武汉大学水力知识学知识题解答水击.docx
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武汉大学水力知识学知识题解答水击
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
tt
tn
hn
h
0.9855
0.6715
0.4495
40.458
1.9710
0.3430
0.4714
42.427
2.9565
1.4487
0.4639
41.751
3.9421
0.0000
-4.2282
-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
t
0L
0.2L
0.4L
0.6L
0.8L
L
开度
.0000
90.0
89.5557
89.1114
88.6671
88.2228
87.7785
1.00000
.2592
90.0
89.5557
89.1114
88.6671
88.2228
91.6467
.956800
.5184
90.0
89.5557
89.1114
88.6671
92.0759
94.7822
.913600
.7776
90.0
89.5557
89.1114
92.5052
95.1996
98.0647
.870400
1.0368
90.0
89.5557
92.9345
95.6171
98.4702
101.4760
.827200
1.2960
90.0
93.3640
96.0348
98.8758
101.8695
105.0463
.784000
1.5552
90.0
96.4525
99.2815
102.2631
105.4277
108.7569
.740800
1.8144
90.0
95.9082
102.6569
105.8092
109.1261
112.6391
.697600
2.0736
90.0
96.2053
102.4251
109.4955
112.9961
116.6735
.654400
2.3328
90.0
96.5149
103.0426
109.6000
117.0184
120.8927
.611200
2.5920
90.0
96.8355
103.6860
110.5624
117.4837
125.2766
.568000
2.8512
90.0
97.1693
104.3516
111.5643
118.8157
124.0071
.524800
3.1104
90.0
97.5144
105.0442
112.6000
118.0863
123.7999
.481600
3.3696
90.0
97.8733
105.7597
111.5662
117.5868
123.3786
.438400
3.6288
90.0
98.2438
104.3966
110.7502
116.8610
122.7122
.395200
3.8880
90.0
96.5256
103.2387
109.6947
115.8786
121.7814
.352000
4.1472
90.0
94.9996
101.8275
108.3707
114.6187
120.5528
.308800
4.4064
90.0
95.3035
100.1355
106.7554
113.0488
118.9996
.265600
4.6656
90.0
95.1358
100.2330
104.8174
111.1403
117.0849
.222400
4.9248
90.0
94.9299
99.8180
104.6198
108.8574
114.7726
.179200
5.1840
90.0
94.6825
99.3173
103.8587
108.2543
112.0208
.136000
5.4432
90.0
94.3877
98.7237
102.9527
107.0231
112.7560
.092800
5.7024
90.0
94.0415
98.0236
101.8889
107.4548
112.8002
.049600
5.9616
90.0
93.6360
97.2070
102.5257
107.6659
112.9935
.006400
6.2208
90.0
93.1656
98.1381
102.9839
108.0645
108.7584
.000000
6.4800
90.0
94.5020
98.9424
103.6768
104.0767
103.9403
.000000
6.7392
90.0
95.7762
100.0402
100.0358
99.5539
99.3957
.000000
6.9984
90.0
95.5377
96.8703
95.9196
95.3561
95.1682
.000000
7.2576
90.0
91.0965
91.4208
92.1928
91.5349
91.3171
.000000
7.5168
90.0
85.8891
86.4236
87.0388
88.1548
87.9022
.000000
7.7760
90.0
85.3304
81.5116
82.3883
83.4072
84.9928
.000000
8.0352
90.0
85.6226
81.2971
77.8829
79.2277
78.9129
.000000
8.2944
90.0
85.9666
81.9938
78.1378
73.3904
73.4639
.000000
8.5536
90.0
86.3710
82.8068
77.5014
72.3747
67.8690
.000000
8.8128
90.0
86.8402
81.8786
77.0439
71.9800
71.2856
.000000
9.0720
90.0
85.5076
81.0774
76.3574
75.9545
76.0904
.000000
9.3312
90.0
84.2378
79.9869
79.9874
80.4665
80.6227
.000000
9.5904
90.0
84.4797
83.1471
84.0938
84.6543
84.8419
.000000
9.8496
90.0
88.9070
88.5829
87.8117
88.4681
88.6853
.000000
10.1088
90.0
94.0973
93.5670
92.9546
91.8418
92.0938
.000000
10.3680
90.0
94.6568
98.4645
97.5943
96.5791
94.9980
.000000
10.6272
90.0
94.3671
98.6821
102.0861
100.7491
101.0638
.000000
10.8864
90.0
94.0254
97.9888
101.8357
106.5690
106.4991
.000000
11.1456
90.0
93.6219
97.1794
102.4717
107.5848
112.0731
.000000
11.4048
90.0
93.1540
98.1047
102.9285
107.9757
108.6705
.000000
11.6640
90.0
94.4827
98.9029
103.6086
104.0144
103.8790
.000000
11.9232
90.0
95.7483
99.9862
99.9894
99.5132
99.3590
.000000
12.1824
90.0
95.5030
96.8356
95.8929
95.3354
95.1480
.000000
12.4416
90.0
91.0896
91.4135
92.1837
91.5289
91.3124
.000000
12.7008
90.0
85.9163
86.4423
87.0520
88.1616
87.9102
.000000
12.9600
90.0
85.3559
81.5593
82.4229
83.4345
85.0112
.000000
13.2192
90.0
85.6432
81.3386
77.9448
79.2739
78.9594
.000000
13.4784
90.0
85.9825
82.0284
78.1908
73.4714
73.5378
.000000
13.7376
90.0
86.3851
82.8344
77.5552
72.4555
67.9846
.000000
13.9968
90.0
86.8518
81.9119
77.0991
72.0683
71.3731
.000000
14.2560
90.0
85.5268
81.1167
76.4252
76.0166
76.1515
.000000
14.5152
90.0
84.2655
80.0406
80.0335
80.5071
80.6592
.000000
14.7744
90.0
84.5142
83.1816
84.1203
84.6749
84.8620
.000000
15.0336
90.0
88.9138
88.5902
87.8208
88.4741
88.6900
.000000
15.2928
90.0
94.0702
93.5485
92.9415
91.8350
92.0858
.000000
15.5520
90.0
94.6315
98.4170
97.5599
96.5520
94.9796
.000000
15.8112
90.0
94.3466
98.6408
102.0246
100.7031
101.0175
.000000
16.0704
90.0
94.0096
97.9544
101.7829
106.4883
106.4255
.000000
(2)关闭指数
t
0L
0.2L
0.4L
0.6L
0.8L
L
开度
.0000
90.0
89.5557
89.1114
88.6671
88.2228
87.7785
1.00000
.2592
90.0
89.5557
89.1114
88.6671
88.2228
94.6442
.915466
.5184
90.0
89.5557
89.1114
88.6671
95.0621
100.8436
.834665
.7776
90.0
89.5557
89.1114
95.4801
101.2392
107.2383
.757596
1.0368
90.0
89.5557
95.8983
101.6349
107.6123
113.7543
.684260
1.2960
90.0
96.3165
102.0308
107.9865
114.1077
120.3959
.614656
1.5552
90.0
102.4269
108.3610
114.4614
120.7300
127.0777
.548785
1.8144
90.0
102.0251
114.8154
121.0644
127.3939
133.7995
.486646
2.0736
90.0
102.3886
114.7098
127.7104
134.0992
140.4664
.428239
2.3328
90.0
102.6830
115.2824
127.7281
140.7514
147.0756
.373565
2.5920
90.0
102.8927
115.6992
128.3221
140.6913
153.5259
.322624
2.8512
90.0
103.0156
115.9313
128.6608
141.0961
148.0676
.275415
3.1104
90.0
103.0384
115.9769
128.7048
136.0432
143.0135
.231939
3.3696
90.0
102.9613
115.8120
123.3640
130.6324
136.9661
.192195
3.6288
90.0
102.7737
110.3508
117.7454
124.2954
129.9431
.156183
3.8880
90.0
97.3898
104.7083
111.2856
117.0629
122.0056
.123904
4.1472
90.0
91.9388
98.3268
104.0275
109.0004
113.2181
.095357
4.4064
90.0
90.9405
91.2636
96.0444
100.1856
103.6744
.070543
4.6656
90.0
89.3265
88.6631
87.4272
90.7213
93.4900
.049462
4.9248
90.0
87.7247
85.4935
83.3449
80.7355
82.8038
.032113
5.1840
90.0
86.1689
82.4098
78.8053
75.4301
71.7832
.018496
5.4432
90.0
84.6866
79.4833
74.4976
69.8545
70.6554
.008612
5.7024
90.0
83.3153
76.7759
70.5337
69.7234
69.5359
.002460
5.9616
90.0
82.0897
74.3661
72.0018
70.2151
69.6431
.000041
6.2208
90.0
81.0511
77.3155
74.0472
71.9215
71.1368
.000000
6.4800
90.0
85.2248
80.7303
77.2343
74.9685
74.2038
.000000
6.7392
90.0
89.6745
85.1404
81.6496
79.5155
78.7997
.000000
6.9984
90.0
89.9126
90.5884
87.4179
85.4788
84.8263
.000000
7.2576
90.0
90.9130
92.1859
94.4117
92.7256
92.1564
.000000
7.5168
90.0
92.2717
94.7338
97.4890
101.0850
100.6227
.000000
7.7760
90.0
93.8189
97.5719
101.4040
105.3833
110.0107
.000000
8.0352
90.0
95.2987
100.4867
105.4637
110.3282
110.1431
.000000
8.2944
90.0
96.6668
103.1889
109.4097
110.2231
110.6457
.000000
8.5536
90.0
97.8899
105.5894
107.9482
109.7272
110.3030
.000000
8.8128
90.0
98.9224
102.6492
105.9072
108.0283
108.8087
.000000
9.0720
90.0
94.7603
99.2420
102.7302
104.9892
105.7537
.000000
9.3312
90.0
90.3244
94.8444
98.3259
100.4566
101.1701
.000000
9.5904
90.0
90.0871
89.4137
92.5746
94.5088
95.1606
.000000
9.8496
90.0
89.0902
87.8213
85.6024
87.2816
87.8491
.000000
10.1088
90.0
87.7359
85.2815
82.5329
78.9470
79.4048
.000000
10.3680
90.0
86.1931
82.4504
78.6291
74.6590
70.0477
.000000
10.6272
90.0
84.7160
79.5432
74.5788
69.7313
69.9139
.000000
10.8864
90.0
83.3511
76.8460
70.6466
69.8342
69.4149
.000000
11.1456
90.0
82.1303
74.4548
72.1015
70.3302
69.7545
.000000
11.4048
90.0
81.1040
77.3858
74.1381
72.0217
71.2454
.000000
11.6640
90.0
85.2544
80.7855
77.3051
75.0529
74.2887
.000000
11.9232
90.0
89.6768
85.1706
81.6983
79.5711
78.8599
.000000
12.1824
90.0
89.9132
90.5843
87.4329
85.5034
84.8525
.000000
12.4416
90.0
90.90