水力学课后习题答案

10绪论1水静力学2液体运动的流束理论3液流型态及水头损失4有压管中的恒定流5明渠恒定均匀流6明渠恒定非均匀流7水跃8堰流及闸孔出流9泄水建筑物下游的水流衔接与消能10有压管中的非恒定流11明渠非恒定流12液体运动的流场理论14恒定平面势流15渗流18相似原理和模型试验基础0绪论0.1ρ＝816.33kg/m30.2当y=0.25H时Hudydum058.1当y=0.5H时Hudydum84.00.4f=g0.5h的量纲为[L]0.6Ff＝184N0.7K=1.96×108N/m2dp=1.96×105N/m21水静力学1.1Pc=107.4KN/m2h=0.959m1.2PB-PA=0.52KN/m2PAK=5.89KN/m2PBK=5.37KN/m221.3h1=2.86mh2=2.14m内侧测压管内油面与桶底的垂距为5m，外侧测压管内油面与桶底的垂距为4.28m。1.4Pc=27.439KN/m21.5PM=750.68hKN/m21.6P2-p1=218.05N/m21.7=BABrArBA1.8P=29.53KN方向向下垂直底板P＝01.9W=34.3rad/sWmax=48.5rad/s1.10a=LhHg)(21.12当下游无水P=3312.4KN(→)P2=862.4KN(↓)当下游有水P=3136KN(→)P2=950.6KN(↓)1.13T=142.9KN1.14当h3=0时T=131.56KN当h3=h2=1.73m时T＝63.7KN1.150－0转轴距闸底的距离应为1.2m1.16P=4.33KNLD=2.256m(压力中心距水面的距离)1.17P=567.24KN1.19P＝45.54KN总压力与水平方向夹角＝14º28´1.20P=353KNP=46.18KN方向向下1.21H=3m1.22=1.0cm1.23F=25.87KN(←)2液体运动的流束理论2.1Q=211.95cm3/sV＝7.5cm/s2.2hw=3.16m2.32p=2.35m2.4PK1=63.8KN/m22.5Q=0.00393m3/s2.6Q=0.0611m3/s32.7=0.9852.8Q=0.058m3/s2.9S点相对压强为－4.9N／cm2，绝对压强为4.9N/cm22.10V3=9.9m/sQ=0.396m3/s2.11R=391.715KN(→)2.12R=3.567KN合力与水平方向夹角＝37º8´2.13R=98.35KN(→)2.14R=2988.27KN(→)2.15R=1.017KN(←)2.16R=153.26KN(→)2.17=2342.18F=Rmv22.19Q=g2H2.52.20F=CdL2222.21mpA44.2mpB44.42.22Q1=1(2Qcos))cos1(22QQ2.23R=2145KN=54º68´2.24m=3.12kg2.25T充＝24分34秒T放＝23分10秒3.液流型态及水头损失3.1d增加，Re减小3.2Re=198019.82000紊流3.3Re=64554500紊流3.4cm0096.0043.5320uv当时vuxhym577.03.6Q3min1654.0m/s20/24.33mN3.7当Q=5000cm3/s时，Re=19450紊流2.00光滑管区027.0当Q＝20000cm3/s时Re=78200紊流775.00过渡粗糙区026.0当Q＝200000cm3/s时Re=780000紊流1.70粗糙区023.0若l＝100m时Q＝5000cm3/s时hf=0.006mQ=2000cm3/s时hf=0.09mQ＝200000cm3/s时hf=7.85m3.8＝0.0423.9n=0.0113.10=0.293.11Q=0.004m3/s3.12h=0.158m3.13Z=11.1m3.14=24.74有压管中的恒定流4.1当n=0.012时Q=6.51m3/s当n=0.013时Q=6.7m3/s当n=0.014时Q=6.3m3/s4.2当n=0.0125时Q=0.68m3/s当n=0.011时Q=0.74m3/s当n=0.014时Q=0.62m3/s4.3Qmax=0.0268m3/sZ=0.82m4.4当n=0.011时H=7.61m当n=0.012时H=7.0m4.5Ht=30.331m4.6n取0.012Q=0.5m3/shmaxv=5.1m4.7n取0.0125时HA＝21.5m水柱高4.8Q1=29.3L/sQ2=30.7L/s=135.21m54.9H=0.9m4.10Q2=0.17m3/sQ3=0.468m3/s4.11Q1=0.7m3/sQ2=0.37m3/sQ3=0.33m3/s4.12H1=2.8m4.13Q=0.0105m3/sPB=10.57KN/m24.14Q1=0.157Q25明渠恒定均匀流5.1V=1.32m/sQ=0.65m3/s5.2Q=20.3m3/s5.3Q=241.3m3/s5.4h=2.34m5.5h=1.25m5.6b=3.2m5.7b=71mV=1.5m/s大于V不冲＝1.41m/s故不满足不冲流速的要求5.8当n=0.011时i=0.0026=51.76m当n=0.012时i=0.0031当n=0.013时i=0.0036当n=0.014时i=0.00425.9i=1/3000V=1.63m/sV允满足通航要求5.10n=0.02V=1.25m/s5.11当n=0.025时b=7.28mh=1.46m当n=0.017时b=6.3mh=1.26m当n=0.03时b=7.8mh=1.56m5.12hf=1m5.13Q=4.6m3/s5.14Q=178.2m3/s5.15hm=2.18mbm=1.32mi=0.000365.162=119.87mQ1=45.16m3/sQ2=354.84m3/s6明渠恒定非均匀流6.1Vw=4.2m/sFr=0.212缓流66.2hk1=0.47mhk2=0.73mh01=0.56mhk1缓流h02=0.8mhk2缓流6.3hk=1.56mVk=3.34m/sVw=5.86m/shkh0缓流VwV缓流6.5iK=0.00344i缓坡6.7L很长时，水面由线为C0、b0b2型。当L很短时，水面曲线可能为C0、C2或C0、b2型，当L较长时，水面曲线可能为C0、b2或b0、b2型。图略。6.8提示：L不同，水跃发生的位置不同。6.9提示：先求h0=0.96mhK=0.61mh0hK缓坡，故产生a1型壅水曲线，在0.97~1.50间内插h,求s。6.10前段ɑ1型，两闸门间ɑ1型，后段C1型接水跃。6.11S=3497.9m6.12S=129.462m6.13进口断面b=8mh=1.37m中间断面b=6mh=0.82ms进一中＝49.71出口断面b=4mh=1.07ms中一出＝50.18图略7水跃7.1h1=0.301m7.2Fr1=9.049.0强水跃h2=6.15m7.3Ej=14.23mPj=6972.7KwEjj=0.40mE=14.63mKj=37.5m7.4Lj=6.73m=1060h2=1.7m7.5h01=0.71mh02=1.55mhK=1.18mh01hKh02水流由急流过渡缓流必产生水跃。设跃后水深为h2=h02=1.55m跃前水深h1=0.87m。h1＞h01发生远驱水跃，即水跃发生在缓坡处，以h01=0.71m和h1=0.87m作控制水深，推求S=55.8m，图略。8堰流及闸孔出流8.1Q=0.77m3/s8.2b=30.52m8.3Hd=17m堰顶高程250.85mXc=28.348mYc=21.89mr=18.588-37.175m取r=25m时，反弧园心点坐标X'0＝75.634mY0=45.85mD点坐标XD＝55.155mYD=60.189m7E点坐标XE=75.634mYE=70.85m图略当上游水位高程为267.0m时，Q＝6167.8m3/s当上游水位为269.0m时Q＝7565.2m3/s当Q＝6000m3/s时上游＝266.53m8.4当下游＝17.75时Q＝414.9m3/s当下游＝16.70时Q＝702.2m3/s8.5Q=8987.8m3/s8.6H=2.72.5H10宽顶堰Q＝91.5m3/s(提示：考虑行进流速V0的影响)8.7当下游＝8.5m时，＝0.66hc=7.145mQ=202.44m3/s当下游＝14时Q＝157.9m3/s8.8Q=24.84m3/s8.9B=5.8m8.10e=1.07m8.11Q=22.02m3/s9泄水建筑物下游的水流衔接与消能9.1hc=0.645mhc=4.21m远驱式水跃9.2hc=0.31mhc=1.89m远驱式水跃9.3以h1求其跃后水深h1=2.32mht远驱式水跃，如水跃从1－1断面开始则所需下游水深为ht=2.32m.9.4d=0.9mLj=25.8mLK=(0.7-0.8)Lj取LK=19m9.5hc=0.99mhc=14.3mht产生远驱式水跃坝高C＝8.54mLK＝（61.2～70）m，取LK=65m9.6l=142.9mts=9.46mi=0.074ik=5.21～51冲刷坑不会危及坝的安全。10有压管中的非恒定流10.1T=1.24sTs直接水击H＝9.87ml=T=9.67m10.2提示：增速减压增速增压减速增压减速减压四个过程10.3阀门突然关闭时H＝227.07m＝88960.5KN／m3当管壁厚度不变D＝400mm时，P=1170.8KN／m210.4200H309.27m810.5AH1=75.2mHA2=67m10.6t=0.71sv=0dtdv=1.96m/s211明渠非恒定流11.1tA=0.68htB=0.768h11.2第二时段波向下游传播，距1断面距离为2800m,每流段S＝4000m,共分7个流段，每个断面的水位流量见下表断面项目12345678水位2504.8498.2491.2484.2477.5470.7464.2457.7流量Q2100197015901242100084076073512液体运动的流场理论12.1恒定流有线变形、角变形，无旋转运动流线方程x2＋y2=C212.5P=P0－)(4922yx14恒定平面势流14.1u=ɑu=-ɑ4=ɑ+c14.4AB=2ɑm3/s.m15渗流15.1q=0.868cm3/s.m15.2h0/m3456Q/m3/s0.0002820.0002550.0002180.00016815.31.53m15.4q=2.36×10-5m3/s.m15.5计算点123456hN/m1213.516.013.013.012.09hf/m01.04.06.09.010.0mrP/1212.512.07.04.02.0Q=4×10-5m3/s.m18相似原理和模型试验基础18.2Qp=322m3/sHp=3.0mVp=15m/s18.3v=5.1Q=3447t=5.1QM=0.0934m3/s0.10m3/s满足实验室最大供水流量要求18.4qM=6.39L/s.m18.3v=5.0h5.1hLQ5.0)(hvc