武汉大学水力学习题解答-水击

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1、精品文档，仅供学习与交流，如有侵权请联系网站删除第十章10-1 解：阀门突然开启过程中，水击波传播四个阶段示意图如下：10-2 解：首先判断水击类型，然后计算各相末水击压强，从中找出最大水击压强。(1) 判断水击类型已知 m，m/s，则相长 s。而阀门关闭时间s，有，为间接水击。(2) 计算首相末水击压强初始全开，有阀门开度；按线性启闭关系，得首相末阀门开度；由于m/s，初始水头m，则管道特性系数 。上述数据代入式(10-4-17) 得 整理 解此二次方程，得 或 m 或 m如果发生直接水击 m而m，故不合理。则首相产生的水击压强增量为 m(水柱高) 或水击压强为 m(水柱高)(3) 计算第二

2、相末水击压强(末相末水击压强)将已知的，代入式(10-4-17)得 解此方程 或 m(水柱高)则第二相(末相)产生得水击压强为 m(水柱高)如应用式(10-4-20)计算末相水击压强，由于系数则有 可得水击压强增量 m(水柱高)或水击压强为 m(水柱高) 首相和末相水击压强比较，最大水击压强发生在末相，即为 m(水柱高)或为 m(水柱高)。10-3 解：首先判断水击类型，然后分别计算两种情况下的水击压强。(1) 判断水击类型已知 m，cm，mm，查表10-2-1，由钢管有，可计算水击波速 m/s以及相长s。而阀门关闭时间s，有，为直接水击。由于，阀门关闭结束时水击压强将保持到首相末，故本题所求

3、阀门断面水头为首相末压强水头。(2) 初始开度等，终止开度情况下阀门断面水头已知m，m/s，由于，以及管道特性系数代入式(10-4-17) 得 整理 解此二次方程，得 (不合理) ， 。可得首相末阀门断面水头 m(水柱高)。(3) 初始开度等，终止开度情况下首相末阀门断面水头此时，代入直接水击压强公式式(10-2-3)或例10-1给出的直接水击压强公式得 m(水柱高)10-4 解：根据题目要求，先对水击类型进行判别，后进行水击压强的计算。(1) 判别水击类型已知 m，m，mm，查表10-2-1，由钢管有，可计算水击波速 m/s以及相长s。当阀门关闭时间s，有，发生直接水击。当关闭时间s，有，则

4、发生间接水击。在设置调压室后，调压室的作用类似于水库，水击波将由调压室而反射，这时管长m，相应的相长s。当阀门关闭时间s，有，则发生间接水击。(2) 管长m时，计算水击压强增量已知流量m3/s，则m/s，水头m，初始开度等，终止开度。当阀门关闭时间s，发生直接水击。则由直接水击压强公式式(10-2-3)，得水击压强增量 m(水柱高)当阀门关闭时间s，发生间接水击。由于，将计算首相末阀门断面水击压强增量，和第二相末(即末相)末水击压强增量。为计算间接水击压强，可令阀门按线性规律启闭，即阀门开度 。在首相末，s，阀门开度，以及管道特性系数代入式(10-4-17) 得 整理 解此二次方程，得 (不合

5、理) ， 。可得首相末阀门断面压强增量 m(水柱高)。在第二相末，将已知的，代入式(10-4-17)得 解此方程 或 m(水柱高)最大水击压强增量发生在首相末。(3) 管长m时，计算水击压强增量相应的相长s，当阀门关闭时间s，发生间接水击。由于，将计算首相末、第二相末、第三相末、第四相末阀门断面水击压强增量，从中找出最大水击压强增量。采用例10-3所给的程序进行计算，计算结果如下tttnhnh0.9855 0.6715 0.4495 40.4581.9710 0.3430 0.4714 42.4272.9565 1.4487 0.4639 41.7513.9421 0.0000-4.2282-

6、38.054从计算结果可见，第二相末水击压强增量最大。10-5 解：已知m，mm，可计算水击波速 m/s以及相长s。由于最大水击压强值产生在第一相末，又考虑阀门按线性关闭，则此时阀门开度为。根据题意，可令，其中K为待求系数。由此第一相末的阀门开度为。又根据题给条件，m/s，m，初始开度，可求管道特性系数并代入式(10-4-17) 得 由于，和题给，则有，代入上式得1解此不等式，得3.64，即阀门关闭时间至少应为相长的3.64倍。10-6 解：本题可使用特征线法进行计算，可采用例10-3所给的程序进行计算，计算结果如下(1) 关闭指数t0L0.2L0.4L0.6L0.8LL开度.000090.0

7、89.555789.111488.667188.222887.77851.00000.259290.089.555789.111488.667188.222891.6467.956800.518490.089.555789.111488.667192.075994.7822.913600.777690.089.555789.111492.505295.199698.0647.8704001.036890.089.555792.934595.617198.4702101.4760.8272001.296090.093.364096.034898.8758101.8695105.0463.7840

8、001.555290.096.452599.2815102.2631105.4277108.7569.7408001.814490.095.9082102.6569105.8092109.1261112.6391.6976002.073690.096.2053102.4251109.4955112.9961116.6735.6544002.332890.096.5149103.0426109.6000117.0184120.8927.6112002.592090.096.8355103.6860110.5624117.4837125.2766.5680002.851290.097.169310

9、4.3516111.5643118.8157124.0071.5248003.110490.097.5144105.0442112.6000118.0863123.7999.4816003.369690.097.8733105.7597111.5662117.5868123.3786.4384003.628890.098.2438104.3966110.7502116.8610122.7122.3952003.888090.096.5256103.2387109.6947115.8786121.7814.3520004.147290.094.9996101.8275108.3707114.61

10、87120.5528.3088004.406490.095.3035100.1355106.7554113.0488118.9996.2656004.665690.095.1358100.2330104.8174111.1403117.0849.2224004.924890.094.929999.8180104.6198108.8574114.7726.1792005.184090.094.682599.3173103.8587108.2543112.0208.1360005.443290.094.387798.7237102.9527107.0231112.7560.0928005.7024

11、90.094.041598.0236101.8889107.4548112.8002.0496005.961690.093.636097.2070102.5257107.6659112.9935.0064006.220890.093.165698.1381102.9839108.0645108.7584.0000006.480090.094.502098.9424103.6768104.0767103.9403.0000006.739290.095.7762100.0402100.035899.553999.3957.0000006.998490.095.537796.870395.91969

12、5.356195.1682.0000007.257690.091.096591.420892.192891.534991.3171.0000007.516890.085.889186.423687.038888.154887.9022.0000007.776090.085.330481.511682.388383.407284.9928.0000008.035290.085.622681.297177.882979.227778.9129.0000008.294490.085.966681.993878.137873.390473.4639.0000008.553690.086.371082.

13、806877.501472.374767.8690.0000008.812890.086.840281.878677.043971.980071.2856.0000009.072090.085.507681.077476.357475.954576.0904.0000009.331290.084.237879.986979.987480.466580.6227.0000009.590490.084.479783.147184.093884.654384.8419.0000009.849690.088.907088.582987.811788.468188.6853.00000010.10889

14、0.094.097393.567092.954691.841892.0938.00000010.368090.094.656898.464597.594396.579194.9980.00000010.627290.094.367198.6821102.0861100.7491101.0638.00000010.886490.094.025497.9888101.8357106.5690106.4991.00000011.145690.093.621997.1794102.4717107.5848112.0731.00000011.404890.093.154098.1047102.92851

15、07.9757108.6705.00000011.664090.094.482798.9029103.6086104.0144103.8790.00000011.923290.095.748399.986299.989499.513299.3590.00000012.182490.095.503096.835695.892995.335495.1480.00000012.441690.091.089691.413592.183791.528991.3124.00000012.700890.085.916386.442387.052088.161687.9102.00000012.960090.

16、085.355981.559382.422983.434585.0112.00000013.219290.085.643281.338677.944879.273978.9594.00000013.478490.085.982582.028478.190873.471473.5378.00000013.737690.086.385182.834477.555272.455567.9846.00000013.996890.086.851881.911977.099172.068371.3731.00000014.256090.085.526881.116776.425276.016676.151

17、5.00000014.515290.084.265580.040680.033580.507180.6592.00000014.774490.084.514283.181684.120384.674984.8620.00000015.033690.088.913888.590287.820888.474188.6900.00000015.292890.094.070293.548592.941591.835092.0858.00000015.552090.094.631598.417097.559996.552094.9796.00000015.811290.094.346698.640810

18、2.0246100.7031101.0175.00000016.070490.094.009697.9544101.7829106.4883106.4255.000000(2) 关闭指数t0L0.2L0.4L0.6L0.8LL开度.000090.089.555789.111488.667188.222887.77851.00000.259290.089.555789.111488.667188.222894.6442.915466.518490.089.555789.111488.667195.0621100.8436.834665.777690.089.555789.111495.48011

19、01.2392107.2383.7575961.036890.089.555795.8983101.6349107.6123113.7543.6842601.296090.096.3165102.0308107.9865114.1077120.3959.6146561.555290.0102.4269108.3610114.4614120.7300127.0777.5487851.814490.0102.0251114.8154121.0644127.3939133.7995.4866462.073690.0102.3886114.7098127.7104134.0992140.4664.42

20、82392.332890.0102.6830115.2824127.7281140.7514147.0756.3735652.592090.0102.8927115.6992128.3221140.6913153.5259.3226242.851290.0103.0156115.9313128.6608141.0961148.0676.2754153.110490.0103.0384115.9769128.7048136.0432143.0135.2319393.369690.0102.9613115.8120123.3640130.6324136.9661.1921953.628890.01

21、02.7737110.3508117.7454124.2954129.9431.1561833.888090.097.3898104.7083111.2856117.0629122.0056.1239044.147290.091.938898.3268104.0275109.0004113.2181.0953574.406490.090.940591.263696.0444100.1856103.6744.0705434.665690.089.326588.663187.427290.721393.4900.0494624.924890.087.724785.493583.344980.735

22、582.8038.0321135.184090.086.168982.409878.805375.430171.7832.0184965.443290.084.686679.483374.497669.854570.6554.0086125.702490.083.315376.775970.533769.723469.5359.0024605.961690.082.089774.366172.001870.215169.6431.0000416.220890.081.051177.315574.047271.921571.1368.0000006.480090.085.224880.73037

23、7.234374.968574.2038.0000006.739290.089.674585.140481.649679.515578.7997.0000006.998490.089.912690.588487.417985.478884.8263.0000007.257690.090.913092.185994.411792.725692.1564.0000007.516890.092.271794.733897.4890101.0850100.6227.0000007.776090.093.818997.5719101.4040105.3833110.0107.0000008.035290

24、.095.2987100.4867105.4637110.3282110.1431.0000008.294490.096.6668103.1889109.4097110.2231110.6457.0000008.553690.097.8899105.5894107.9482109.7272110.3030.0000008.812890.098.9224102.6492105.9072108.0283108.8087.0000009.072090.094.760399.2420102.7302104.9892105.7537.0000009.331290.090.324494.844498.32

25、59100.4566101.1701.0000009.590490.090.087189.413792.574694.508895.1606.0000009.849690.089.090287.821385.602487.281687.8491.00000010.108890.087.735985.281582.532978.947079.4048.00000010.368090.086.193182.450478.629174.659070.0477.00000010.627290.084.716079.543274.578869.731369.9139.00000010.886490.08

26、3.351176.846070.646669.834269.4149.00000011.145690.082.130374.454872.101570.330269.7545.00000011.404890.081.104077.385874.138172.021771.2454.00000011.664090.085.254480.785577.305175.052974.2887.00000011.923290.089.676885.170681.698379.571178.8599.00000012.182490.089.913290.584387.432985.503484.8525.

27、00000012.441690.090.906692.171494.383592.711392.1453.00000012.700890.092.256694.703397.4452101.0212100.5678.00000012.960090.093.794997.5275101.3380105.2990109.8943.00000013.219290.095.2694100.4271105.3788110.2095110.0294.00000013.478490.096.6312103.1192109.2975110.1088110.5248.00000013.737690.097.84

28、95105.5013107.8491109.6128110.1883.00000013.996890.098.8698102.5794105.8168107.9286108.7008.00000014.256090.094.730999.1871102.6598104.9053105.6692.00000014.515290.090.322194.814598.2775100.4014101.1102.00000014.774490.090.086589.417892.559794.484495.1345.00000015.033690.089.096687.835885.630487.295

29、987.8601.00000015.292890.087.750985.311882.576579.010479.4594.00000015.552090.086.217082.494578.694874.742870.1634.00000015.811290.084.745179.602474.663269.849370.0270.00000016.070490.083.386476.915370.758169.947869.5351.00000010-7 解：在同一水位情况下，有流量公式，其中 恒定流流量 非恒定流流量 由于 此处，为附加水面坡度。对于恒定流有，；对于非恒定流，涨水时一般总

30、是上游先涨水，则有，；落水时一般总是上游先退水，则有，。这样由于附加水面坡度的影响，对于同一水位，有。整个洪水期的水位流量关系曲线将呈现绳套形曲线。可参见教材图10-5-2(a)。10-8 解：由明槽非恒定流运动方程式(10-6-11)，有将代入上式，得在上式中，有 其中由连续性方程(无旁侧入流)可得，又由棱柱体渠道则 将上述各项代入运动方程，得由此得证。10-9 解：由于 将上式对求偏导，有又对水深与水位的关系式或求偏导，并考虑，可得式中为底坡。另外，对于同一断面有，以及，则得证毕。10-10解：首先从数学上说明最大值出现的性质，再讨论各种水力要素最大值的出现顺序。1 从数学上说明某函数A出

31、现最大值的性质(1) 从时间方面分析。对某断面，设t时刻某函数值为，时刻某函数值为，则有函数对时间的偏导数为。还未出现最大值时，最高点未到，函数随时间增加，有，故；当已出现最大值时，最高点已过，函数随时间减少，有，故；正处在最大值时，函数随时间不变化，有，故 。(2) 从位置方面分析。某函数A最大值的出现是从上游到下游依次出现的。假定最大值发生在断面处，在以某断面为中心的领域内，即在范围内，必有 。下面分两种情况进行说明。在说明之前对此偏微分作下列变形还未出现函数最大值的地方，在此最大值处的下游，函数曲线的斜率小于零，并且随时间的增加，函数的最大值点处将向下游移动，还未出现最大值处的函数值将逼

32、近最大值点，函数曲线的斜率的绝对值将趋近于零，即有，可得 ；已出现过函数最大值的地方，在此最大值处的上游，函数曲线的斜率大于零，并且随时间的增加，函数的最大值点处将向下游移动，出现过最大值处的函数值将远离最大值点，函数曲线的斜率将由趋近于零逐渐增加，即有，可得 。2 分析各种水力要素最大值的出现顺序。关于与。由于，而。如果水位最大值未出现，按照前述数学推论，有，这时，说明的最大值已出现过。也就是说，出现在之前。关于与、。由z、v表示的运动方程，令，即忽略惯性力影响，可得 ，并微分得当时，同时有，也就是水位值正出现最大值时，由前知水面坡度已出现，即，由上式可得，也就是说出现在之前。另外，当时，即

33、正在出现时，还未出现，也未出现，即有，由上式可知，应有，也就是说在说之前出现。关于与、。由于，对其求偏导，有。当已知水位正出现时，面积A也应处于最大值，即 。此时如果流速已出现，亦即，则可得，也就是说出现在之前。另外，当时，即正在出现时，如果有，也就是还未出现，可有，也就是还未出现，即在说之前出现。由上述讨论可知，所讨论的这些水力要素最大值出现的先后顺序是：、 。10-11 解：可使用例10-5所给出的计算程序进行计算，计算时需将水深h折算成水位z进行计算，上下游边界条件需改写。下表给出了用特征线法计算的部分成果th1Q1h2Q2h3Q3h4Q401.26015.00001.26015.000

34、01.26015.00001.26015.0000301.34016.78771.33116.57991.32216.37751.31316.1823601.42018.58721.41118.36941.40118.15251.39217.9369901.53021.28001.51820.97431.50520.67131.49320.37251201.64024.05181.62823.73761.61623.42541.60523.11681501.73526.51611.72526.24051.71525.96731.70625.69881801.83029.14641.82128.

35、86921.81228.59681.80428.33322101.91531.56021.90731.31161.90031.06941.89430.83842402.00034.10651.99333.85821.98733.61911.98233.39522702.07536.38582.06936.16932.06535.96402.06235.77683002.15038.78142.14538.56722.14138.36742.14038.19003302.18539.71642.18439.63262.18539.56372.18839.51813602.22040.85782.

36、22040.78022.22140.72162.22540.69163902.21540.47312.21940.52632.22440.59772.23240.69734202.21040.29392.21440.35092.22040.42862.22940.53804502.16538.61242.17338.79432.18238.99492.19439.22444802.12037.16442.12837.34492.13737.54532.14937.77555102.08536.11532.09236.26082.10036.42552.11036.61875402.05035.

37、03522.05635.17632.06435.33422.07435.51835701.97532.58271.98532.83871.99633.10812.00933.39856001.90030.38761.91030.63851.92130.90281.93431.18756301.83528.59361.84428.80831.85429.03501.86529.28006601.77026.81371.77827.02101.78827.23811.79827.46996901.68524.49161.69524.74801.70625.01091.71825.28427201.

38、60022.33781.61122.58761.62122.84321.63323.10797501.57521.92301.57922.00551.58322.09601.58922.19857801.55021.32171.55321.39801.55721.47841.56221.56528101.51020.31501.51520.42951.52020.54611.52620.66658401.47019.37431.47519.48781.48019.60371.48619.72358701.38517.32201.39517.54911.40517.77511.41618.000

39、19001.30015.49461.31115.71881.32115.94351.33216.1690th5Q5h6Q6h7Q7h8Q8 01.26015.00001.26015.00001.26015.00001.26015.0000301.30515.99601.29715.82051.29015.65671.28315.5053601.38217.72371.37317.51421.36517.31091.35817.1183901.48220.08001.47119.79751.46219.53081.45519.28981201.59422.81501.58422.52521.57

40、722.25651.57322.02461501.69825.43921.69225.19581.68824.98131.69024.81651801.79728.08401.79327.85951.79327.67581.80027.55782101.89030.62611.88930.44461.89330.31341.90630.26082401.97933.19601.98133.03591.98832.93722.00532.93102702.06235.61892.06735.50632.07835.46412.10035.52513002.14138.04772.14837.95

41、942.16337.95112.19038.05863302.19539.50942.20739.55692.22839.68882.26139.93903602.23440.70522.24840.78312.27140.95402.30841.25293902.24540.84012.26341.04662.29141.34562.33241.77114202.24240.69412.26140.91832.28941.23862.33141.68954502.21139.49702.23339.83312.26440.26032.30740.81154802.16538.04932.18

42、738.38672.21738.81422.25939.36445102.12536.85382.14437.14992.17237.53262.21138.03415402.08835.74082.10636.01982.13236.38002.16936.85325702.02533.72062.04634.09092.07334.53232.11035.07486001.94931.50301.96931.86371.99532.29122.02932.81296301.87829.55221.89629.86531.91830.23791.94830.69606601.81127.72

43、431.82628.01281.84628.35221.87328.76616901.73225.57441.74825.89071.76726.24731.79226.66487201.64623.38661.66123.68731.67924.02131.70124.40557501.59522.31791.60422.46131.61522.63891.63022.86577801.56721.66221.57421.77481.58221.91221.59522.08758101.53220.79351.53920.93161.54921.08851.56121.27568401.49

44、219.84961.49919.98591.50820.13891.51920.31818701.42618.22551.43618.45291.44818.68651.46118.93269001.34316.39631.35416.62621.36516.86071.37717.1017th9Q9h10Q10h11Q11 01.26015.00001.26015.00001.26015.0000301.27715.36531.27215.23691.26915.1201601.35316.94491.35216.80591.35916.7286901.45219.09111.45818.9

45、6311.47718.94871201.57621.85541.59121.78831.62621.87581501.70224.73311.72724.77631.77624.99821801.81827.54191.85427.67461.91528.00192101.93130.32601.97630.55482.04830.98572402.03733.05812.09033.36172.17333.87072702.13935.73102.20036.12062.29236.71423002.23538.32122.30338.77452.40439.42813302.31340.3

46、4782.38840.94592.49541.74003602.36341.71672.44342.37422.55343.22603902.39142.36032.47443.14022.58744.11484202.39042.30662.47443.11712.58744.12384502.36741.52332.45142.42462.56243.52524802.31740.07282.39740.97072.50442.07095102.26638.69032.34239.53402.44540.58145402.22137.47542.29438.28172.39339.2916

47、5702.16135.75462.23136.60862.32537.66406002.07533.46342.13934.28042.22635.29576301.98931.27252.04732.00552.12532.93056601.91029.28591.96129.94942.03230.79546901.82627.17141.87127.80361.93428.60197201.73024.86391.76825.42801.82126.13717501.65223.16201.68223.55681.72624.08657801.61322.32131.63922.6424

48、1.67823.08978101.57721.51151.60221.82281.63722.24618401.53420.53891.55520.82381.58521.20458701.47519.20201.49419.51001.51719.87979001.38917.35231.40117.61601.41417.8960使用直接差分法的程序也可进行计算，上下游边界的处理与特征线法类拟，计算成果与上述成果类拟。也可使用水深h、流量Q作为待求变量进行求解，这时将重新编写程序。计算成果应与上述成果类拟。10-12 解：可使用例10-5所给出的计算程序进行计算，计算时需将水深h折算成水位

49、z进行计算，上游边界条件需改写为计算流量Q的边界条件，下游边界条件需改写为计算水位z的边界条件。下表给出了用特征线法计算的部分成果。th1Q1h2Q2h3Q3h4Q401.26015.0001.26015.0001.26015.0001.26015.000601.30017.0001,26014.9011,26014.9011,26014.9011201.35819.0001.28716.2801.26014.8901.26014.8906001.53521.0001.52321.6241.48421.2041.42920.07313201.29215.0001.31915.4841.3481

50、6.0891.37216.768th5Q5h6Q6h7Q7h8Q801.26015.0001.26015.0001.26015.0001.26015.000601,26014.9011,26014.9011,26014.9011,26014.9011201.26014.8901.26014.8901.26014.8901.26014.8906001.37017.1291.32317.1291.28915.9391.27115.35913201.38917.3251.39717.1981.39317.9301.38117.891th9Q9h10Q10h11Q1101.26015.0001.26015.0001.26015.000601,26014.9011,26014.9011,25814.9441201.26014.8901.25914.9031.25714.8976001.26215.0221.25914.9261.25514.85313201.36217.5611.33817.1191.30916.579【精品文档】第 97 页