- Email: [email protected]
RAYLEIGH FLOW OF A PERFECT GAS - ONE-DIMENSIONAL, FRICTIONLESS FLOW OF A PERFECT GAS IN A DUCT OF CONSTANT CROSS -SECTIONAL AREA WITH STAGNATION TEMPERATURE CHANGE
TABLE 4 RAYLEIGH FLOW OF A PERFECT GAS - ONE-DIMENSIONAL, FRICTIONLESS FLOW OF A PERFECT GAS IN A DUCT OF CONSTANT CROSS -SECTIONAL AREA WITH STAGNATION TEMPERATURE CHANGE U
M
Ta
To*
T
= 1.400 R
o
V
T*
Ρ Ρ*
R ,.~'
1*
0
0.00
0.0000
0.0000
2.400
1.268
0.0000
0.02
0.0019
0.0023
2.399
1.268
0.0010
0.04
0.0076
0.0092
2.395
1.266
0.0038
0.06
0.0171
0.0205
2.388
1.265
0.0086
0.08
0.0302
0.0362
2.379
1.262
0.0152
0.10
0.0468
0.0560
2.367
1.259
0.0237
0.12
0.0666
0.0797
2.353
1.255
0.0339
0.14
0.0895
0.1069
2.336
1.251
0.0458
0.16
0.1151
0.1374
2.317
1.246
0.0593
0.18
0.1432
0.1708
2.296
1.241
0.0744
0.20
0.1736
0.2066
2.273
1.235
0.0909
0.22
0.2057
0.2445
2.248
1.228
0.1088
0.24
0.2395
0.2841
2.221
1.221
0.1279
0.26
0.2745
0.3250
2.193
1.214
0.1482
0.28
0.3104
0.3667
2.163
1.206
0.1696
0.30
0.3469
0.4089
2.131
1.199
0.1918
0.32
0.3837
0.4512
2.099
1.190
0.2149
0.34
0.4206
0.4933
2.066
1.182
0.2388
0.36
0.4572
0.5348
2.031
1.174
0.2633
0.38
0.4935
0.5755
1.996
1.165
0.2883
0.40
0.5290
0.6151
1.961
1.157
0.3137
0.42
0.5638
0.6535
1.925
1.148
0.3395
0.44
0.5975
0.6903
1.888
1.139
0.3656
0.46
0.6301
0.7254
1.852
1.131
0.3918
0.48
0.6614
0.7587
1.815
1.122
0.4181
154
Table 4
155
RAYLEIGH FLOW OF A PERFECT GAS g
Μ
To To*
=
1.400 Ρ
ο
Τ Τ*
Ρ Ρ*
Ρ
ο
V
ν*
0.50
0.6914
0.7901
1.778
1.114
0.4444
0.52
0.7199
0.8196
1.741
1.106
0.4708
0.54
0.7470
0.8469
1.704
1.098
0. 49 70
0.56
0.7725
0.8723
1.668
1.090
0.5230
0.58
0.7965
0.8955
1.632
1.083
0.5489
0.60
0.8189
0.9167
1.596
1.075
0.5745
0.62
0.8398
0.9358
1.560
1.068
0.5998
0.64
0.8592
0.9530
1.525
1.061
0.6248
0.66
0.8771
0.9682
1.491
1.055
0.6494
0.68
0.8935
0.9814
1.457
1.049
0.6737
0.70
0.9085
0.9929
1.423
1.043
0.6975
0.72
0.9221
1.0026
1.391
1.038
0.7209
0.74
0.9344
1.0106
1.359
1.033
0.7439
0.76
0.9455
1.0171
1.327
1.028
0.7665
0.78
0.9553
1.0220
1.296
1.023
0.7885
0.80
0.9639
1.0255
1.266
1.019
0.8101
0.82
0.9715
1.0276
1.236
1.016
0.8313
0.84
0.9781
1.0285
1.207
1.012
0.8519
0.86
0.9836
1.0283
1.179
1.010
0.8721
0.88
0.9883
1.0269
1.152
1.007
0.8918
0.90
0.9921
1.0245
1.125
1.005
0.9110
0.92
0.9951
1.0212
1.098
1.003
0.9297
0.94
0.9973
1.0170
1.073
1.002
0.9480
0.96
0.9988
1.0120
1.048
1.001
0.9658
0.98
0.9997
1.0064
1.024
1.000
0.9831
156
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g = Μ
To To*
Τ Τ*
1.400 Ρ
ο
Ρ Ρ*
Ρ
ο
V
ν*
1.00
1.000
1.000
1.000
1.000
1.000
1.02
1.000
0.993
0.977
1.000
1.016
1.04
0.999
0.986
0.955
1.001
1.032
1.06
0.998
0.978
0.933
1.002
1.048
1.08
0.996
0.969
0.912
1.003
1.063
1.10
0.994
0.960
0.891
1.005
1.078
1.12
0.991
0.951
0.871
1.007
1.092
1.14
0.989
0.942
0.851
1.010
1.106
1.16
0.986
0.932
0.832
1.012
1.120
1.18
0.982
0.922
0.814
1.016
1.133
1.20
0.979
0.912
0.796
1.019
1.146
1.22
0.975
0.902
0.778
1.023
1.158
1.24
0.971
0.891
0.761
1.028
1.171
1.26
0.967
0.881
0.745
1.033
1.182
1.28
0.962
0.870
0.729
1.038
1.194
1.30
0.958
0.859
0.713
1.044
1.205
1.32
0.953
0.848
0.698
1.050
1.216
1.34
0.949
0.838
0.683
1.056
1.226
1.36
0.944
0.827
0.669
1.063
1.237
1.38
0.939
0.816
0.655
1.070
1.247
1.40
0.934
0.805
0.641
1.078
1.256
1.42
0.929
0.795
0.628
1.086
1.266
1.44
0.924
0.784
0.615
1.094
1.275
1.46
0.919
0.773
0.602
1.103
1.284
1.48
0.914
0.763
0.590
1.112
1.293
157
Table 4
RAYLEIGH FLOW OF A PERFECT GAS g =1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
1.50
0.909
0.753
0.578
1.122
1.301
1.52
0.904
0.742
0.567
1.132
1.309
1.54
0.899
0.732
0.556
1.142
1.317
1.56
0.894
0.722
0.545
1.153
1.325
1.58
0.889
0.712
0.534
1.164
1.333
1.60
0.884
0.702
0.524
1.176
1.340
1.62
0.879
0.692
0.513
1.188
1.348
1.64
0.874
0.682
0.504
1.200
1.355
1.66
0.869
0.673
0.494
1.213
1.361 1.368
Μ
ο
ν*
1.68
0.865
0.663
0.485
1.226
1.70
0.860
0.654
0.476
1.240
1.375 1.381 1.387
1.72
0.855
0.645
0.467
1.254
1.74
0.850
0.635
0.458
1.269
1.76
0.846
0.626
0.450
1.284
1.393
0.442
1.300
1.399
1.78
0.841
0.618
1.80
0.836
0.609
0.434
1.316
1.405
1.82
0.832
0.600
0.426
1.332
1.410
1.84
0.827
0.592
0.418
1.349
1.416
1.86
0.823
0.584
0.411
1.367
1.421
1.88
0.818
0.575
0.403
1.385
1.426
1.90
0.814
0.567
0.396
1.403
1.431
1.92
0.810
0.559
0.390
1.422
1.436
1.94
0.806
0.552
0.383
1.442
1.441
1.96
0.802
0.544
0.376
1.462
1.446
1.98
0.797
0.536
0.370
1.482
1.450
One-dimensional Compressible Flow
158
RAYLEIGH FLOW OF A PERFECT GAS g =
1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.00
0.793
0.529
0.364
1.503
1.455
2.02
0.789
0.522
0.358
1.525
1.459
2.04
0.785
0.514
0.352
1.547
1.463
2.06
0. 782
0.507
0.346
1.569
1.467
2.08
0.778
0.500
0.340
1.592
1.471
2.10
0.774
0.494
0.335
1.616
1.475
2.12
0.770
0.487
0.329
1.640
1.479
2.14
0.767
0.480
0.324
1.665
1.483
2.16
0. 763
0.474
0.319
1.691
1.487
2.18
0.760
0.467
0.314
1.717
1.490
2.20
0.756
0.461
0.309
1.743
1.494
2.22
0.753
0.455
0.304
1.771
1.497
2.24
0.749
0.449
0.299
1.799
1.501
2.26
0.746
0.443
0.294
1.827
1.504
2.28
0.743
0.437
c1. 290
1.856
1.507
2.30
0.740
0.431
0.286
1.886
1.510
1.916
1.513
Μ
ο
ν*
2.32
0.736
0.426
0.281
2.34
0.733
0.420
0.277
1.948
1.516
2.36
0.730
0.415
0.273
1.979
1.519
2.38
0.727
0.409
0.269
2.012
1.522
2.40
0.724
0.404
0.265
2.045
1.525
2.42
0.721
0.399
0.261
2.079
1.528
2.44
0. 718
0.394
0.257
2.114
1.531
2.46
0.716
0.388
0.253
2.149
1.533
2.48
0.713
0.384
0.250
2.185
1.536
Table 4
159
RAYLE IGH FLOW OF A PERFECT GAS g
=
1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.5
0.710
0.379
0.246
2.222
2.6
0.697
0.356
0.229
2.418
1.550
0.214
2.634
1.561
Μ
ο
ν* 1.538
2.7
0.685
0.334
2.8
0.674
0.315
0.200
2.873
1.571
2.9
0.664
0.297
0.188.
3.136
1.580
3.0
0.654
0.280
0.176
3.424
1.588
3.1
0.645
0.265
0.166
3.741
1.596
3.2
0.637
0.251
0.156
4.087
1.603
3.3
0.629
0.238
0.148
4.465
1.609
3.4
0.622
0.225
0.140
4.878
1.615
3.5
0.616
0.214
0.132
5.328
1.620
3.6
0.610
0.204
0.125
5.817
1.625
3.7
0.604
0.194
0.119
6.349
1.629
3.8
0.599
0.185
0.113
6.926
1.633
3.9
0.594
0.176
0.108
7.550
1.637
4.0
0.589
0.1683
0.1026
8.23
1.641
4.5
0.570
0.1354
0.0818
12.50
1.656
5.0
0.556
0.1111
0.0667
18.63
1.667
5.5
0.545
0.0927
0.0554
27.21
1.675
6.0
0.536
0.0785
0.0467
38.95
1.681
6.5
0.530
0.0673
0.0399
54.68
1.686
7.0
0.524
0.0583
0.0345
75.41
1.690
7.5
0.520
0.0509
0.0301
102.29
1.693
8.0
0.516
0.0449
0.0265
136.62
1.695
8.5
0.513
0.0399
0.0235
179.92
1.698
9.0
0.511
0.0356
0.0210
233.88
1.699
9.5
0.509
0.0321
0.0188
300.41
1.701
F
0.490
0
0
F
1.714
160
One-dimensional Compressible Flow
RAYLE IGH FLOW OF A PERFECT GAS U
Μ
0.00
To To*
0.0000
Τ Τ*
0.0000
= 1.333 V
Ρ Ρ*
Ρ
2.333
1.259
0.0000
Ρ
ο ο
ν*
0.02
0.0019
0.0022
2.332
1.259
0.0009
0.04
0.0074
0.0087
2.328
1.258
0.0037
0.06
0.0166
0.0194
2.322
1.256
0.0084
0.08
0.0294
0.0342
2.313
1.254
0.0148
0.10
0.0455
0.0530
2.302
1.251
0.0230
0.12
0.0648
0.0755
2.289
1.248
0.0330
0.14
0.0871
0.1013
2.274
1.243
0.0446
0.16
0.1122
0.1303
2.256
1.239
0.0578
0.18
0.1397
0.1620
2.236
1.234
0.0725
0.20
0.1693
0.1962
2.215
1.228
0.0886
0.22
0.2009
0.2325
2.192
1.222
0.1061
0.24
0.2340
0.2704
2.167
1.215
0.1248
0.26
0.2684
0.3096
2.140
1.208
0.1447
0.28
0.3038
0.3498
2.112
1.201
0.1656
0.30
0.3398
0.3905
2.083
1.194
0.1875
0.32
0.3762
0.4315
2.053
1.186
0.2102
0.34
0.4128
0.4724
2.021
1.178
0.2337
0.36
0.4492
0.5129
1.989
1.170
0.2578
0.38
0.4852
0.5527
1.956
1.162
0.2825
0.40
0.5207
0.5916
1.923
1.153
0.3077
0.42
0.5554
0.6294
1.889
1.145
0.3332
0.44
0.5891
0.6658
1.854
1.137
0.3590
0.46
0.6218
0.7007
1.820
1.128
0.3851
0.48
0.6533
0.7340
1.785
1.120
0.4112
Table 4
161
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.333 V
To To*
Τ Τ*
0.50
0.6836
0.7655
1.750
1.112
0.4375
0.52
0.7124
0.7952
1.715
1.104
0.4637
0.54
0.7398
0.8230
1.680
1.096
0.4899
0.56
0.7657
0.8489
1.645
1.089
0.5159
0.58
0.7901
0.8728
1.611
1.081
0.5418
0.60
0.8130
0.8947
1.576
1.074
0.5675
0.62
0.8343
0.9147
1.543
1.067
0.5930
0.64
0.8542
0.9328
1.509
1.061
0.6181
0.66
0.8725
0.9490
1.476
1.055
0.6429
0.68
0.8894
0.9633
1.443
1.049
0.6674
Μ
Ρ Ρ*
Ρ
ο
Ρ
ο
ν*
0.70
0.9048
0.9759
1.411
1.043
0.6915
0.72
0.9189
0.9867
1.380
1.037
0.7152
0.74
0.9316
0.9959
1.349
1.032
0.7385
0.76
0.9430
1.0035
1.318
1.028
0.7613
0.78
0.9532
1.0097
1.288
1.023
0.7838
0.80
0.9623
1.0144
1.259
1.019
0.8057
0.82
0.9702
1.0177
1.230
1.016
0.8272
0.84
0.9770
1.0198
1.202
1.012
0.8483
0.86
0.9828
1.0207
1.175
1.010
0.8689
0.88
0.9877
1.0205
1.148
1.007
0.8890
0.90
0.9917
1.0193
1.122
1.005
0.9086
0.92
0.9948
1.0171
1.096
1.003
0.9278
0.94
0.9971
1.0140
1.071
1.002
0.9466
0.96
0.9988
1.0101
1.047
1.001
0.9648
0.98
0.9997
1.0054
1.023
1.000
0.9826
162
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.333 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
1.00
1.000
1.000
1.000
1.000
1.000
1.02
1.000
0.994
0.977
1.000
1.017
1.04
0.999
0.987
0.955
1.001
1.033
1.06
0.998
0.980
0.934
1.002
1.049
1.08
0.996
0.973
0.913
1.003
1.065
1.10
0.994
0.965
0.893
1.005
1.080
1.12
0.991
0.956
0.873
1.007
1.095
1.14
0.988
0.947
0.854
1.010
1.110
1.16
0.985
0.938
0.835
1.013
1.124
1.18
0.981
0.929
0.817
1.016
1.137
1.20
0.977
0.920
0.799
1.020
1.151
1.22
0.973
0.910
0.782
1.024
1.164
1.24
0.969
0.900
0.765
1.028
1. 176
1.26
0.964
0.890
0.749
1.033
1.189
1.28
0.960
0.880
0.733
1.039
1.201
0.869
p.717
1.045
1.212
1.051
1.223
Μ
Ρ
ο ο
ν*
1. 30
0.955
1.32
0.950
0.859
0.702
1.34
0.945
0.849
0.687
1.057
1.234
1.36
0.940
0.838
0.673
1.064
1.245
1.38
0.935
0.828
0.659
1.072
1.256
1.080
1.266
1.40
0.929
0.817
0.646
1.42
0.924
0.807
0.633
1.088
1.276
1.44
0.919
0.797
0.620
1.097
1.285
1.46
0.913
0.786
0.607
1.106
1.295
1.48
0.908
0.776
0.595
1.115
1.304
Table 4
163
RAYLEIGH FLOW OF A PERFECT GAS g
M
TQ
T
T oo;,*
T ~T*
1.50 1.52
0.902 0.897
1.54
0.891
=
1.333 1 ;.~.
P
o
V
R
~R ;.
V ;, ,.
0.766 0.756
0.583 0.572
1.126 1.136
1.313
0.745
0.561
1.147
o
1.321 1.330
1.56
0.886
0.735
0.550
1.158
1.338
1.58
0.880
0.725
o.539
1.17o
1.346
1.60
0.875
0.716
0.529
1. 82
1.354
1.62
0.870
0.706
0.519
1.195
1.361
1.64
0.864
0.696
0.509
1.208
1.368
1.66
0.859
0.687
0.499
1.222
1.376
1.68
0.854
0.677
0.490
1.236
1.383
1.70
0.848
0.668
0.481
1.251
1.389
1.72
0.843
0.659
0.472
1.266
1.396
1.74
0.838
0.650
0.463
1.282
1.403
1.76
0.833
0.641
0.455
1.298
1.409
1.78
0.828
0.632
0.447
1.314
1.415
1.80
0.823
0.623
0.439
1.332
1.421
0.431
1.349
1.427
1.82
0.818
0.615
1.84
0.813
0.606
0.423
1.368
1.433
1.86
0.808
0.598
0.416
1.387
1.438
1.88
0.803
0.590
0.408
1.406
1.444
1.90
0.798
0.582
0.401.
1.426
1.449
0.574
0.394
1.446
1.454
1.92
0.794
1.94
0.789
0.566
0.388
1.468
1.459
1.96
0.784
0.558
0.381
1.489
1.464
1.98
0.780
0.550
0.375
1.512
1.469
One-dimensional Compressible Flow
164
RAYLE IGH FLOW OF A PERFECT GAS g
To To*
Τ Τ*
2.00
0.776
2.02
0.771
Μ
=
1.333 V
Ρ Ρ*
Ρ
0.543
0.368
1.535
1.474
0.536
0.362
1.558
1.478
Ρ
ο ο
ν*
2.04
0.767
0.528
0.356
1.582
1.483
2.06
0.763
0.521
0.350
1.607
1.487
2.08
0.758
0.514
0.345
1.633
1.492
1.496
2.10
0.754
0.507
0.339
1.659
2.12
0.750
0.501
0.334
1.686
1.500
2.14
0.746
0.494
0.328
1.714
1.504
2.16
0.742
0.487
0.323
1.742
1.508
2.18
0.738
0.481
0.318
1.771
1.512
2.20
0.734
0.474
0.313
1.801
1.515
2.22
0.731
0.468
0.308
1.831
1.519
2.24
0.727
0.462
0.303
1.862
1.523
2.26
0.723
0.456
0.299
1.894
1.526
2.28
0.720
0.450
0.294
1.927
1.529
2.30
0.716
0.444
0.290
1.961
1.533
2.32
0.713
0.438
0.285
1.995
1.536
2.34
0.709
0.433
0.281
2.031
1.539
2.36
0.706
0.427
0.277
2.067
1.542
2.38
0.702
0.422
0.273
2.104
1.546
2.40
0.699
0.416
0.269
2.142
1.549
2.42
0.696
0.411
0.265
2.181
1.551
2.44
0.693
0.406
0.261
2.220
1.554
2.46
0.690
0.401
0.257
2.261
1.557
2.48
0.686
0.396
0.254
2.303
1.560
Table 4
165
RAYLE IGH FLOW OF A PERFECT GAS g
Μ
To To*
Τ Τ*
=
1.333 Ρ Ρ*
Ρ
ο
Ρ
ο
V
ν*
2.5
0.683
0.391
0.250
2.345
1.563
2.6
0.669
0.367
0.233
2.574
1.575
2.7
0.656
0.345
0.218
2.829
1.587
2.8
0.643
0.325
0.204
3.114
1.597
2.9
0.632
0.307
0.191
3.433
1.607
3.0
0.621
0.290
0.180
3.787
1.616
3.1
0.611
0.274
0.169
4.180
1.623
3.2
0.602
0.260
0.159
4.616
1.631
3.3
0.594
0.246
0.150
5.099
1.637
3.4
0.586
0.234
0.142
5.634
1.644
1.649
3.5
0.579
0.222
0.135
6.225
3.6
0.572
0.211
0.128
6.876
1.654
3.7
0.565
0.201
0.121
7.594
1.659
3.8
0.559
0.192
0.115
8.384
1.664
3.9
0.554
0.183
0.110
9.253
1.668
4.0
0.549
0.1747
0.1045
10.21
1.672
4.5
0.527
0.1407
0.0833
16.51
1.688
5.0
0.511
0.1155
0.0680
26.19
1.699
5.5
0.499
0.0964
0.0565
40.69
1.708
6.0
0.490
0.0816
0.0476
61.88
1.714
6.5
0.482
0.0700
0.0407
92.14
1.720
7.0
0.476
0.0606
0.0352
134.50
1.724 1.727
7.5
0.471
0.0530
0.0307
192.71
8.0
0.467
0.0468
0.0270
271.33
1.730
8.5
0.464
0.0415
0.0240
375.92
1.732
9.0
0.461
0.0371
0.0214
513.09
1. 734
690.70
1.736
f
1.750
9.5
0.459
0.0334
0.0192
f
0.437
0
0
166
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.667
To P0;, *~-
T T;,-
Ρ R ;,~_
0.00
0.0000
0.0000
0.02
0.0021
0.0028
0.04
0.0085
0.0113
M
p0
V
R o;,
V „..
2.667
1.299
0.0000
2.665
1.299
0.0011
2.660
1.297
0.0043
~.
0.06
0.0190
0.0253
2.651
1.295
0.0095
0.08
0.0335
0.0446
2.639
1.292
0.0169
0.10
0.0518
0.0688
2.623
1.288
0.0262
0.12
0.0736
0.0977
2.604
1.284
0.0375
0.14
0.0987
0.1307
2.583
1.279
0.0506
0.16
0.1267
0.1675
2.558
1.273
0.0655
0.18
0.1572
0.2074
2.530
1.266
0.0820
0.20
0.1900
0.2501
2.500
1.259
0.1000
0.22
0.2245
0.2948
2.468
1.251
0.1194
0.24
0.2607
0.3411
2.433
1.243
0.1402
0.26
0.2978
0.3884
2.397
1.234
0.1620
0.28
0.3357
0.4362
2.359
1.225
0.1849
0.30
0.3739
0.4840
2.319
1.216
0.2087
0.32
0.4121
0.5314
2.278
1.207
0.2333
0.34
0.4502
0.5780
2.236
1.197
0.2585
0.36
0.4877
0.6234
2.193
1.187
0.2842
0.38
0.5244
0.6672
2.150
1.178
0.3104
0.40
0.5603
0.7093
2.105
1.168
0.3369
0.42
0.5949
0.7493
2.061
1.158
0.3636
0.44
0.6283
0.7871
2.016
1.148
0.3904
0.46
0.6603
0.8225
1.972
1.139
0.4172
0.48
0.6908
0.8555
1.927
1.129
0.4440
Table 4
167
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.667 Ρ
ο
V
To To*
Τ Τ*
0.50
0.7198
0.8859
1.882
1.120
0.4706
0.52
0.7471
0.9138
1.838
1.111
0.4971
0.9392
1.795
1.102
0.5233
Μ
Ρ Ρ*
Ρ
ο
ν*
0.54
0.7728
0.56
0.7968
0.9619
1.751
1.094
0.5492
0.58
0.8192
0.9822
1.709
1.086
0.5748
0.60
0.8400
1.0001
1.667
1.078
0.6000
0.62
0.8592
1.0156
1.625
1.070
0.6248
0.64
0.8769
1.0288
1.585
1.063
0.6492
0.66
0.8931
1.0399
1.545
1.056
0.6730
0.68
0.9078
1.0489
1.506
1.050
0.6964
0.70
0.9219
1.0559
1.468
1.044
0.7193
0.72
0.9333
1.0611
1.431
1.038
0.7417 0.7635
0.74
0.9441
1.0645
1.394
1.033
0.76
0.9537
1.0663
1.359
1.028
0.7848
0.78
0.9622
1.0667
1.324
1.023
0.8056
0.80
0.9697
1.0656
1.290
1.019
0.8258
0.82
0.9761
1.0633
1.257
1.016
0.8455
1.226
1.012
0.8647
0.84
0.9817
1.0597
0.86
0.9864
1.0551
1.194
1.009
0.8834
0.88
0.9903
1.0495
1.164
1.007
0.9015
0.90
0.9935
1.0430
1.135
1.005
0.9192
0.92
0.9959
1.0357
1.106
1.003
0.9363 0.9529
0.94
0.9978
1.0277
1.078
1.002
0.96
0.9990
1.0190
1.052
1.001
0.9691
0.98
0.9998
1.0098
1.025
1.000
0.9848
One-dimensional Compressible Flow
168
RAYLEIGH FLOW OF A PERFECT GAS g = Μ
To To*
1.667
Τ Τ*
Ρ Ρ*
Ρ
Ρ
ο ο
V
ν*
1.00
1.000
1.000
1.0,00
1.000
1.000
1.02
1.000
0.990
0.975
1.000
1.015
1.04
0.999
0.979
0.951
1.001
1.029
1.06
0.998
0.968
0.928
1.002
1.043
1.08
0.997
0.957
0.906
1.003
1.057
1.10
0.995
0.945
0.884
1.005
1.070
1.12
0.993
0.934
0.863
1.007
1.082
1.009
1.095
1.14
0.991
0.922
0.842
1.16
0.989
0.910
0.822
1.012
1.107
1.18
0.986
0.898
0.803
1.015
1.118
1.20
0.983
0.886
0.784
1.018
1.129
1.22
0.980
0.874
0.766
1.022
1.140
1.026
1.151
1.24
0.977
0.861
0.748
1.26
0.974
0.849
0.731
1.030
1.161
1.28
0.971
0.837
0.715
1.035
1.171
1.30
0.967
0.825
0.699
1.040
1.181
1.32.
0.964
0.813
0.683
1.045
1.190
1.051
1.199
1.34
0.960
0.801
0.668
1.36
0.957
0.789
0.653
1.057
1.208
1.38
0.953
0.777
0.639
1.063
1.217
1.40
0.949
0.766
0.625
0.070
1.225
1.42
0.946
0.754
0.612
1.077
1.233
1.44
0.942
0.743
0.598
1.084
1.241
1.46
0.938
0.731
0.586
1.092
1.249
1.48
0.935
0.720
0.573
1.100
1.256
Table 4
169
RAYLEIGH FLOW OF A PERFECT GAS g
Μ
To To*
Τ Τ*
=
1.667 Ρ Ρ*
Ρ
ο
Ρ
ο
V
ν*
1.50
0.931
0.709
1.52
0.927
0.698
0.550
1.116
1.270
1.54
0.923
0.687
0.538
1.125
1.277
1.56
0.920
0.677
0.527
1.134
1.283
1.58
0.916
0.667
0.517
1.144
1.290
1.60
0.912
0.656
0.506
1.153
1.296
1.62
0.909
0.646
0.496
1.163
1.302
0.561
1.108
1.263
1.64
0.905
0.636
0.486
1.174
1.308
1.66
0.901
0.626
0.477
1.184
1.314
1.68
0.898
0.617
0.467
1.195
1.319
1.70
0.894
0.607
0.458
1.206
1.325
1.72
0.891
0.598
0.450
1.218
1.330
1.74
0.888
0.589
0.441
1.229
1.335
1.76
0.884
0.580
0.433
1.241
1.340 1.345 1.350 1.355 1.359
1.78
0.881
0.571
0.425
1.254
1.80 1.82 1.84
0.878 0.874 0.871
0.562 u.554 0.545
0.417 0.409 0.401
1.266 1.279 1.293
1.86
0.868
0.537
0.394
1.306
1.363
1.88
0.865
0.529
0.387
1.320
1.368
1.90
0.862
0.521
0.380
1.334
1.372
1.92
0.859
0.514
0.373
o.348
1.376
1.94
0.856
0.506
0.367
1.363
1.380
1.96
0.853
0.498
0.360
1.378
1.384
1.98
0.850
0.491
0.354
1.393
1.388
One-dimensional Compressible Flow
170
RAYLE IGH FLOW OF A PERFECT GAS U
Μ
2.00
= 1.667 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
0.847
0.484
0.348
1.409
1.391 1.395
Ρ
ο ο
ν*
2.02
0.844
0.477
0.342
1.425
2.04
0.841
0.470
0.336
1.441
1.398
2.06
0.839
0.463
0.330
1.458
1.402
2.08
0.836
0.456
0.325
1.474
1.405
2.10
0.833
0.450
0.319
1.492
1.408
2.12
0.831
0.443
0.314
1.509
1.411
2.14
0.828
0.437
0.309
1.527
1.415
2.16
0.826
0.431
0.304
1.545
1.418 1.421
2.18
0.823
0.425
0.299
1.563
2.20
0.821
0.419
0.294
1.582
1.423
2.22
0.818
0.413
0.289
1.601
1.426
2.24
0.816
0.407
0.285
1.620
1.429
2.26
0.814
0.401
0.280
1.639
1.432
2.28
0.811
0.396
0.276
1.659
1.434
2.30
0.809
0.390
0.272
1.680
1.437
2.32
0.807
0.385
0.267
1.700
1.439
2.34
0.805
0.380
0.263
1.721
1.442
2.36
0.803
0.375
0.259
1.742
1.444
2.38
0.800
0.369
0.255
1.764
1.447
2.40
0.798
0.365
0.252
1.785
1.449
2.42
0.796
0.360
0.248
1.807
1.451
2.44
0.794
0.355
0.244
1.830
1.453
2.46
0.792
0.350
0.241
1.853
1.456
0.237
1.876
1.458
2.48
0.791
0.345
171
Table 4
RAYLE IGH FLOW OF A PERFECT GAS g
=
1.667 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.5
0.789
0.341
0.234
1.899
1.460
2.6
0.780
0.319
0.217
2.021
1.469
2.7
0.771
0.300
0.203
2.152
1.478
2.8
0.764
0.282
0.190
2.291
1.486
2.9
0.757
0.265
0.178
2.440
1.493
3.0
0.750
0.250
0.167
2.597
1.500
3.1
0.744
0.236
0.157
2.764
1.506
3.2
0.739
0.223
0.148
2.941
1.511
3.3
0.733
0.211
0.139
3.128
1.516
3.4
0.729
C.200
0.132
3.325
1.521
Μ
Ρ
ο ο
ν*
3.5
0.724
0.190
0.125
3.532
1.525
3.6
0.720
0.180
0.118
3.751
1.529
3.7
0.716
0.172
0.112
3.980
1.533
3.8
0.713
0.163
0.106
4.221
1.536
3.9
0.709
0.156
0.101
4.473
1.539
4.0
0.706
0.1486
0.0964
4.74
1.542
4.5
0.693
0.1192
0.0767
6.25
1.554
5.0
0.684
0.0976
0.0625
8.10
1.562
5.5
0.677
0.0814
0.0519
10.32
1.569
6.0
0.671
0.0688
0.0437
12.96
1.574
6.5
0.667
0.0589
0.0373
16.06
1.577 1.581
7.0
0.663
0.0510
0.0323
19.63
7.5
0.660
0.0445
0.0281
23.74
1.583
8.0
0.658
0.0393
0.0248
28.40
1.585
8.5
0.656
0.0348
0.0220
33.67
1.587
9.0
0.654
0.0311
0.0196
39.57
1.588
9.5
0.653
0.0280
0.0176
46.14
1.589
0.640
0
0
1.600
M
Ta
To*
T
= 1.400 R
o
V
T*
Ρ Ρ*
R ,.~'
1*
0
0.00
0.0000
0.0000
2.400
1.268
0.0000
0.02
0.0019
0.0023
2.399
1.268
0.0010
0.04
0.0076
0.0092
2.395
1.266
0.0038
0.06
0.0171
0.0205
2.388
1.265
0.0086
0.08
0.0302
0.0362
2.379
1.262
0.0152
0.10
0.0468
0.0560
2.367
1.259
0.0237
0.12
0.0666
0.0797
2.353
1.255
0.0339
0.14
0.0895
0.1069
2.336
1.251
0.0458
0.16
0.1151
0.1374
2.317
1.246
0.0593
0.18
0.1432
0.1708
2.296
1.241
0.0744
0.20
0.1736
0.2066
2.273
1.235
0.0909
0.22
0.2057
0.2445
2.248
1.228
0.1088
0.24
0.2395
0.2841
2.221
1.221
0.1279
0.26
0.2745
0.3250
2.193
1.214
0.1482
0.28
0.3104
0.3667
2.163
1.206
0.1696
0.30
0.3469
0.4089
2.131
1.199
0.1918
0.32
0.3837
0.4512
2.099
1.190
0.2149
0.34
0.4206
0.4933
2.066
1.182
0.2388
0.36
0.4572
0.5348
2.031
1.174
0.2633
0.38
0.4935
0.5755
1.996
1.165
0.2883
0.40
0.5290
0.6151
1.961
1.157
0.3137
0.42
0.5638
0.6535
1.925
1.148
0.3395
0.44
0.5975
0.6903
1.888
1.139
0.3656
0.46
0.6301
0.7254
1.852
1.131
0.3918
0.48
0.6614
0.7587
1.815
1.122
0.4181
154
Table 4
155
RAYLEIGH FLOW OF A PERFECT GAS g
Μ
To To*
=
1.400 Ρ
ο
Τ Τ*
Ρ Ρ*
Ρ
ο
V
ν*
0.50
0.6914
0.7901
1.778
1.114
0.4444
0.52
0.7199
0.8196
1.741
1.106
0.4708
0.54
0.7470
0.8469
1.704
1.098
0. 49 70
0.56
0.7725
0.8723
1.668
1.090
0.5230
0.58
0.7965
0.8955
1.632
1.083
0.5489
0.60
0.8189
0.9167
1.596
1.075
0.5745
0.62
0.8398
0.9358
1.560
1.068
0.5998
0.64
0.8592
0.9530
1.525
1.061
0.6248
0.66
0.8771
0.9682
1.491
1.055
0.6494
0.68
0.8935
0.9814
1.457
1.049
0.6737
0.70
0.9085
0.9929
1.423
1.043
0.6975
0.72
0.9221
1.0026
1.391
1.038
0.7209
0.74
0.9344
1.0106
1.359
1.033
0.7439
0.76
0.9455
1.0171
1.327
1.028
0.7665
0.78
0.9553
1.0220
1.296
1.023
0.7885
0.80
0.9639
1.0255
1.266
1.019
0.8101
0.82
0.9715
1.0276
1.236
1.016
0.8313
0.84
0.9781
1.0285
1.207
1.012
0.8519
0.86
0.9836
1.0283
1.179
1.010
0.8721
0.88
0.9883
1.0269
1.152
1.007
0.8918
0.90
0.9921
1.0245
1.125
1.005
0.9110
0.92
0.9951
1.0212
1.098
1.003
0.9297
0.94
0.9973
1.0170
1.073
1.002
0.9480
0.96
0.9988
1.0120
1.048
1.001
0.9658
0.98
0.9997
1.0064
1.024
1.000
0.9831
156
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g = Μ
To To*
Τ Τ*
1.400 Ρ
ο
Ρ Ρ*
Ρ
ο
V
ν*
1.00
1.000
1.000
1.000
1.000
1.000
1.02
1.000
0.993
0.977
1.000
1.016
1.04
0.999
0.986
0.955
1.001
1.032
1.06
0.998
0.978
0.933
1.002
1.048
1.08
0.996
0.969
0.912
1.003
1.063
1.10
0.994
0.960
0.891
1.005
1.078
1.12
0.991
0.951
0.871
1.007
1.092
1.14
0.989
0.942
0.851
1.010
1.106
1.16
0.986
0.932
0.832
1.012
1.120
1.18
0.982
0.922
0.814
1.016
1.133
1.20
0.979
0.912
0.796
1.019
1.146
1.22
0.975
0.902
0.778
1.023
1.158
1.24
0.971
0.891
0.761
1.028
1.171
1.26
0.967
0.881
0.745
1.033
1.182
1.28
0.962
0.870
0.729
1.038
1.194
1.30
0.958
0.859
0.713
1.044
1.205
1.32
0.953
0.848
0.698
1.050
1.216
1.34
0.949
0.838
0.683
1.056
1.226
1.36
0.944
0.827
0.669
1.063
1.237
1.38
0.939
0.816
0.655
1.070
1.247
1.40
0.934
0.805
0.641
1.078
1.256
1.42
0.929
0.795
0.628
1.086
1.266
1.44
0.924
0.784
0.615
1.094
1.275
1.46
0.919
0.773
0.602
1.103
1.284
1.48
0.914
0.763
0.590
1.112
1.293
157
Table 4
RAYLEIGH FLOW OF A PERFECT GAS g =1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
1.50
0.909
0.753
0.578
1.122
1.301
1.52
0.904
0.742
0.567
1.132
1.309
1.54
0.899
0.732
0.556
1.142
1.317
1.56
0.894
0.722
0.545
1.153
1.325
1.58
0.889
0.712
0.534
1.164
1.333
1.60
0.884
0.702
0.524
1.176
1.340
1.62
0.879
0.692
0.513
1.188
1.348
1.64
0.874
0.682
0.504
1.200
1.355
1.66
0.869
0.673
0.494
1.213
1.361 1.368
Μ
ο
ν*
1.68
0.865
0.663
0.485
1.226
1.70
0.860
0.654
0.476
1.240
1.375 1.381 1.387
1.72
0.855
0.645
0.467
1.254
1.74
0.850
0.635
0.458
1.269
1.76
0.846
0.626
0.450
1.284
1.393
0.442
1.300
1.399
1.78
0.841
0.618
1.80
0.836
0.609
0.434
1.316
1.405
1.82
0.832
0.600
0.426
1.332
1.410
1.84
0.827
0.592
0.418
1.349
1.416
1.86
0.823
0.584
0.411
1.367
1.421
1.88
0.818
0.575
0.403
1.385
1.426
1.90
0.814
0.567
0.396
1.403
1.431
1.92
0.810
0.559
0.390
1.422
1.436
1.94
0.806
0.552
0.383
1.442
1.441
1.96
0.802
0.544
0.376
1.462
1.446
1.98
0.797
0.536
0.370
1.482
1.450
One-dimensional Compressible Flow
158
RAYLEIGH FLOW OF A PERFECT GAS g =
1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.00
0.793
0.529
0.364
1.503
1.455
2.02
0.789
0.522
0.358
1.525
1.459
2.04
0.785
0.514
0.352
1.547
1.463
2.06
0. 782
0.507
0.346
1.569
1.467
2.08
0.778
0.500
0.340
1.592
1.471
2.10
0.774
0.494
0.335
1.616
1.475
2.12
0.770
0.487
0.329
1.640
1.479
2.14
0.767
0.480
0.324
1.665
1.483
2.16
0. 763
0.474
0.319
1.691
1.487
2.18
0.760
0.467
0.314
1.717
1.490
2.20
0.756
0.461
0.309
1.743
1.494
2.22
0.753
0.455
0.304
1.771
1.497
2.24
0.749
0.449
0.299
1.799
1.501
2.26
0.746
0.443
0.294
1.827
1.504
2.28
0.743
0.437
c1. 290
1.856
1.507
2.30
0.740
0.431
0.286
1.886
1.510
1.916
1.513
Μ
ο
ν*
2.32
0.736
0.426
0.281
2.34
0.733
0.420
0.277
1.948
1.516
2.36
0.730
0.415
0.273
1.979
1.519
2.38
0.727
0.409
0.269
2.012
1.522
2.40
0.724
0.404
0.265
2.045
1.525
2.42
0.721
0.399
0.261
2.079
1.528
2.44
0. 718
0.394
0.257
2.114
1.531
2.46
0.716
0.388
0.253
2.149
1.533
2.48
0.713
0.384
0.250
2.185
1.536
Table 4
159
RAYLE IGH FLOW OF A PERFECT GAS g
=
1.400 Ρ
ο
V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.5
0.710
0.379
0.246
2.222
2.6
0.697
0.356
0.229
2.418
1.550
0.214
2.634
1.561
Μ
ο
ν* 1.538
2.7
0.685
0.334
2.8
0.674
0.315
0.200
2.873
1.571
2.9
0.664
0.297
0.188.
3.136
1.580
3.0
0.654
0.280
0.176
3.424
1.588
3.1
0.645
0.265
0.166
3.741
1.596
3.2
0.637
0.251
0.156
4.087
1.603
3.3
0.629
0.238
0.148
4.465
1.609
3.4
0.622
0.225
0.140
4.878
1.615
3.5
0.616
0.214
0.132
5.328
1.620
3.6
0.610
0.204
0.125
5.817
1.625
3.7
0.604
0.194
0.119
6.349
1.629
3.8
0.599
0.185
0.113
6.926
1.633
3.9
0.594
0.176
0.108
7.550
1.637
4.0
0.589
0.1683
0.1026
8.23
1.641
4.5
0.570
0.1354
0.0818
12.50
1.656
5.0
0.556
0.1111
0.0667
18.63
1.667
5.5
0.545
0.0927
0.0554
27.21
1.675
6.0
0.536
0.0785
0.0467
38.95
1.681
6.5
0.530
0.0673
0.0399
54.68
1.686
7.0
0.524
0.0583
0.0345
75.41
1.690
7.5
0.520
0.0509
0.0301
102.29
1.693
8.0
0.516
0.0449
0.0265
136.62
1.695
8.5
0.513
0.0399
0.0235
179.92
1.698
9.0
0.511
0.0356
0.0210
233.88
1.699
9.5
0.509
0.0321
0.0188
300.41
1.701
F
0.490
0
0
F
1.714
160
One-dimensional Compressible Flow
RAYLE IGH FLOW OF A PERFECT GAS U
Μ
0.00
To To*
0.0000
Τ Τ*
0.0000
= 1.333 V
Ρ Ρ*
Ρ
2.333
1.259
0.0000
Ρ
ο ο
ν*
0.02
0.0019
0.0022
2.332
1.259
0.0009
0.04
0.0074
0.0087
2.328
1.258
0.0037
0.06
0.0166
0.0194
2.322
1.256
0.0084
0.08
0.0294
0.0342
2.313
1.254
0.0148
0.10
0.0455
0.0530
2.302
1.251
0.0230
0.12
0.0648
0.0755
2.289
1.248
0.0330
0.14
0.0871
0.1013
2.274
1.243
0.0446
0.16
0.1122
0.1303
2.256
1.239
0.0578
0.18
0.1397
0.1620
2.236
1.234
0.0725
0.20
0.1693
0.1962
2.215
1.228
0.0886
0.22
0.2009
0.2325
2.192
1.222
0.1061
0.24
0.2340
0.2704
2.167
1.215
0.1248
0.26
0.2684
0.3096
2.140
1.208
0.1447
0.28
0.3038
0.3498
2.112
1.201
0.1656
0.30
0.3398
0.3905
2.083
1.194
0.1875
0.32
0.3762
0.4315
2.053
1.186
0.2102
0.34
0.4128
0.4724
2.021
1.178
0.2337
0.36
0.4492
0.5129
1.989
1.170
0.2578
0.38
0.4852
0.5527
1.956
1.162
0.2825
0.40
0.5207
0.5916
1.923
1.153
0.3077
0.42
0.5554
0.6294
1.889
1.145
0.3332
0.44
0.5891
0.6658
1.854
1.137
0.3590
0.46
0.6218
0.7007
1.820
1.128
0.3851
0.48
0.6533
0.7340
1.785
1.120
0.4112
Table 4
161
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.333 V
To To*
Τ Τ*
0.50
0.6836
0.7655
1.750
1.112
0.4375
0.52
0.7124
0.7952
1.715
1.104
0.4637
0.54
0.7398
0.8230
1.680
1.096
0.4899
0.56
0.7657
0.8489
1.645
1.089
0.5159
0.58
0.7901
0.8728
1.611
1.081
0.5418
0.60
0.8130
0.8947
1.576
1.074
0.5675
0.62
0.8343
0.9147
1.543
1.067
0.5930
0.64
0.8542
0.9328
1.509
1.061
0.6181
0.66
0.8725
0.9490
1.476
1.055
0.6429
0.68
0.8894
0.9633
1.443
1.049
0.6674
Μ
Ρ Ρ*
Ρ
ο
Ρ
ο
ν*
0.70
0.9048
0.9759
1.411
1.043
0.6915
0.72
0.9189
0.9867
1.380
1.037
0.7152
0.74
0.9316
0.9959
1.349
1.032
0.7385
0.76
0.9430
1.0035
1.318
1.028
0.7613
0.78
0.9532
1.0097
1.288
1.023
0.7838
0.80
0.9623
1.0144
1.259
1.019
0.8057
0.82
0.9702
1.0177
1.230
1.016
0.8272
0.84
0.9770
1.0198
1.202
1.012
0.8483
0.86
0.9828
1.0207
1.175
1.010
0.8689
0.88
0.9877
1.0205
1.148
1.007
0.8890
0.90
0.9917
1.0193
1.122
1.005
0.9086
0.92
0.9948
1.0171
1.096
1.003
0.9278
0.94
0.9971
1.0140
1.071
1.002
0.9466
0.96
0.9988
1.0101
1.047
1.001
0.9648
0.98
0.9997
1.0054
1.023
1.000
0.9826
162
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.333 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
1.00
1.000
1.000
1.000
1.000
1.000
1.02
1.000
0.994
0.977
1.000
1.017
1.04
0.999
0.987
0.955
1.001
1.033
1.06
0.998
0.980
0.934
1.002
1.049
1.08
0.996
0.973
0.913
1.003
1.065
1.10
0.994
0.965
0.893
1.005
1.080
1.12
0.991
0.956
0.873
1.007
1.095
1.14
0.988
0.947
0.854
1.010
1.110
1.16
0.985
0.938
0.835
1.013
1.124
1.18
0.981
0.929
0.817
1.016
1.137
1.20
0.977
0.920
0.799
1.020
1.151
1.22
0.973
0.910
0.782
1.024
1.164
1.24
0.969
0.900
0.765
1.028
1. 176
1.26
0.964
0.890
0.749
1.033
1.189
1.28
0.960
0.880
0.733
1.039
1.201
0.869
p.717
1.045
1.212
1.051
1.223
Μ
Ρ
ο ο
ν*
1. 30
0.955
1.32
0.950
0.859
0.702
1.34
0.945
0.849
0.687
1.057
1.234
1.36
0.940
0.838
0.673
1.064
1.245
1.38
0.935
0.828
0.659
1.072
1.256
1.080
1.266
1.40
0.929
0.817
0.646
1.42
0.924
0.807
0.633
1.088
1.276
1.44
0.919
0.797
0.620
1.097
1.285
1.46
0.913
0.786
0.607
1.106
1.295
1.48
0.908
0.776
0.595
1.115
1.304
Table 4
163
RAYLEIGH FLOW OF A PERFECT GAS g
M
TQ
T
T oo;,*
T ~T*
1.50 1.52
0.902 0.897
1.54
0.891
=
1.333 1 ;.~.
P
o
V
R
~R ;.
V ;, ,.
0.766 0.756
0.583 0.572
1.126 1.136
1.313
0.745
0.561
1.147
o
1.321 1.330
1.56
0.886
0.735
0.550
1.158
1.338
1.58
0.880
0.725
o.539
1.17o
1.346
1.60
0.875
0.716
0.529
1. 82
1.354
1.62
0.870
0.706
0.519
1.195
1.361
1.64
0.864
0.696
0.509
1.208
1.368
1.66
0.859
0.687
0.499
1.222
1.376
1.68
0.854
0.677
0.490
1.236
1.383
1.70
0.848
0.668
0.481
1.251
1.389
1.72
0.843
0.659
0.472
1.266
1.396
1.74
0.838
0.650
0.463
1.282
1.403
1.76
0.833
0.641
0.455
1.298
1.409
1.78
0.828
0.632
0.447
1.314
1.415
1.80
0.823
0.623
0.439
1.332
1.421
0.431
1.349
1.427
1.82
0.818
0.615
1.84
0.813
0.606
0.423
1.368
1.433
1.86
0.808
0.598
0.416
1.387
1.438
1.88
0.803
0.590
0.408
1.406
1.444
1.90
0.798
0.582
0.401.
1.426
1.449
0.574
0.394
1.446
1.454
1.92
0.794
1.94
0.789
0.566
0.388
1.468
1.459
1.96
0.784
0.558
0.381
1.489
1.464
1.98
0.780
0.550
0.375
1.512
1.469
One-dimensional Compressible Flow
164
RAYLE IGH FLOW OF A PERFECT GAS g
To To*
Τ Τ*
2.00
0.776
2.02
0.771
Μ
=
1.333 V
Ρ Ρ*
Ρ
0.543
0.368
1.535
1.474
0.536
0.362
1.558
1.478
Ρ
ο ο
ν*
2.04
0.767
0.528
0.356
1.582
1.483
2.06
0.763
0.521
0.350
1.607
1.487
2.08
0.758
0.514
0.345
1.633
1.492
1.496
2.10
0.754
0.507
0.339
1.659
2.12
0.750
0.501
0.334
1.686
1.500
2.14
0.746
0.494
0.328
1.714
1.504
2.16
0.742
0.487
0.323
1.742
1.508
2.18
0.738
0.481
0.318
1.771
1.512
2.20
0.734
0.474
0.313
1.801
1.515
2.22
0.731
0.468
0.308
1.831
1.519
2.24
0.727
0.462
0.303
1.862
1.523
2.26
0.723
0.456
0.299
1.894
1.526
2.28
0.720
0.450
0.294
1.927
1.529
2.30
0.716
0.444
0.290
1.961
1.533
2.32
0.713
0.438
0.285
1.995
1.536
2.34
0.709
0.433
0.281
2.031
1.539
2.36
0.706
0.427
0.277
2.067
1.542
2.38
0.702
0.422
0.273
2.104
1.546
2.40
0.699
0.416
0.269
2.142
1.549
2.42
0.696
0.411
0.265
2.181
1.551
2.44
0.693
0.406
0.261
2.220
1.554
2.46
0.690
0.401
0.257
2.261
1.557
2.48
0.686
0.396
0.254
2.303
1.560
Table 4
165
RAYLE IGH FLOW OF A PERFECT GAS g
Μ
To To*
Τ Τ*
=
1.333 Ρ Ρ*
Ρ
ο
Ρ
ο
V
ν*
2.5
0.683
0.391
0.250
2.345
1.563
2.6
0.669
0.367
0.233
2.574
1.575
2.7
0.656
0.345
0.218
2.829
1.587
2.8
0.643
0.325
0.204
3.114
1.597
2.9
0.632
0.307
0.191
3.433
1.607
3.0
0.621
0.290
0.180
3.787
1.616
3.1
0.611
0.274
0.169
4.180
1.623
3.2
0.602
0.260
0.159
4.616
1.631
3.3
0.594
0.246
0.150
5.099
1.637
3.4
0.586
0.234
0.142
5.634
1.644
1.649
3.5
0.579
0.222
0.135
6.225
3.6
0.572
0.211
0.128
6.876
1.654
3.7
0.565
0.201
0.121
7.594
1.659
3.8
0.559
0.192
0.115
8.384
1.664
3.9
0.554
0.183
0.110
9.253
1.668
4.0
0.549
0.1747
0.1045
10.21
1.672
4.5
0.527
0.1407
0.0833
16.51
1.688
5.0
0.511
0.1155
0.0680
26.19
1.699
5.5
0.499
0.0964
0.0565
40.69
1.708
6.0
0.490
0.0816
0.0476
61.88
1.714
6.5
0.482
0.0700
0.0407
92.14
1.720
7.0
0.476
0.0606
0.0352
134.50
1.724 1.727
7.5
0.471
0.0530
0.0307
192.71
8.0
0.467
0.0468
0.0270
271.33
1.730
8.5
0.464
0.0415
0.0240
375.92
1.732
9.0
0.461
0.0371
0.0214
513.09
1. 734
690.70
1.736
f
1.750
9.5
0.459
0.0334
0.0192
f
0.437
0
0
166
One-dimensional Compressible Flow
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.667
To P0;, *~-
T T;,-
Ρ R ;,~_
0.00
0.0000
0.0000
0.02
0.0021
0.0028
0.04
0.0085
0.0113
M
p0
V
R o;,
V „..
2.667
1.299
0.0000
2.665
1.299
0.0011
2.660
1.297
0.0043
~.
0.06
0.0190
0.0253
2.651
1.295
0.0095
0.08
0.0335
0.0446
2.639
1.292
0.0169
0.10
0.0518
0.0688
2.623
1.288
0.0262
0.12
0.0736
0.0977
2.604
1.284
0.0375
0.14
0.0987
0.1307
2.583
1.279
0.0506
0.16
0.1267
0.1675
2.558
1.273
0.0655
0.18
0.1572
0.2074
2.530
1.266
0.0820
0.20
0.1900
0.2501
2.500
1.259
0.1000
0.22
0.2245
0.2948
2.468
1.251
0.1194
0.24
0.2607
0.3411
2.433
1.243
0.1402
0.26
0.2978
0.3884
2.397
1.234
0.1620
0.28
0.3357
0.4362
2.359
1.225
0.1849
0.30
0.3739
0.4840
2.319
1.216
0.2087
0.32
0.4121
0.5314
2.278
1.207
0.2333
0.34
0.4502
0.5780
2.236
1.197
0.2585
0.36
0.4877
0.6234
2.193
1.187
0.2842
0.38
0.5244
0.6672
2.150
1.178
0.3104
0.40
0.5603
0.7093
2.105
1.168
0.3369
0.42
0.5949
0.7493
2.061
1.158
0.3636
0.44
0.6283
0.7871
2.016
1.148
0.3904
0.46
0.6603
0.8225
1.972
1.139
0.4172
0.48
0.6908
0.8555
1.927
1.129
0.4440
Table 4
167
RAYLEIGH FLOW OF A PERFECT GAS g
=
1.667 Ρ
ο
V
To To*
Τ Τ*
0.50
0.7198
0.8859
1.882
1.120
0.4706
0.52
0.7471
0.9138
1.838
1.111
0.4971
0.9392
1.795
1.102
0.5233
Μ
Ρ Ρ*
Ρ
ο
ν*
0.54
0.7728
0.56
0.7968
0.9619
1.751
1.094
0.5492
0.58
0.8192
0.9822
1.709
1.086
0.5748
0.60
0.8400
1.0001
1.667
1.078
0.6000
0.62
0.8592
1.0156
1.625
1.070
0.6248
0.64
0.8769
1.0288
1.585
1.063
0.6492
0.66
0.8931
1.0399
1.545
1.056
0.6730
0.68
0.9078
1.0489
1.506
1.050
0.6964
0.70
0.9219
1.0559
1.468
1.044
0.7193
0.72
0.9333
1.0611
1.431
1.038
0.7417 0.7635
0.74
0.9441
1.0645
1.394
1.033
0.76
0.9537
1.0663
1.359
1.028
0.7848
0.78
0.9622
1.0667
1.324
1.023
0.8056
0.80
0.9697
1.0656
1.290
1.019
0.8258
0.82
0.9761
1.0633
1.257
1.016
0.8455
1.226
1.012
0.8647
0.84
0.9817
1.0597
0.86
0.9864
1.0551
1.194
1.009
0.8834
0.88
0.9903
1.0495
1.164
1.007
0.9015
0.90
0.9935
1.0430
1.135
1.005
0.9192
0.92
0.9959
1.0357
1.106
1.003
0.9363 0.9529
0.94
0.9978
1.0277
1.078
1.002
0.96
0.9990
1.0190
1.052
1.001
0.9691
0.98
0.9998
1.0098
1.025
1.000
0.9848
One-dimensional Compressible Flow
168
RAYLEIGH FLOW OF A PERFECT GAS g = Μ
To To*
1.667
Τ Τ*
Ρ Ρ*
Ρ
Ρ
ο ο
V
ν*
1.00
1.000
1.000
1.0,00
1.000
1.000
1.02
1.000
0.990
0.975
1.000
1.015
1.04
0.999
0.979
0.951
1.001
1.029
1.06
0.998
0.968
0.928
1.002
1.043
1.08
0.997
0.957
0.906
1.003
1.057
1.10
0.995
0.945
0.884
1.005
1.070
1.12
0.993
0.934
0.863
1.007
1.082
1.009
1.095
1.14
0.991
0.922
0.842
1.16
0.989
0.910
0.822
1.012
1.107
1.18
0.986
0.898
0.803
1.015
1.118
1.20
0.983
0.886
0.784
1.018
1.129
1.22
0.980
0.874
0.766
1.022
1.140
1.026
1.151
1.24
0.977
0.861
0.748
1.26
0.974
0.849
0.731
1.030
1.161
1.28
0.971
0.837
0.715
1.035
1.171
1.30
0.967
0.825
0.699
1.040
1.181
1.32.
0.964
0.813
0.683
1.045
1.190
1.051
1.199
1.34
0.960
0.801
0.668
1.36
0.957
0.789
0.653
1.057
1.208
1.38
0.953
0.777
0.639
1.063
1.217
1.40
0.949
0.766
0.625
0.070
1.225
1.42
0.946
0.754
0.612
1.077
1.233
1.44
0.942
0.743
0.598
1.084
1.241
1.46
0.938
0.731
0.586
1.092
1.249
1.48
0.935
0.720
0.573
1.100
1.256
Table 4
169
RAYLEIGH FLOW OF A PERFECT GAS g
Μ
To To*
Τ Τ*
=
1.667 Ρ Ρ*
Ρ
ο
Ρ
ο
V
ν*
1.50
0.931
0.709
1.52
0.927
0.698
0.550
1.116
1.270
1.54
0.923
0.687
0.538
1.125
1.277
1.56
0.920
0.677
0.527
1.134
1.283
1.58
0.916
0.667
0.517
1.144
1.290
1.60
0.912
0.656
0.506
1.153
1.296
1.62
0.909
0.646
0.496
1.163
1.302
0.561
1.108
1.263
1.64
0.905
0.636
0.486
1.174
1.308
1.66
0.901
0.626
0.477
1.184
1.314
1.68
0.898
0.617
0.467
1.195
1.319
1.70
0.894
0.607
0.458
1.206
1.325
1.72
0.891
0.598
0.450
1.218
1.330
1.74
0.888
0.589
0.441
1.229
1.335
1.76
0.884
0.580
0.433
1.241
1.340 1.345 1.350 1.355 1.359
1.78
0.881
0.571
0.425
1.254
1.80 1.82 1.84
0.878 0.874 0.871
0.562 u.554 0.545
0.417 0.409 0.401
1.266 1.279 1.293
1.86
0.868
0.537
0.394
1.306
1.363
1.88
0.865
0.529
0.387
1.320
1.368
1.90
0.862
0.521
0.380
1.334
1.372
1.92
0.859
0.514
0.373
o.348
1.376
1.94
0.856
0.506
0.367
1.363
1.380
1.96
0.853
0.498
0.360
1.378
1.384
1.98
0.850
0.491
0.354
1.393
1.388
One-dimensional Compressible Flow
170
RAYLE IGH FLOW OF A PERFECT GAS U
Μ
2.00
= 1.667 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
0.847
0.484
0.348
1.409
1.391 1.395
Ρ
ο ο
ν*
2.02
0.844
0.477
0.342
1.425
2.04
0.841
0.470
0.336
1.441
1.398
2.06
0.839
0.463
0.330
1.458
1.402
2.08
0.836
0.456
0.325
1.474
1.405
2.10
0.833
0.450
0.319
1.492
1.408
2.12
0.831
0.443
0.314
1.509
1.411
2.14
0.828
0.437
0.309
1.527
1.415
2.16
0.826
0.431
0.304
1.545
1.418 1.421
2.18
0.823
0.425
0.299
1.563
2.20
0.821
0.419
0.294
1.582
1.423
2.22
0.818
0.413
0.289
1.601
1.426
2.24
0.816
0.407
0.285
1.620
1.429
2.26
0.814
0.401
0.280
1.639
1.432
2.28
0.811
0.396
0.276
1.659
1.434
2.30
0.809
0.390
0.272
1.680
1.437
2.32
0.807
0.385
0.267
1.700
1.439
2.34
0.805
0.380
0.263
1.721
1.442
2.36
0.803
0.375
0.259
1.742
1.444
2.38
0.800
0.369
0.255
1.764
1.447
2.40
0.798
0.365
0.252
1.785
1.449
2.42
0.796
0.360
0.248
1.807
1.451
2.44
0.794
0.355
0.244
1.830
1.453
2.46
0.792
0.350
0.241
1.853
1.456
0.237
1.876
1.458
2.48
0.791
0.345
171
Table 4
RAYLE IGH FLOW OF A PERFECT GAS g
=
1.667 V
To To*
Τ Τ*
Ρ Ρ*
Ρ
2.5
0.789
0.341
0.234
1.899
1.460
2.6
0.780
0.319
0.217
2.021
1.469
2.7
0.771
0.300
0.203
2.152
1.478
2.8
0.764
0.282
0.190
2.291
1.486
2.9
0.757
0.265
0.178
2.440
1.493
3.0
0.750
0.250
0.167
2.597
1.500
3.1
0.744
0.236
0.157
2.764
1.506
3.2
0.739
0.223
0.148
2.941
1.511
3.3
0.733
0.211
0.139
3.128
1.516
3.4
0.729
C.200
0.132
3.325
1.521
Μ
Ρ
ο ο
ν*
3.5
0.724
0.190
0.125
3.532
1.525
3.6
0.720
0.180
0.118
3.751
1.529
3.7
0.716
0.172
0.112
3.980
1.533
3.8
0.713
0.163
0.106
4.221
1.536
3.9
0.709
0.156
0.101
4.473
1.539
4.0
0.706
0.1486
0.0964
4.74
1.542
4.5
0.693
0.1192
0.0767
6.25
1.554
5.0
0.684
0.0976
0.0625
8.10
1.562
5.5
0.677
0.0814
0.0519
10.32
1.569
6.0
0.671
0.0688
0.0437
12.96
1.574
6.5
0.667
0.0589
0.0373
16.06
1.577 1.581
7.0
0.663
0.0510
0.0323
19.63
7.5
0.660
0.0445
0.0281
23.74
1.583
8.0
0.658
0.0393
0.0248
28.40
1.585
8.5
0.656
0.0348
0.0220
33.67
1.587
9.0
0.654
0.0311
0.0196
39.57
1.588
9.5
0.653
0.0280
0.0176
46.14
1.589
0.640
0
0
1.600