|
Normal Shock WavesStaff posted on October 20, 2006 |
Normal Shock Waves
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Normal Shock Waves Equations:
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|
|
|
M1
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|
p2 / p1
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pt2/pt1
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|
r2 / r1
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T2 / T1
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|
M2
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|
1.00
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|
1.0000
|
|
1.0000
|
|
1.0000
|
|
1.0000
|
|
1.00
|
|
1.01
|
|
1.0235
|
|
1.0000
|
|
1.0167
|
|
1.0066
|
|
0.99
|
|
1.02
|
|
1.0471
|
|
1.0000
|
|
1.0334
|
|
1.0132
|
|
0.98
|
|
1.03
|
|
1.0711
|
|
1.0000
|
|
1.0502
|
|
1.0198
|
|
0.97
|
|
1.04
|
|
1.0952
|
|
0.9999
|
|
1.0671
|
|
1.0263
|
|
0.96
|
|
1.05
|
|
1.1196
|
|
0.9999
|
|
1.0840
|
|
1.0328
|
|
0.95
|
|
1.06
|
|
1.1442
|
|
0.9998
|
|
1.1009
|
|
1.0393
|
|
0.94
|
|
1.07
|
|
1.1691
|
|
0.9996
|
|
1.1179
|
|
1.0458
|
|
0.94
|
|
1.08
|
|
1.1941
|
|
0.9994
|
|
1.1349
|
|
1.0522
|
|
0.93
|
|
1.09
|
|
1.2195
|
|
0.9992
|
|
1.1520
|
|
1.0586
|
|
0.92
|
|
1.10
|
|
1.2450
|
|
0.9989
|
|
1.1691
|
|
1.0649
|
|
0.91
|
|
1.11
|
|
1.2708
|
|
0.9986
|
|
1.1862
|
|
1.0713
|
|
0.90
|
|
1.12
|
|
1.2968
|
|
0.9982
|
|
1.2034
|
|
1.0776
|
|
0.90
|
|
1.13
|
|
1.3231
|
|
0.9978
|
|
1.2206
|
|
1.0840
|
|
0.89
|
|
1.14
|
|
1.3495
|
|
0.9973
|
|
1.2378
|
|
1.0903
|
|
0.88
|
|
1.15
|
|
1.3763
|
|
0.9967
|
|
1.2550
|
|
1.0966
|
|
0.88
|
|
1.16
|
|
1.4032
|
|
0.9961
|
|
1.2723
|
|
1.1029
|
|
0.87
|
|
1.17
|
|
1.4304
|
|
0.9953
|
|
1.2896
|
|
1.1092
|
|
0.86
|
|
1.18
|
|
1.4578
|
|
0.9946
|
|
1.3069
|
|
1.1154
|
|
0.85
|
|
1.19
|
|
1.4855
|
|
0.9937
|
|
1.3243
|
|
1.1217
|
|
0.85
|
|
1.20
|
|
1.5133
|
|
0.9928
|
|
1.3416
|
|
1.1280
|
|
0.84
|
| |
|
1.21
|
|
1.5415
|
|
0.9918
|
|
1.3590
|
|
1.1343
|
|
0.84
|
|
1.22
|
|
1.5698
|
|
0.9907
|
|
1.3764
|
|
1.1405
|
|
0.83
|
|
1.23
|
|
1.5984
|
|
0.9896
|
|
1.3938
|
|
1.1468
|
|
0.82
|
|
1.24
|
|
1.6272
|
|
0.9884
|
|
1.4112
|
|
1.1531
|
|
0.82
|
|
1.25
|
|
1.6563
|
|
0.9871
|
|
1.4286
|
|
1.1594
|
|
0.81
|
|
1.26
|
|
1.6855
|
|
0.9857
|
|
1.4460
|
|
1.1657
|
|
0.81
|
|
1.27
|
|
1.7151
|
|
0.9842
|
|
1.4634
|
|
1.1720
|
|
0.80
|
|
1.28
|
|
1.7448
|
|
0.9827
|
|
1.4808
|
|
1.1783
|
|
0.80
|
|
1.29
|
|
1.7748
|
|
0.9811
|
|
1.4983
|
|
1.1846
|
|
0.79
|
|
1.30
|
|
1.8050
|
|
0.9794
|
|
1.5157
|
|
1.1909
|
|
0.79
|
|
1.31
|
|
1.8355
|
|
0.9776
|
|
1.5331
|
|
1.1972
|
|
0.78
|
|
1.32
|
|
1.8661
|
|
0.9758
|
|
1.5505
|
|
1.2035
|
|
0.78
|
|
1.33
|
|
1.8971
|
|
0.9738
|
|
1.5680
|
|
1.2099
|
|
0.77
|
|
1.34
|
|
1.9282
|
|
0.9718
|
|
1.5854
|
|
1.2162
|
|
0.77
|
|
1.35
|
|
1.9596
|
|
0.9697
|
|
1.6028
|
|
1.2226
|
|
0.76
|
|
1.36
|
|
1.9912
|
|
0.9676
|
|
1.6202
|
|
1.2290
|
|
0.76
|
|
1.37
|
|
2.0231
|
|
0.9653
|
|
1.6376
|
|
1.2354
|
|
0.75
|
|
1.38
|
|
2.0551
|
|
0.9630
|
|
1.6549
|
|
1.2418
|
|
0.75
|
|
1.39
|
|
2.0875
|
|
0.9607
|
|
1.6723
|
|
1.2482
|
|
0.74
|
|
1.40
|
|
2.1200
|
|
0.9582
|
|
1.6897
|
|
1.2547
|
|
0.74
|
| |
|
1.41
|
|
2.1528
|
|
0.9557
|
|
1.7070
|
|
1.2612
|
|
0.74
|
|
1.42
|
|
2.1858
|
|
0.9531
|
|
1.7243
|
|
1.2676
|
|
0.73
|
|
1.43
|
|
2.2191
|
|
0.9504
|
|
1.7416
|
|
1.2741
|
|
0.73
|
|
1.44
|
|
2.2525
|
|
0.9476
|
|
1.7589
|
|
1.2807
|
|
0.72
|
|
1.45
|
|
2.2863
|
|
0.9448
|
|
1.7761
|
|
1.2872
|
|
0.72
|
|
1.46
|
|
2.3202
|
|
0.9420
|
|
1.7934
|
|
1.2938
|
|
0.72
|
|
1.47
|
|
2.3544
|
|
0.9390
|
|
1.8106
|
|
1.3003
|
|
0.71
|
|
1.48
|
|
2.3888
|
|
0.9360
|
|
1.8278
|
|
1.3069
|
|
0.71
|
|
1.49
|
|
2.4235
|
|
0.9329
|
|
1.8449
|
|
1.3136
|
|
0.70
|
|
1.50
|
|
2.4583
|
|
0.9298
|
|
1.8621
|
|
1.3202
|
|
0.70
|
|
1.51
|
|
2.4935
|
|
0.9266
|
|
1.8792
|
|
1.3269
|
|
0.70
|
|
1.52
|
|
2.5288
|
|
0.9233
|
|
1.8963
|
|
1.3336
|
|
0.69
|
|
1.53
|
|
2.5644
|
|
0.9200
|
|
1.9133
|
|
1.3403
|
|
0.69
|
|
1.54
|
|
2.6002
|
|
0.9166
|
|
1.9303
|
|
1.3470
|
|
0.69
|
|
1.55
|
|
2.6363
|
|
0.9132
|
|
1.9473
|
|
1.3538
|
|
0.68
|
|
1.56
|
|
2.6725
|
|
0.9097
|
|
1.9643
|
|
1.3606
|
|
0.68
|
|
1.57
|
|
2.7091
|
|
0.9062
|
|
1.9812
|
|
1.3674
|
|
0.68
|
|
1.58
|
|
2.7458
|
|
0.9026
|
|
1.9981
|
|
1.3742
|
|
0.67
|
|
1.59
|
|
2.7828
|
|
0.8989
|
|
2.0149
|
|
1.3811
|
|
0.67
|
|
1.60
|
|
2.8200
|
|
0.8952
|
|
2.0317
|
|
1.3880
|
|
0.67
|
| |
|
1.61
|
|
2.8575
|
|
0.8915
|
|
2.0485
|
|
1.3949
|
|
0.67
|
|
1.62
|
|
2.8951
|
|
0.8877
|
|
2.0653
|
|
1.4018
|
|
0.66
|
|
1.63
|
|
2.9331
|
|
0.8838
|
|
2.0820
|
|
1.4088
|
|
0.66
|
|
1.64
|
|
2.9712
|
|
0.8799
|
|
2.0986
|
|
1.4158
|
|
0.66
|
|
1.65
|
|
3.0096
|
|
0.8760
|
|
2.1152
|
|
1.4228
|
|
0.65
|
|
1.66
|
|
3.0482
|
|
0.8720
|
|
2.1318
|
|
1.4299
|
|
0.65
|
|
1.67
|
|
3.0871
|
|
0.8680
|
|
2.1484
|
|
1.4369
|
|
0.65
|
|
1.68
|
|
3.1261
|
|
0.8639
|
|
2.1649
|
|
1.4440
|
|
0.65
|
|
1.69
|
|
3.1655
|
|
0.8599
|
|
2.1813
|
|
1.4512
|
|
0.64
|
|
1.70
|
|
3.2050
|
|
0.8557
|
|
2.1977
|
|
1.4583
|
|
0.64
|
|
1.71
|
|
3.2448
|
|
0.8516
|
|
2.2141
|
|
1.4655
|
|
0.64
|
|
1.72
|
|
3.2848
|
|
0.8474
|
|
2.2304
|
|
1.4727
|
|
0.64
|
|
1.73
|
|
3.3251
|
|
0.8431
|
|
2.2467
|
|
1.4800
|
|
0.63
|
|
1.74
|
|
3.3655
|
|
0.8389
|
|
2.2629
|
|
1.4873
|
|
0.63
|
|
1.75
|
|
3.4063
|
|
0.8346
|
|
2.2791
|
|
1.4946
|
|
0.63
|
|
1.76
|
|
3.4472
|
|
0.8302
|
|
2.2952
|
|
1.5019
|
|
0.63
|
|
1.77
|
|
3.4884
|
|
0.8259
|
|
2.3113
|
|
1.5093
|
|
0.62
|
|
1.78
|
|
3.5298
|
|
0.8215
|
|
2.3273
|
|
1.5167
|
|
0.62
|
|
1.79
|
|
3.5715
|
|
0.8171
|
|
2.3433
|
|
1.5241
|
|
0.62
|
|
1.80
|
|
3.6133
|
|
0.8127
|
|
2.3592
|
|
1.5316
|
|
0.62
|
| |
|
1.81
|
|
3.6555
|
|
0.8082
|
|
2.3751
|
|
1.5391
|
|
0.61
|
|
1.82
|
|
3.6978
|
|
0.8038
|
|
2.3909
|
|
1.5466
|
|
0.61
|
|
1.83
|
|
3.7404
|
|
0.7993
|
|
2.4067
|
|
1.5541
|
|
0.61
|
|
1.84
|
|
3.7832
|
|
0.7948
|
|
2.4224
|
|
1.5617
|
|
0.61
|
|
1.85
|
|
3.8263
|
|
0.7902
|
|
2.4381
|
|
1.5693
|
|
0.61
|
|
1.86
|
|
3.8695
|
|
0.7857
|
|
2.4537
|
|
1.5770
|
|
0.60
|
|
1.87
|
|
3.9131
|
|
0.7811
|
|
2.4693
|
|
1.5847
|
|
0.60
|
|
1.88
|
|
3.9568
|
|
0.7765
|
|
2.4848
|
|
1.5924
|
|
0.60
|
|
1.89
|
|
4.0008
|
|
0.7720
|
|
2.5003
|
|
1.6001
|
|
0.60
|
|
1.90
|
|
4.0450
|
|
0.7674
|
|
2.5157
|
|
1.6079
|
|
0.60
|
|
1.91
|
|
4.0895
|
|
0.7627
|
|
2.5310
|
|
1.6157
|
|
0.59
|
|
1.92
|
|
4.1341
|
|
0.7581
|
|
2.5463
|
|
1.6236
|
|
0.59
|
|
1.93
|
|
4.1791
|
|
0.7535
|
|
2.5616
|
|
1.6314
|
|
0.59
|
|
1.94
|
|
4.2242
|
|
0.7488
|
|
2.5767
|
|
1.6394
|
|
0.59
|
|
1.95
|
|
4.2696
|
|
0.7442
|
|
2.5919
|
|
1.6473
|
|
0.59
|
|
1.96
|
|
4.3152
|
|
0.7395
|
|
2.6069
|
|
1.6553
|
|
0.58
|
|
1.97
|
|
4.3611
|
|
0.7349
|
|
2.6220
|
|
1.6633
|
|
0.58
|
|
1.98
|
|
4.4071
|
|
0.7302
|
|
2.6369
|
|
1.6713
|
|
0.58
|
|
1.99
|
|
4.4535
|
|
0.7255
|
|
2.6518
|
|
1.6794
|
|
0.58
|