2gA

])( 2gA 2gay12x式中 2gA 2gay12x水面的距离为aa1

vxvt

12.75

y1gt2

tx xx

y12

x2ga

x

x

a(aa(a

2g(av2g(a将上式代入式（3）

tx 2g(a2g(a

由上式解 x

y42(a(ab(ab)(a

h2如图示，当两股水舌相遇于空中某一点，求证h1yh21

v1

12.76

xv1t

y1gt

tx

xx

yx2/(42h

1111

x242h

12v2

tx

x44222x242h22

因为水股在空汇于一点，所以x相等，42h

42h

1 2yxHAHyxHAc，射流轨迹中某点的坐标为（xyx2x2

12.77

(dc)x2x2

xvct

2gH

y2

txgt212

xx2g2

x

2x2/(4yHx2x2

c (c)2

(dc)2x2x2

，如图所示开口向上的管嘴出流水位 ， 定液流通过管嘴向上喷成喷泉设水头损失为 20%，已知水头h05m，求

12.78

管嘴出0-01-1v2 v2h000010.2

v1

29.829.81-12-2

v001h000v2h1

2

4.17b0.8m，孔高e1.2m，闸孔上游在水面下的H12m0.7，试计2gHQ2gH

ebHbHHHHH1H2Q

221.22Q2 QH0H

2.6

2.6gHQgH求得Q6.72m3/s

Q2

2.)

Q2

Q

29.829.8

4.80202vc H宽b10m，闸前水头H8m，开度e2 HeeeH280.25查表12-13得收缩系0.622

12.84

Q0ebQ2

0.2559.2H9.2H

Q2

HHgHH0HgH

H2g(bH

8

8Q8Q8解得Q140.352m3/s

Q49.142

88，形断面宽度B12m已知渠底宽度b10m，边坡系数m1.5，粗糙系数n0.0225，底坡i0.0002，每个闸孔的宽度b3m，共三孔，闸前水深H4m，行近流速v01.0m/s ，开度e1m，试求通过该闸的泄流量Q

He12.81 Hev2HH

4

2

gH00.60.18e/H0.60.181/4gHQ0

0.255

验算出流条件。求收缩断面水深hcQAvcQA

Q

12

FrFr

Frc

2281(c 1)

求下游中的正常水深，对于梯形，正常水深的计算式nQ(b21m2h)2/

0.022544.51(10211.52h)2/

(10211.52h)2/h ]3/5 ]3/5 ]3/i000 (bmh)5/i000

(101.5h)5/

(101.5h)5/求淹没系数s

11.52

)2/

)2/0h ]3/5 ]3/0

)5/

)5/由上式得h02.215m，

QAvcQAc

Q

12

Frc1.41.7hhc(1Fr'2)0.622(11.42)0.921

ss

Q44.5144.510.6060将26.83m3/s代入正常水深求得h2.264m0vc12

Frc

9.8

h

Fr'2

(

0 sQ44.5144.510.602s两次计算已很接近，取Q26.80m3/s由以上计算可以看出，使用的不同，计算出的流量也不同323028H28.5m开度e323028Heb5me0.95，求通过平板的流量

12.82eH140.250.6512-13得0.622hce0.6221H022(Hh

20.952(4hcFr2 chcc

FrcFrc2

.1(

hc2.46ht00.600.18e/H0.600.180.25（3）2gHQ2gH

0.5555

Q22Q229.8429.8(5Q24迭代得Q24.81m3/sH eccL如图所示闸后接一平底已知闸孔为两孔每度b6m开度e1.0m水头H5m，v01.0m/sL500m，此间为矩形断面，宽度B14mn0.017，今欲在跌坎处建一折线形实用堰以抬高渠中水位，堰的流量系数mH eccL12.83v2HH

5

29.8 29.82gHQ2gH

0.56426

67.34m3由eH0.212-13得收缩系数0.619 qQ67.344.81m3/(s q

9.8

hhc

1)2.4718Fr18Frc118

Lj6.9(hchc)6.9(2.470.619)QmBQmB0.4214 2H0

)2/3

)2/3L0LLj

50012.77计算

LEs2i

Es

v2/(2g)

v2/(2g)

v

)/2

R

)/221 RABh/(B2hC(CC2CR16/njv2/(C2Ri0。21 EsvRCjmmmmmmm4m7059428285700912322825300103429060200074594560709725445040L0487.23mh2.094mqHH0

2 29.8

闸下游接一陡坡已知上游水深H3moHrec形门轴高cm，半径rm，oHrec开度e宽度b

m，下泄流量Q

m3s

12.841）求

ecr(0.970.258

.0(

求闸1e1e2g(3

Q

Q

3 .33m Horce有一平底闸，共3孔，每度bHorce闸上设弧形，的圆弧半径r

m开度e1）求

m

ecr

12.85

按我国水工建筑物测流规范推荐的计算流量系110.016607231

Q

0

Qv01Q

H

v2H016

2

Q1

384.95m3

384.951.782m/s366

v2H

6

2

Q2

385.091.783m/s366

385.09m3

v2H036

2

Q3

385.09m3求得Q385.09m3/sH0e某宽顶堰式水闸共10孔每度b4m，闸上设平板底缘上游部分为圆弧形圆弧半径r0.2m，上游河宽B60mH0e高于河床2.0m，已知开启高度e2m，速系数0.95

3m

12.86孔的流量Q465m3/s，求闸上水头H对于底缘上游部分为圆弧形的平板，值可按下列经验计1/{1 K[1(e/H)2式中，K值决定于比值r/e（r为底缘圆弧半径可用下式计2K0.4/2.71816r/e21/{

/{

/(H0HHQ2/[2gB2(H2)2]4.534652/[29.8602(4.532)2]01/(12g(H02

14/H2)1/(1

14/4.532)Q

0.950.797104

H4.53m

qQ/(nb)465/(104)11.625m3/(s

Frq Frq ccFrc

hsht232hchsH4.53m，Horc e流量闸度b10m弧门半径r15m轴高程为16.0m，上游水位高程为18.0m底8.5m，Horc e1）求

c16610

12.87arccos(ce)arccos(102)

e/H2/120.187(0.970.258)(0.560.258)

(0.970.258

().2g2g(HQ2)

0.)2gHQ2gHQ229.8)Q212Q229.8)Q212

29.8

迭代得Q211.49m3/s

12.1102761

vQ

c cvFr2cc c

hhc

1)1.3775

1)7.4818Fr18Frc18.5mht8.56.02.5mh114.0mht14.06.08.0mhc对于淹没出流，流量2g(H02g(H02g(H02g(H0M42e2(hthc)40.685222(81.3775) h 8th2M(Hh2M(HMt04824.512042

4.5122

69.09Q69.09

0H0H69.0969.09

2.25669.094.51269.094.5122g(H0

2.2561212Qv02Qv2

147.051.225m/s1012H

H

12

2

h2

69.094.512H02H0Q2H0

12.077

2.256

Q148.566 v2

H

12

2

h3

69.09

2.25669.0969.09

H0 14.0m时，闸孔出流量QH0 某平底平 ，已知上游水深H2.5m，宽度b4.2m，流量系数00.65，下游水th2.0m，为了通过流量Q2.25m3/s，求的开度e。t29.8zH0.52.50.2。由eH0.2zH0.2查图12-21得淹没系数29.8Qs

0.550.654.2

5.26m3/s29.8重新假定e0.25m，eH0.252.50.1zH0.212-21得淹没系数29.8Qs

0.490.654.2

2.34m3/s29.829.8Qs

0.490.654.20.24

因为高度淹没，流速水头可以忽略，所求闸孔开度为e0.24m仍按淹没出流计算，流量2g(H02g(H0M42e2(hthch2mQ e

h2h2M(HMt04hHg0.)212.0862.512.0862.5

e

22.52.5 2.5 2.5

e/H0.263/2.50.61590.0343H

eHe

20.61590.0343 1M42e2(hthc)40.6520.2632(20.1616)1h2M(Hh2M(HMt044212.0862.5e12.0862.5

20.665212.0862.512.0862.5

e/H0.24/2.50.61590.0343H

0.1923(H

)20.61590.03430.0960.19230.0962M42e2(hthc)40.6520.242(20.14745) h 2th2M(Hh2M(HMt042

22220.6115(2.5412.0862.512.08612.0862.512.086 2.5

0.242

e/H0.242/2.50.61590.0343H

0.1923(H

)20.61590.03430.09680.19230.096821M1

hthch

0

0.)th2M(Hh2M(HMt04220.6161(2.54212.0862.5e12.0862.5

212.086 2.512.086 2.5所求闸孔开度为e0.242m以上两种算法计算结果很接近，第二种算法虽繁一些，但逐次近，避免了任意假定的缺点oHeP某实用堰上共有7孔，每度b5m。堰上设弧形。已知闸前水头H5.6m，闸孔开度e1.5mP30m，堰前渠B46m，下游水位在堰顶以下，求通过闸孔oHePe/H1.5/5.60.268

12.89

H

Q

0.258

H0H0 H0

QH0H

2 5.6 Q25.6Q25.6迭代得Q363.504m3/s已知堰上水头H6m，共4孔，每度b8m，底缘向上游倾斜，倾斜角度为45°，下泄流量Q431m3/s，下游水位低于堰顶，试求开度e。

用王涌泉计算流量系HeP12.90HeP0.650.186H

(0.250.375e)H

0.650.186e(0.256

0.8268H0Q

0

26.096e2286.916e431286.916 286.91624286.916 286.9162426.096由上式解得e