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FANNO FLOW OF A PERFECT GAS - ONE-DIMENSIONAL ADIABATIC FLOW OF A PERFECT GAS IN A DUCT OF CONSTANT CROSS-SECTIONAL AREA WITH FRICTION
TABLE 3 FANNO FLOW OF A PERFECT GAS - ONE-DIMENSIONAL ADIABATIC FLOW OF A PERFECT GAS IN A DUCT OF CONSTANT CROSS-SECTIONAL AREA WITH FRICTION y = 1.400 M
T T;.
_2_
p
P*
P *
o
I 1*
4 f
m ax
D
f
f
0
1.200
0.02
1.200
54.770
28.942
22.834
177,8.451
0.04
1.200
27.382
14.481
11.435
440.352
0.06
1.199
18.251
9.666
7.643
193.031
0.08
1.198
13.684
7.262
5.753
106.718
0.10
1.198
10.944
5.822
4.624
66.922
0.12
1.197
9.116
4.864
3.875
45.408
0.14
1.195
7.809
4.182
3.343
32.511
0.16
1.194
6.829
3.673
2.947
24.198
0.18
1.192
6.066
3.278
2.642
18.543
0.20
1.190
5.455
2.964
2.400
14.533
0.22
1.188
4.955
2.708
2.205
11.596
0.24
1.186
4.538
2.496
2.043
9.386
0.26
1.184
4.185
2.317
1.909
7.688
0.28
1.181
3.882
2.166
1.795
6.357
0.30
1.179
3.619
2.035
1.698
5.299
0.32
1.176
3.389
1.922
1.614
4.447
0.34
1.173
3.185
1.823
1.542
3.752
0.36
1.170
3.004
1.736
1.479
3.180
0.38
1.166
2.842
1.659
1.424
2.705
0.40
1.163
2.696
1.590
1.375
2.308
0.42
1.159
2.563
1.529
1.332
1.974
0.44
1.155
2.443
1.474
1.294
1.692
0.46
1.151
2.333
1.425
1.260
1.451
0.48
1.147
2.231
1.380
1.230
1.245
136
137
Table 3
FANNO FLOW OF A PERFECT GAS g = M
T T;.
~
1.400 R
o
;.
o
I
I;,''
4f
m ax D
2.138
1.340
1.203
1.069
1.138
2.052
1.303
1.179
0.917
1.134
1.972
1.270
1.157
0.787
0.56
1.129
1.898
1.240
1.138
0.674
0.58
1.124
1.828
1.213
1.121
0.576
0.60
1.119
1.763
1.188
1.105
0.491
1.091
0.417
0.50
1.143
0.52 0.54
0.62
1.114
1.703
1.166
0.64
1.109
1.646
1.145
1.079
0.353
0.66
1.104
1.592
1.127
1.068
0.298 0.250
0.68
1.098
1.541
1.110
1.058
0.70
1.093
1.493
1.094
1.049
0.208
0.72
1.087
1.448
1.081
1.041
0.172
0.74
1.082
1.405
1.068
1.034
0.141
0.76
1.076
1.365
1.057
1.028
0.114
0.78
1.070
1.326
1.047
1.023
0.092
0.80
1.064
1.289
1.038
1.019
0.072
1.015
0.056
0.82
1.058
1.254
1.030
0.84
1.052
1.221
1.024
1.011
0.042
0.86
1.045
1.189
1.018
1.008
0.031
0.88
1.039
1.158
1.013
1.006
0.022
0.90
1.033
1.129
1.009
1.004
0.015
0.92
1.026
1.101
1.006
1.002
0.009
0.94
1.020
1.074
1.003
1.001
0.005
0.96
1.013
1.049
1.001
1.001
0.002
0.98
1.007
1.024
1.000
1.000
0.000
138
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g M
T T;.
=
1.400
_2_
p
P*
P *
o
I 1*
4 f
m ax
D
1.00
1.000
1.000
1.000
1.000
0.000
1.02
0.993
0.977
1.000
1.000
0.000
1.04
0.987
0.955
1.001
1.001
0.002
1.06
0.980
0.934
1.003
1.001
0.004
1.08
0.973
0.913
1.005
1.002
0.007
1.10
0.966
0.894
1.008
1.003
0.010
1.12
0.959
0.875
1.011
1.004
0.014
1.14
0.952
0.856
1.015
1.006
0.018
1.16
0.946
0.838
1.020
1.007
0.023
1.18
0.939
0.821
1.025
1.009
0.028
1.20
0.932
0.804
1.030
1.011
0.034
1.22
0.925
0.788
1.037
1.013
0.039
1.24
0.918
0.773
1.043
1.015
0.045
1.26
0.911
0.757
1.050
1.017
0.052
1.28
0.904
0.743
1.058
1.019
0.058
1.30
0.897
0.728
1.066
1.022
0.065
1.32
0.890
0.715
1.075
1.024
0.072
1.34
0.883
0.701
1.084
1.027
0.079
1.36
0.876
0.688
1.094
1.029
0.086
1.38
0.869
0.676
1.104
1.032
0.093
1.40
0.862
0.663
1.115
1.035
0.100
1.42
0.855
0.651
1.126
1.037
0.107
1.44
0.848
0.640
1.138
1.040
0.114
1.46
0.841
0.628
1.150
1.043
0.121
1.48
0.834
0.617
1.163
1.046
0.129
1.50 1.52
0.828 0.821
0.606 0.596
1.176 1.190
1.049 1.052
0.136 0.143
1.54
0.814
0.586
1.204
1.055
0.151
Table 3
U = 1.400
FAul FLOW OF A PERFECT GAS
M
T T -
139
_ -
o
I
P
o
I:
4f
m ax D
1.56
0.807
0.576
1.219
1.058
0.158
1.58
0.800
0.566
1.234
1.060
0.165
1.u0 1.62
0.794 0.787
0.557 0.548
1.250 1.267
1.063 1.066
0.172 0.180
1.64
0.780
0.539
1.284
1.069
0.187
1.66
0.774
0.530
1.301
1.072
0.194
1.68
0.767
0.521
1.319
1.075
0.201
1.70
0.760
0.513
1.338
1.079
0.208
1.72
0.754
0.505
1.357
1.082
0.215
1.74
0.747
0.497
1.376
1.085
0.222
1.76
0.741
0.489
1.397
1.088
0.228
1.78
0.735
0.481
1.418
1.091
0.235
1.80
0.728
0.474
1.439
1.094
0.242
1.82
0.722
0.467
1.461
1.096
0.249
1.84
0.716
0.460
1.484
1.099
0.255
1.86
0.709
0.453
1.507
1.102
0.262
1.88
0.703
0.446
1.531
1.105
0.268
1.90
0.697
0.439
1.555
1.108
0.274
1.92
0.691
0.433
1.580
1.111
0.281
1.94
0.685
0.427
1.606
1.114
0.287
1.96
0.679
0.420
1.633
1.117
0.293
1.98
0.673
0.414
1.660
1.120
0.299
2.00
0.667
0.408
1.688
1.123
0.305 0.311
2.02
0.661
0.402
1.716
1.126
2.04
0.655
0.397
1.745
1.128
0.317
2.06
0.649
0.391
1.775
1.131
0.323
0.643
0.386
1.806
1.134
0.328
2.08
140
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g =
1.400
Ρ ο
I I*
4fL max D
1.837
1.137
0.334
0.375
1.869
1.139
0.339
0.370
1.902
1.142
0.345
0.621
0.365
1.935
1.145
0.350
2.18
0.615
0.360
1.970
1.147
0.356
0.361
Μ
Ρ
Τ Τ*
Ρ*
V
0.638
0.380
2.12
0.632
2.14
0.626
2.16
2.10
2.2o
0.61o
o.355
2.005
1.15o
2.22
0.604
0.350
2.041
1.153
0.366
2.24
0.599
0.345
2.078
1.155
0.371
2.26
0.594
0.341
2.115
1.158
0.376
2.28
0.588
0.336
2.154
1.160
0.381
2.30
0.583
0.332
2.193
1.163
0.386
2.32
0.578
0.328
2.233
1.165
0.391
2.34
0.563
0.323
2.274
1.168
0.396
2.36
0.568
0.319
2.316
1.170
0.401
2.38
0.563
0.315
2.359
1.173
0.405
2.40
0.558
0.311
2.403
1.175
0.410
2.42
0.553
0.307
2.448
1.177
0.414
2.44
0.548
0.303
2.494
1.180
0.419
2.46
0.543
0.300
2.540
1.182
0.423
2.48
0.538
0.296
2.588
1.184
0.428
2.5
0.533
0.292
2.637
1.187
0.432
2.6
0.510
0.275
2.896
1.198
0.453
2.7
0.488
0.259
3.183
1.208
0.472
2.8
0.467
0.244
3.500
1.218
0.490
2.9
0.447
0.231
3.850
1.228
0.507
141
Table 3
FANNO FLOW OF A PERFECT GAS g
Μ
Ρ
=
1.400
Ρ ο
I I*
4fL max D
Τ Τ*
Ρ*
V
3.0
0.429
0.218
4.235
1.237
0.522
3.1
0.411
0.207
4.657
1.245
0.537
3.2
0.394
0.196
5.121
1.253
0.550
3.3
0.378
0.186
5.629
1.260
0.563
3.4
0.362
0.177
6.184
1.268
0.575
3.5
0.348
0.169
6.790
1.274
0.586
3.6
0.334
0.161
7.450
1.281
0.597
3.7
0.321
0.153
8.169
1.287
0.607
3.8
0.309
0.146
8.951
1.292
0.616
3.9
0.297
0.140
9.799
1.298
0.625
4.0
0.286
0.134
10. 7
1.303
0.633
4.5
0.238
0.108
16.6
1.325
0.668
5.0
0.200
0.089
25.0
1.342
0.694
5.5
0.170
0.075
36.9
1.355
0.714
6.0
0.146
0.064
53.2
1.365
0.730
6.5
0.127
0.055
75.1
1.374
0.743
7.0
0.111
0.048
104.1
1.381
0.753
7.5
0.098
0.042
141.8
1.387
0.761
8.0
0.087
0.037
190.1
1.391
0.768
251.1
1.396
0.774
8.5
0.078
0.033
9.0
0.070
0.029
327.2
1.399
0.779
9.5
0.063
0.026
421.1
1.402
0.783
0
0
1.429
0.822
f
142
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
M
T T*
0
1.167
0.02
1.166
0.04 0.06
=
1.333 p
..~
r ;.''
I
0
;.~r o
1*
4fL max D
54.001
29.159
23.159
1868.007
1.166
26.998
14.590
11.597
462.618
1.166
17.995
9.739
7.750
202.845
0.08
1.165
13.493
7.315
5.833
112.180
0.10
1.165
10.791
5.865
4.687
70.372
0.12
1.164
8.990
4.900
3.927
47.768
0.14
1.163
7.702
4.212
3.388
34.216
0.16
1.162
6.736
3.699
2.986
25.478
0.18
1.160
5.984
3.301
2.676
19.533
0.20
1.159
5.382
2.984
2.430
15.317
0.22
1.157
4.890
2.726
2.231
12.227
0.24
1.155
4.479
2.512
2.067
9.903
0.26
1.154
4.131
2.332
1.930
8.115
0.28
1.151
3.832
2.179
1.814
6.714
0.30
1.149
3.573
2.047
1.715
5.600
0.32
1.147
3.347
1.933
1.630
4.702
0.34
1.144
3.146
1.833
1.557
3.969
0.36
1.142
2.968
1.745
1.492
3.366
0.38
1.139
2.809
1.667
1.436
2.866
0.40
1.136
2.665
1.598
1.386
2.447
0.42
1.133
2.535
1.536
1.342
2.094
0.44
1.130
2.416
1.481
1.303
1.795
0.46
1.127
2.308
1.431
1.268
1.541
1.386
1
0.48
1.123
2.208
.237
1.323
143
Table 3
FANNO FLOW FOR A PERFECT GAS U
Μ
Ρ
=
1.333
Ρ ο
I I*
4fL max D
1.345
1.210
1.137
1.308
1.185
0.976
Τ Τ*
Ρ*
V
0.50
1.120
2.116
0.52
1.116
2.032
0.54
1.112
1.953
1.275
1.163
0.837
0.56
1.109
1.880
1.244
1.143
0.717
0.58
1.105
1.812
1.217
1.125
0.614
0.60
1.101
1.748
1.192
1.109
0.523
0.62
1.096
1.689
1.169
1.095
0.445
1.082
0.377
0.64
1.092
1.633
1.148
0.66
1.088
1.580
1.129
1.071
0.318
0.68
1.083
1.530
1.112
1.060
0.267
0.70
1.079
1.484
1.096
1.051
0.223
0.72
1.074
1.439
1.082
1.043
0.184 0.151
0.74
1.069
1.397
1.070
1.036
0.76
1.064
1.357
1.058
1.030
0.123
0.78
1.059
1.319
1.048
1.024
0.098
0.80
1.054
1.283
1.039
1.019
0.078
0.82
1.049
1.249
1.031
1.015
0.060 0.045
0.84
1.044
1.216
1.024
1.012
0.86
1.039
1.185
1.018
1.009
0.033
0.88
1.033
1.155
1.013
1.006
0.023
0.90
1.028
1.126
1.009
1.004
0.016
0.92
1.022
1.099
1.006
1.003
0.010 0.005
0.94
1.017
1.073
1.003
1.001
0.96
1.011
1.048
1.001
1.001
0.002
0.98
1.006
1.023
1.000
1.000
0.001
144
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
Μ
Ρ
=
1.333
Ρ ο
I I*
4fL max D
Τ Τ*
Ρ*
V
1.00
1.000
1.000
1.000
1.000
0.000
1.02
0.994
~.978
1.000
1.000
0.000
1.04
0.988
0.956
1.001
1.001
0.002
1.06
0.983
0.935
1.003
1.001
0.004
1.08
0.977
0.915
1.005
1.002
0.007
1.10
0.971
0.896
1.008
1.003
0.011
1.12
0.965
0.877
1.012
1.005
0.015
1.14
0.959
0.859
1.016
1.006
0.020
1.16
0.953
0.842
1.020
1.008
0.025
1.18
0.947
0.825
1.026
1.010
0.031
1.20
0.941
0.808
1.032
1.012
0.037
1.22
0.935
0.793
1.038
1.014
0.043
1.016
0.049
1.24
0.929
0.777
1.045
1.26
0.923
0.762
1.052
1.018
0.056
1.28
0.916
0.748
1.060
1.021
0.063
1.30
0.910
0.734
1.069
1.023
0.071
1.32
0.904
0.720
1.078
1.026
0.078
1.029
0.086
1.34
0.898
0.707
1.088
1.36
0.892
0.694
1.098
1.031
0.093
1.38
0.886
0.682
1.109
1.034
0.101
1.40
0.879
0.670
1.120
1.037
0.109
1.42
0.873
0.658
1.132
1.040
0.117
1.44
0.867
0.647
1.144
1.043
0.125
1.46
0.861
0.636
1.157
1.046
0.133
1.48
0.855
0.625
1.171
1.050
0.141
Table 3
145
F ANNO FLOW OF A PERFECT GAS g
=
1.333 rO R 0,. * r
4fL
M
T T*
~ ,.
1.50
0.849
0.614
1.185
1.053
0.149
1.52
u.842
u.hu4
1.200
1.056
0.157
1.54
0.836
0.594
1.215
1.059
0.165
1.56
0.830
0.584
1.231
1.062
0.173
1.58
0.824
0.575
1.247
1.066
0.181
1.60
0.818
0.565
1.264
1.069
0.190
1.62
0.812
0.556
1.281
1.072
0.198
1.64
0.806
0.547
1.300
1.076
0.205
* R:.
;,,. I
I
max D
1.66
0.800
0.539
1.318
1.079
0.213
1.68
0.794
0.530
1.338
1.082
0.221
0.229
1.70
0.788
0.522
1.358
1.086
1.72
0.782
0.514
1.379
1.089
0.237
1.74
0.776
0.506
1.400
1.092
0.245
1.76
0.770
0.498
1.422
1.096
0.252
1.78
0.764
0.491
1.445
1.099
0.260
1.103
0.267
1.80
0.758
0.484
1.468
1.82
0.752
0.476
1.492
1.106
0.275
1.84
0.746
0.469
1.517
1.109
0.282
1.86
0.740
0.463
1.543
1.113
0.289
1.88
0.734
0.456
1.569
1.116
0.297
1.90
0.729
0.449
1.596
1.119
0.304
1.92
0.723
0.443
1.624
1.122
0.311
1.94
0.717
0.437
1.652
1.126
0.318
1.96
0.711
0.430
1.682
1.129
0.325
1.98
0.706
0.424
1.712
1.132
0.332
146
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
=
1.333 p
4fL max
Τ Τ*
Ρ
2.00
0.700
0.418
1.743
1.136
0.339
2.02
0.695
0.413
1.774
1.139
0.345
2.04
0.689
0.407
1.807
1.142
0.352
2.06
0.684
0.401
1.841
1.145
0.359
2.08
0.678
0.396
1.875
1.148
0.365
2.10
0.673
0.391
1.910
1.151
0.371
2.12
0.667
0.385
1.947
1.155
0.378
2.14
0.662
0.380
1.984
1.158
0.384
2.16
0.657
0.375
2.022
1.161
0.390
2.18
0.651
0.370
2.061
1.164
0.396
2.20
0.646
0.365
2.101
1.167
0.402
2.22
1.170
0.408
M
Ρ*
0
0
I I ''
D
0.641
0.361
2.142
2.24
0.636
0.356
2.184
1.173
0.414
2.26
0.630
0.351
2.228
1.176
0.420
2.28
0.625
0.347
2.272
1.179
0.426
2.30
0.620
0.342
2.317
1.182
0.431
0.338
2.364
1.185
0.437
2.32
0.615
2.34
0.610
0.334
2.412
1.187
0.442
2.36
0.605
0.330
2.460
1.190
0.448
2.38
0.600
0.326
2.510
1.193
0.453
2.40
0.595
0.322
2.562
1.196
0.459
2.42
0.591
0.318
2.614
1.199
0.464
2.44
0.586
0.314
2.668
1.201
0.469
2.46
0.581
0.310
2.723
1.204
0.474
2.48
0.576
0.306
2.779
1.207
0.479
147
Table 3
FANNO FLOW OF A PERFECT GAS g
T
=
1.333 R
o
I
4fL
max
T*
~ ,. * R:.
Ro
2.5
0.572
0.302
2.837
1.210
0.484
2.6
0.549
0.285
3.147
1.223
0.508
2.7
0.527
0.269
3.494
1.235
0.530
2.8
0.506
0.254
3.883
1.247
0.551
2.9
0.486
0.240
4.319
1.258
0.571
3.0
0.467
0.228
4.805
1.269
0.589
3.1
0.449
0.216
5.346
1.279
0.607
3.2
0.431
0.205
5.949
1.289
0.623
3.'3
0.415
0.195
6.618
1.298
0.638
3.4
0.399
0.186
7.361
1.306
0.652
3.5
0.384
0.177
8.184
1.315
0.666
3.6
0.369
0.169
9.094
1.323
0.678
3.7
0.356
0.161
10.100
1.330
0.690
3.8
0.343
0.154
11.210
1.337
0.701
3.9
0.330
0.147
12.432
1.344
0.712
4.0
0.318
0.141
13.8
1.350
0.721
4.5
0.267
0.115
22.7
1.377
0.763
5.0
0.226
0.095
36.6
1.399
0.795 0.820
M
..
I*
D
5.5
0.193
0.080
57.6
1.416
6.0
0.167
0.068
88.4
1.429
0.839
6.5
0.145
0.059
132.7
1.440
0.855
7.0
0.127
0.051
194.9
1.449
0.868
7.5
0.113
0.045
280.7
1.457
0.878
8.0
0.100
0.040
397.0
1.463
0.887
8.5
0.090
0.035
551.9
1.468
0.894
9.0 9.5
0.081 0.073
0.032 0.028
755.6 1019.9
1.473 1.477
0.900 0.905
0
0
1.512
0.953
f
148
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS
g
Μ
0
Τ Τ* 1.333
Ρ
Ρ* f
=
1.667
Ρ ο
V f
I I* f
4fL max D f
0.02
1.333
57.732
28.132
21.662
0.04
1.333
28.862
14.077
10.851
369.405
0.06
1.332
19.235
9.397
7.255
161.762
0.08
1.331
14.419
7.061
5.464
89.319
0.10
1.329
11.529
5.662
4.395
55.932
3.686
37.893
1493.072
0.12
1.327
9.600
4.732
0.14
1.325
8.222
4.070
3.183
27.086
0.16
1.322
7.187
3.576
2.810
20.124
0.18
1.319
6.381
3.193
2.522
15.393
0.20
1.316
5.736
2.888
2.294
12.042 9.589
0.22
1.312
5.207
2.640
2.110
0.24
1.308
4.766
2.435
1.959
7.747
0.26
1.304
4.392
2.262
1.832
6.331
0.28
1.300
4.071
2.115
1.726
5.225
0.30
1.295
3.793
1.989
1.635
4.346
3.549
1.880
1.558
3.639
0.32
1.289
0.34
1.284
3.333
1.784
1.490
3.063
0.36
1.278
3.141
1.700
1.432
2.591
0.38
1.272
2.968
1.626
1.381
2.199
0.40
1.266
2.813
1.560
1.336
1.872 1.597
0.42
1.259
2.672
1.501
1.296
0.44
1.253
2.544
1.449
1.262
1.365
0.46
1.246
2.426
1.401
1.231
1.168
0.48
1.238
2.318
1.359
1.203
1.001
Table 3
149
FANNO FLOW OF A PERFECT GAS g
M
T
r ,. R*
=
1.667 O
:,,_
Ro
I
I;,,.
4f
Lmax D
0.50
1.231
2.219
1.320
0.52
1.223
2.127
1.285
1.157
0.734
0.54
1.215
2.042
1.254
1.138
0.627
0.56
1.207
1.962
1.225
1.120
0.536
0.58
1.199
1.888
1.200
1.105
0.457
1.819
1.176
1.091
0.389
1.179
0.857
0.60
1.191
0.62
1.182
1.754
1.155
1.079
0.330
0.64
1.173
1.692
1.135
1.068
0.278
0.66
1.164
1.635
1.118
1.058
0.234
0.68
1.155
1.581
1.102
1.050
0.196
0.70
1.146
1.529
1.087
1.042
0.163
0.72
1.137
1.481
1.075
1.035
0.134
0.74
1.128
1.435
1.063
1.029
0.110
0.76
1.118
1.391
1.053
1.024
0.089
0.78
1.109
1.350
1.043
1.019
0.071
0.80
1.099
1.310
1.035
1.016
0.056
0.82
1.089
1.273
1.028
1.012
0.043
0.84
1.079
1.237
1.022
1.009
0.033
0.86
1.070
1.203
1.016
1.007
0.024
0.88
1.060
1.170
1.012
1.005
0.017
0.90
1.050
1.138
1.008
1.003
0.011
0.92
1.040
1.108
1.005
1.002
0.007
0.94
1.030
1.080
1.003
1.001
0.004
0.96
1.020
1.052
1.001
1.000
0.002
0.98
1.010
1.025
1.000
1.000
0.000
150
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS
g M
Τ Τ*
=
1.667
I
4fL
ro ,. r ,.
t,.
1.000
1.000
1.000
0.000
~ ,.
o
max
D
1.00
1.000
1.02
0.990
0.975
1.000
1.000
0.000
1.04
0.980
0.952
1.001
1.000
0.001
1.06
0.970
0.929
1.003
1.001
0.003
1.08
0.960
0.907
1.005
1.002
0.005
1.10
0.950
0.886
1.007
1.002
0.007
1.12
0.940
0.866
1.010
1.003
0.010
1.14
0.930
0.846
1.014
1.005
0.014
1.16
0.920
0.827
1.017
1.006
0.017
1.18
0.911
0.809
1.022
1.007
0.021
1.20
0.901
0.791
1.027
1.008
0.025 0.029
1.22
0.891
0.774
1.032
1.010
1.24
0.881
0.757
1.038
1.012
0.034
1.26
0.872
0.741
1.044
1.013
0.038
1.28
0.862
0.725
1.051
1.015
0.043
1.30
0.853
0.710
1.057
1.017
0.047
1.32
0.843
0.696
1.065
1.019
0.052
1.34
0.834
0.682
1.073
1.020
0.057
1.36
0.825
0.668
1.081
1.022
0.062
1.38
0.816
0.654
1.089
1.024
0.067
1.40
0.806
0.641
1.098
1.026
0.072
1.028
0.077
1.42
0.797
0.629
1.108
1.44
0.788
0.617
1.117
1.030
0.083
1.46
0.779
0.605
1.127
1.032
0.088
1.48
0.771
0.593
1.138
1.034
0.093
Table 3
151
FANNO FLOW OF A PERFECT GAS g = M
T
1..
r,.
1.667 R
R
o
,_
;, o
I 1*
4f1,
ax
D
1.50
0.762
0.582
1.148
1.037
0.098
1.52
0.753
0.571
1.160
1.039
0.103
1.171
1.041
0.108
1.54
0.745
0.560
1.56
0.736
0.550
1.183
1.043
0.113
1.58
0. 728
0.540
1.195
1.045
0.118
1.60
0. 719
0.530
1.208
1.047
0.123
1.62
0.711
0.521
1.220
1.049
0.128
1.64
0.703
0.511
1.234
1.051
0.133
1.66
0.695
0.502
1.247
1.053
0.137
1.68
0.687
0.493
1.261
1.055
0.142
1.70
0.679
0.485
1.275
1.057
0.147
1.72
0.671
0.476
1.290
1.059
0.152
1.74
0.664
0.468
1.305
1.061
0.156
1.76
0.656
0.460
1.320
1.063
0.161
1.78
0.648
0.452
1.336
1.065
0.165
1.80
0.641
0.445
1.352
1.067
0.170
1.82
0.634
0.437
1.368
1.069
0.174
1.84
0.626
0.430
1.385
1.071
0.179
1.86
0.619
0.423
1.402
1.073
0.183
1.88
0.612
0.416
1.419
1.075
0.187
1.90
0.605
0.409
1.437
1.077
0.191
1.92
0.598
0.403
1.455
1.079
0.195
1.94
0.591
0.396
1.474
1.081
0.199
1.96
0.585
0.390
1.492
1.083
0.203
1.98
0.578
0.384
1.512
1.085
0.207
152
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g = M
T
.
E, ~.
1.667 r
p
p
o
;,,.
o
I I :,,.
4f
max
, D
2.00
0.571
0.378
1.531
1.087
0.211
2.02
0.565
0.372
1.551
1.088
0.215
2.04
0.558
0.366
1.571
1.090
0.219
2.06
0.552
0.361
1.592
1.092
0.223
2.08
0.546
0.355
1.613
1.094
0.226
2.10
0.540
0.350
1.634
1.095
0.230
2.12
0.534
0.345
1.656
1.097
0.233
2.14
0.528
0.339
1.678
1.099
0.237
2.16
0.522
0.334
1.700
1.101
0.240
2.18
0.516
0.329
1.723
1.102
0.244
2.20
0.510
0.325
1.746
1.104
0.247 0.250
2.22
0.504
0.320
1.769
1.105
2.24
0.499
0.315
1.793
1.107
0.254
2.26
0.493
0.311
1.818
1.109
0.257
2.28
0.488
0.306
1.842
1.110
0.260
2.30
0.482
0.302
1.867
1.112
0.263
2.32
0.477
0.298
1.893
1.113
0.266
2.34
0.472
0.294
1.918
1.115
0.269
2.36
0.467
0.289
1.945
1.116
0.272
2.38
0.462
0.285
1.971
1.118
0.275
2.40
0.457
0.282
1.998
1.119
0.278 0.280
2.42
0.452
0.278
2.025
1.121
2.44
0.447
0.274
2.053
1.122
0.283
2.46
0.442
0.270
2.081
1.123
0.286
2.48
0.437
0.267
2.110
1.125
0.289
Table 3
153
FAul FLOW OF A PERFECT GAS g
Μ
Ρ
Τ Τ*
Ρ*
2.5
0.432
0.263
2.6
0.410
0.246
2.7
0.389
0.231
2.8
0.369
0.217
=
1.667
Ρ ο
I I*
4fL max D
2.139
1.126
0.291
2.289
1.133
0.304
2.450
1.139
0.315
2.622
1.144
0.326 0.336
V
2.9
0.350
0.204
2.805
1.150
3.0
0.333
0.192
2.999
1.155
0.345
3.1
0.317
0.182
3.205
1.159
0.354
3.2
0.302
0.172
3.422
1.164
0.362
3.3
0.288
0.163
3.553
1.168
0.369 0.376
3.4
0.275
0.154
3.895
1.172
3.5
0.262
0.146
4.151
1.175
0.383
3.6
0.251
0.139
4.420
1.178
0.389
3.7
0.240
0.132
4. 703
1.182
0.394
3.8
0.229
0.126
5.000
1.185
0.399
3.9
P. 220
0.120
5.311
1.187
0.404
4.0
0.210
0.115
5.6
1.190
0.409
4.5
0.172
0.092
7.5
1.201
0.428
5.0
0.143
0.076
9.8
1.209
0.442
5.5
0.120
0.063
12.6
1.216
0.453
6.0
0.103
0.053
15.8
1.221
0.461
6.5
0.088
0.046
19.7
1.225
0.468
7.0
0.077
0.040
24.1
1.228
0.474
7.5
0.067
0.035
29.2
1.231
0.478
8.0
0.060
0.031
35.0
1.233
0.482
8.5
0.053
0.027
41.6
1.235
0.485
9.0
0.048
0.024
48.9
1.236
0.487
9.5
0.043
0.022
57.1
1.238
0.489
0
0
1.250
0.509
f
f
T T;.
_2_
p
P*
P *
o
I 1*
4 f
m ax
D
f
f
0
1.200
0.02
1.200
54.770
28.942
22.834
177,8.451
0.04
1.200
27.382
14.481
11.435
440.352
0.06
1.199
18.251
9.666
7.643
193.031
0.08
1.198
13.684
7.262
5.753
106.718
0.10
1.198
10.944
5.822
4.624
66.922
0.12
1.197
9.116
4.864
3.875
45.408
0.14
1.195
7.809
4.182
3.343
32.511
0.16
1.194
6.829
3.673
2.947
24.198
0.18
1.192
6.066
3.278
2.642
18.543
0.20
1.190
5.455
2.964
2.400
14.533
0.22
1.188
4.955
2.708
2.205
11.596
0.24
1.186
4.538
2.496
2.043
9.386
0.26
1.184
4.185
2.317
1.909
7.688
0.28
1.181
3.882
2.166
1.795
6.357
0.30
1.179
3.619
2.035
1.698
5.299
0.32
1.176
3.389
1.922
1.614
4.447
0.34
1.173
3.185
1.823
1.542
3.752
0.36
1.170
3.004
1.736
1.479
3.180
0.38
1.166
2.842
1.659
1.424
2.705
0.40
1.163
2.696
1.590
1.375
2.308
0.42
1.159
2.563
1.529
1.332
1.974
0.44
1.155
2.443
1.474
1.294
1.692
0.46
1.151
2.333
1.425
1.260
1.451
0.48
1.147
2.231
1.380
1.230
1.245
136
137
Table 3
FANNO FLOW OF A PERFECT GAS g = M
T T;.
~
1.400 R
o
;.
o
I
I;,''
4f
m ax D
2.138
1.340
1.203
1.069
1.138
2.052
1.303
1.179
0.917
1.134
1.972
1.270
1.157
0.787
0.56
1.129
1.898
1.240
1.138
0.674
0.58
1.124
1.828
1.213
1.121
0.576
0.60
1.119
1.763
1.188
1.105
0.491
1.091
0.417
0.50
1.143
0.52 0.54
0.62
1.114
1.703
1.166
0.64
1.109
1.646
1.145
1.079
0.353
0.66
1.104
1.592
1.127
1.068
0.298 0.250
0.68
1.098
1.541
1.110
1.058
0.70
1.093
1.493
1.094
1.049
0.208
0.72
1.087
1.448
1.081
1.041
0.172
0.74
1.082
1.405
1.068
1.034
0.141
0.76
1.076
1.365
1.057
1.028
0.114
0.78
1.070
1.326
1.047
1.023
0.092
0.80
1.064
1.289
1.038
1.019
0.072
1.015
0.056
0.82
1.058
1.254
1.030
0.84
1.052
1.221
1.024
1.011
0.042
0.86
1.045
1.189
1.018
1.008
0.031
0.88
1.039
1.158
1.013
1.006
0.022
0.90
1.033
1.129
1.009
1.004
0.015
0.92
1.026
1.101
1.006
1.002
0.009
0.94
1.020
1.074
1.003
1.001
0.005
0.96
1.013
1.049
1.001
1.001
0.002
0.98
1.007
1.024
1.000
1.000
0.000
138
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g M
T T;.
=
1.400
_2_
p
P*
P *
o
I 1*
4 f
m ax
D
1.00
1.000
1.000
1.000
1.000
0.000
1.02
0.993
0.977
1.000
1.000
0.000
1.04
0.987
0.955
1.001
1.001
0.002
1.06
0.980
0.934
1.003
1.001
0.004
1.08
0.973
0.913
1.005
1.002
0.007
1.10
0.966
0.894
1.008
1.003
0.010
1.12
0.959
0.875
1.011
1.004
0.014
1.14
0.952
0.856
1.015
1.006
0.018
1.16
0.946
0.838
1.020
1.007
0.023
1.18
0.939
0.821
1.025
1.009
0.028
1.20
0.932
0.804
1.030
1.011
0.034
1.22
0.925
0.788
1.037
1.013
0.039
1.24
0.918
0.773
1.043
1.015
0.045
1.26
0.911
0.757
1.050
1.017
0.052
1.28
0.904
0.743
1.058
1.019
0.058
1.30
0.897
0.728
1.066
1.022
0.065
1.32
0.890
0.715
1.075
1.024
0.072
1.34
0.883
0.701
1.084
1.027
0.079
1.36
0.876
0.688
1.094
1.029
0.086
1.38
0.869
0.676
1.104
1.032
0.093
1.40
0.862
0.663
1.115
1.035
0.100
1.42
0.855
0.651
1.126
1.037
0.107
1.44
0.848
0.640
1.138
1.040
0.114
1.46
0.841
0.628
1.150
1.043
0.121
1.48
0.834
0.617
1.163
1.046
0.129
1.50 1.52
0.828 0.821
0.606 0.596
1.176 1.190
1.049 1.052
0.136 0.143
1.54
0.814
0.586
1.204
1.055
0.151
Table 3
U = 1.400
FAul FLOW OF A PERFECT GAS
M
T T -
139
_ -
o
I
P
o
I:
4f
m ax D
1.56
0.807
0.576
1.219
1.058
0.158
1.58
0.800
0.566
1.234
1.060
0.165
1.u0 1.62
0.794 0.787
0.557 0.548
1.250 1.267
1.063 1.066
0.172 0.180
1.64
0.780
0.539
1.284
1.069
0.187
1.66
0.774
0.530
1.301
1.072
0.194
1.68
0.767
0.521
1.319
1.075
0.201
1.70
0.760
0.513
1.338
1.079
0.208
1.72
0.754
0.505
1.357
1.082
0.215
1.74
0.747
0.497
1.376
1.085
0.222
1.76
0.741
0.489
1.397
1.088
0.228
1.78
0.735
0.481
1.418
1.091
0.235
1.80
0.728
0.474
1.439
1.094
0.242
1.82
0.722
0.467
1.461
1.096
0.249
1.84
0.716
0.460
1.484
1.099
0.255
1.86
0.709
0.453
1.507
1.102
0.262
1.88
0.703
0.446
1.531
1.105
0.268
1.90
0.697
0.439
1.555
1.108
0.274
1.92
0.691
0.433
1.580
1.111
0.281
1.94
0.685
0.427
1.606
1.114
0.287
1.96
0.679
0.420
1.633
1.117
0.293
1.98
0.673
0.414
1.660
1.120
0.299
2.00
0.667
0.408
1.688
1.123
0.305 0.311
2.02
0.661
0.402
1.716
1.126
2.04
0.655
0.397
1.745
1.128
0.317
2.06
0.649
0.391
1.775
1.131
0.323
0.643
0.386
1.806
1.134
0.328
2.08
140
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g =
1.400
Ρ ο
I I*
4fL max D
1.837
1.137
0.334
0.375
1.869
1.139
0.339
0.370
1.902
1.142
0.345
0.621
0.365
1.935
1.145
0.350
2.18
0.615
0.360
1.970
1.147
0.356
0.361
Μ
Ρ
Τ Τ*
Ρ*
V
0.638
0.380
2.12
0.632
2.14
0.626
2.16
2.10
2.2o
0.61o
o.355
2.005
1.15o
2.22
0.604
0.350
2.041
1.153
0.366
2.24
0.599
0.345
2.078
1.155
0.371
2.26
0.594
0.341
2.115
1.158
0.376
2.28
0.588
0.336
2.154
1.160
0.381
2.30
0.583
0.332
2.193
1.163
0.386
2.32
0.578
0.328
2.233
1.165
0.391
2.34
0.563
0.323
2.274
1.168
0.396
2.36
0.568
0.319
2.316
1.170
0.401
2.38
0.563
0.315
2.359
1.173
0.405
2.40
0.558
0.311
2.403
1.175
0.410
2.42
0.553
0.307
2.448
1.177
0.414
2.44
0.548
0.303
2.494
1.180
0.419
2.46
0.543
0.300
2.540
1.182
0.423
2.48
0.538
0.296
2.588
1.184
0.428
2.5
0.533
0.292
2.637
1.187
0.432
2.6
0.510
0.275
2.896
1.198
0.453
2.7
0.488
0.259
3.183
1.208
0.472
2.8
0.467
0.244
3.500
1.218
0.490
2.9
0.447
0.231
3.850
1.228
0.507
141
Table 3
FANNO FLOW OF A PERFECT GAS g
Μ
Ρ
=
1.400
Ρ ο
I I*
4fL max D
Τ Τ*
Ρ*
V
3.0
0.429
0.218
4.235
1.237
0.522
3.1
0.411
0.207
4.657
1.245
0.537
3.2
0.394
0.196
5.121
1.253
0.550
3.3
0.378
0.186
5.629
1.260
0.563
3.4
0.362
0.177
6.184
1.268
0.575
3.5
0.348
0.169
6.790
1.274
0.586
3.6
0.334
0.161
7.450
1.281
0.597
3.7
0.321
0.153
8.169
1.287
0.607
3.8
0.309
0.146
8.951
1.292
0.616
3.9
0.297
0.140
9.799
1.298
0.625
4.0
0.286
0.134
10. 7
1.303
0.633
4.5
0.238
0.108
16.6
1.325
0.668
5.0
0.200
0.089
25.0
1.342
0.694
5.5
0.170
0.075
36.9
1.355
0.714
6.0
0.146
0.064
53.2
1.365
0.730
6.5
0.127
0.055
75.1
1.374
0.743
7.0
0.111
0.048
104.1
1.381
0.753
7.5
0.098
0.042
141.8
1.387
0.761
8.0
0.087
0.037
190.1
1.391
0.768
251.1
1.396
0.774
8.5
0.078
0.033
9.0
0.070
0.029
327.2
1.399
0.779
9.5
0.063
0.026
421.1
1.402
0.783
0
0
1.429
0.822
f
142
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
M
T T*
0
1.167
0.02
1.166
0.04 0.06
=
1.333 p
..~
r ;.''
I
0
;.~r o
1*
4fL max D
54.001
29.159
23.159
1868.007
1.166
26.998
14.590
11.597
462.618
1.166
17.995
9.739
7.750
202.845
0.08
1.165
13.493
7.315
5.833
112.180
0.10
1.165
10.791
5.865
4.687
70.372
0.12
1.164
8.990
4.900
3.927
47.768
0.14
1.163
7.702
4.212
3.388
34.216
0.16
1.162
6.736
3.699
2.986
25.478
0.18
1.160
5.984
3.301
2.676
19.533
0.20
1.159
5.382
2.984
2.430
15.317
0.22
1.157
4.890
2.726
2.231
12.227
0.24
1.155
4.479
2.512
2.067
9.903
0.26
1.154
4.131
2.332
1.930
8.115
0.28
1.151
3.832
2.179
1.814
6.714
0.30
1.149
3.573
2.047
1.715
5.600
0.32
1.147
3.347
1.933
1.630
4.702
0.34
1.144
3.146
1.833
1.557
3.969
0.36
1.142
2.968
1.745
1.492
3.366
0.38
1.139
2.809
1.667
1.436
2.866
0.40
1.136
2.665
1.598
1.386
2.447
0.42
1.133
2.535
1.536
1.342
2.094
0.44
1.130
2.416
1.481
1.303
1.795
0.46
1.127
2.308
1.431
1.268
1.541
1.386
1
0.48
1.123
2.208
.237
1.323
143
Table 3
FANNO FLOW FOR A PERFECT GAS U
Μ
Ρ
=
1.333
Ρ ο
I I*
4fL max D
1.345
1.210
1.137
1.308
1.185
0.976
Τ Τ*
Ρ*
V
0.50
1.120
2.116
0.52
1.116
2.032
0.54
1.112
1.953
1.275
1.163
0.837
0.56
1.109
1.880
1.244
1.143
0.717
0.58
1.105
1.812
1.217
1.125
0.614
0.60
1.101
1.748
1.192
1.109
0.523
0.62
1.096
1.689
1.169
1.095
0.445
1.082
0.377
0.64
1.092
1.633
1.148
0.66
1.088
1.580
1.129
1.071
0.318
0.68
1.083
1.530
1.112
1.060
0.267
0.70
1.079
1.484
1.096
1.051
0.223
0.72
1.074
1.439
1.082
1.043
0.184 0.151
0.74
1.069
1.397
1.070
1.036
0.76
1.064
1.357
1.058
1.030
0.123
0.78
1.059
1.319
1.048
1.024
0.098
0.80
1.054
1.283
1.039
1.019
0.078
0.82
1.049
1.249
1.031
1.015
0.060 0.045
0.84
1.044
1.216
1.024
1.012
0.86
1.039
1.185
1.018
1.009
0.033
0.88
1.033
1.155
1.013
1.006
0.023
0.90
1.028
1.126
1.009
1.004
0.016
0.92
1.022
1.099
1.006
1.003
0.010 0.005
0.94
1.017
1.073
1.003
1.001
0.96
1.011
1.048
1.001
1.001
0.002
0.98
1.006
1.023
1.000
1.000
0.001
144
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
Μ
Ρ
=
1.333
Ρ ο
I I*
4fL max D
Τ Τ*
Ρ*
V
1.00
1.000
1.000
1.000
1.000
0.000
1.02
0.994
~.978
1.000
1.000
0.000
1.04
0.988
0.956
1.001
1.001
0.002
1.06
0.983
0.935
1.003
1.001
0.004
1.08
0.977
0.915
1.005
1.002
0.007
1.10
0.971
0.896
1.008
1.003
0.011
1.12
0.965
0.877
1.012
1.005
0.015
1.14
0.959
0.859
1.016
1.006
0.020
1.16
0.953
0.842
1.020
1.008
0.025
1.18
0.947
0.825
1.026
1.010
0.031
1.20
0.941
0.808
1.032
1.012
0.037
1.22
0.935
0.793
1.038
1.014
0.043
1.016
0.049
1.24
0.929
0.777
1.045
1.26
0.923
0.762
1.052
1.018
0.056
1.28
0.916
0.748
1.060
1.021
0.063
1.30
0.910
0.734
1.069
1.023
0.071
1.32
0.904
0.720
1.078
1.026
0.078
1.029
0.086
1.34
0.898
0.707
1.088
1.36
0.892
0.694
1.098
1.031
0.093
1.38
0.886
0.682
1.109
1.034
0.101
1.40
0.879
0.670
1.120
1.037
0.109
1.42
0.873
0.658
1.132
1.040
0.117
1.44
0.867
0.647
1.144
1.043
0.125
1.46
0.861
0.636
1.157
1.046
0.133
1.48
0.855
0.625
1.171
1.050
0.141
Table 3
145
F ANNO FLOW OF A PERFECT GAS g
=
1.333 rO R 0,. * r
4fL
M
T T*
~ ,.
1.50
0.849
0.614
1.185
1.053
0.149
1.52
u.842
u.hu4
1.200
1.056
0.157
1.54
0.836
0.594
1.215
1.059
0.165
1.56
0.830
0.584
1.231
1.062
0.173
1.58
0.824
0.575
1.247
1.066
0.181
1.60
0.818
0.565
1.264
1.069
0.190
1.62
0.812
0.556
1.281
1.072
0.198
1.64
0.806
0.547
1.300
1.076
0.205
* R:.
;,,. I
I
max D
1.66
0.800
0.539
1.318
1.079
0.213
1.68
0.794
0.530
1.338
1.082
0.221
0.229
1.70
0.788
0.522
1.358
1.086
1.72
0.782
0.514
1.379
1.089
0.237
1.74
0.776
0.506
1.400
1.092
0.245
1.76
0.770
0.498
1.422
1.096
0.252
1.78
0.764
0.491
1.445
1.099
0.260
1.103
0.267
1.80
0.758
0.484
1.468
1.82
0.752
0.476
1.492
1.106
0.275
1.84
0.746
0.469
1.517
1.109
0.282
1.86
0.740
0.463
1.543
1.113
0.289
1.88
0.734
0.456
1.569
1.116
0.297
1.90
0.729
0.449
1.596
1.119
0.304
1.92
0.723
0.443
1.624
1.122
0.311
1.94
0.717
0.437
1.652
1.126
0.318
1.96
0.711
0.430
1.682
1.129
0.325
1.98
0.706
0.424
1.712
1.132
0.332
146
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g
=
1.333 p
4fL max
Τ Τ*
Ρ
2.00
0.700
0.418
1.743
1.136
0.339
2.02
0.695
0.413
1.774
1.139
0.345
2.04
0.689
0.407
1.807
1.142
0.352
2.06
0.684
0.401
1.841
1.145
0.359
2.08
0.678
0.396
1.875
1.148
0.365
2.10
0.673
0.391
1.910
1.151
0.371
2.12
0.667
0.385
1.947
1.155
0.378
2.14
0.662
0.380
1.984
1.158
0.384
2.16
0.657
0.375
2.022
1.161
0.390
2.18
0.651
0.370
2.061
1.164
0.396
2.20
0.646
0.365
2.101
1.167
0.402
2.22
1.170
0.408
M
Ρ*
0
0
I I ''
D
0.641
0.361
2.142
2.24
0.636
0.356
2.184
1.173
0.414
2.26
0.630
0.351
2.228
1.176
0.420
2.28
0.625
0.347
2.272
1.179
0.426
2.30
0.620
0.342
2.317
1.182
0.431
0.338
2.364
1.185
0.437
2.32
0.615
2.34
0.610
0.334
2.412
1.187
0.442
2.36
0.605
0.330
2.460
1.190
0.448
2.38
0.600
0.326
2.510
1.193
0.453
2.40
0.595
0.322
2.562
1.196
0.459
2.42
0.591
0.318
2.614
1.199
0.464
2.44
0.586
0.314
2.668
1.201
0.469
2.46
0.581
0.310
2.723
1.204
0.474
2.48
0.576
0.306
2.779
1.207
0.479
147
Table 3
FANNO FLOW OF A PERFECT GAS g
T
=
1.333 R
o
I
4fL
max
T*
~ ,. * R:.
Ro
2.5
0.572
0.302
2.837
1.210
0.484
2.6
0.549
0.285
3.147
1.223
0.508
2.7
0.527
0.269
3.494
1.235
0.530
2.8
0.506
0.254
3.883
1.247
0.551
2.9
0.486
0.240
4.319
1.258
0.571
3.0
0.467
0.228
4.805
1.269
0.589
3.1
0.449
0.216
5.346
1.279
0.607
3.2
0.431
0.205
5.949
1.289
0.623
3.'3
0.415
0.195
6.618
1.298
0.638
3.4
0.399
0.186
7.361
1.306
0.652
3.5
0.384
0.177
8.184
1.315
0.666
3.6
0.369
0.169
9.094
1.323
0.678
3.7
0.356
0.161
10.100
1.330
0.690
3.8
0.343
0.154
11.210
1.337
0.701
3.9
0.330
0.147
12.432
1.344
0.712
4.0
0.318
0.141
13.8
1.350
0.721
4.5
0.267
0.115
22.7
1.377
0.763
5.0
0.226
0.095
36.6
1.399
0.795 0.820
M
..
I*
D
5.5
0.193
0.080
57.6
1.416
6.0
0.167
0.068
88.4
1.429
0.839
6.5
0.145
0.059
132.7
1.440
0.855
7.0
0.127
0.051
194.9
1.449
0.868
7.5
0.113
0.045
280.7
1.457
0.878
8.0
0.100
0.040
397.0
1.463
0.887
8.5
0.090
0.035
551.9
1.468
0.894
9.0 9.5
0.081 0.073
0.032 0.028
755.6 1019.9
1.473 1.477
0.900 0.905
0
0
1.512
0.953
f
148
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS
g
Μ
0
Τ Τ* 1.333
Ρ
Ρ* f
=
1.667
Ρ ο
V f
I I* f
4fL max D f
0.02
1.333
57.732
28.132
21.662
0.04
1.333
28.862
14.077
10.851
369.405
0.06
1.332
19.235
9.397
7.255
161.762
0.08
1.331
14.419
7.061
5.464
89.319
0.10
1.329
11.529
5.662
4.395
55.932
3.686
37.893
1493.072
0.12
1.327
9.600
4.732
0.14
1.325
8.222
4.070
3.183
27.086
0.16
1.322
7.187
3.576
2.810
20.124
0.18
1.319
6.381
3.193
2.522
15.393
0.20
1.316
5.736
2.888
2.294
12.042 9.589
0.22
1.312
5.207
2.640
2.110
0.24
1.308
4.766
2.435
1.959
7.747
0.26
1.304
4.392
2.262
1.832
6.331
0.28
1.300
4.071
2.115
1.726
5.225
0.30
1.295
3.793
1.989
1.635
4.346
3.549
1.880
1.558
3.639
0.32
1.289
0.34
1.284
3.333
1.784
1.490
3.063
0.36
1.278
3.141
1.700
1.432
2.591
0.38
1.272
2.968
1.626
1.381
2.199
0.40
1.266
2.813
1.560
1.336
1.872 1.597
0.42
1.259
2.672
1.501
1.296
0.44
1.253
2.544
1.449
1.262
1.365
0.46
1.246
2.426
1.401
1.231
1.168
0.48
1.238
2.318
1.359
1.203
1.001
Table 3
149
FANNO FLOW OF A PERFECT GAS g
M
T
r ,. R*
=
1.667 O
:,,_
Ro
I
I;,,.
4f
Lmax D
0.50
1.231
2.219
1.320
0.52
1.223
2.127
1.285
1.157
0.734
0.54
1.215
2.042
1.254
1.138
0.627
0.56
1.207
1.962
1.225
1.120
0.536
0.58
1.199
1.888
1.200
1.105
0.457
1.819
1.176
1.091
0.389
1.179
0.857
0.60
1.191
0.62
1.182
1.754
1.155
1.079
0.330
0.64
1.173
1.692
1.135
1.068
0.278
0.66
1.164
1.635
1.118
1.058
0.234
0.68
1.155
1.581
1.102
1.050
0.196
0.70
1.146
1.529
1.087
1.042
0.163
0.72
1.137
1.481
1.075
1.035
0.134
0.74
1.128
1.435
1.063
1.029
0.110
0.76
1.118
1.391
1.053
1.024
0.089
0.78
1.109
1.350
1.043
1.019
0.071
0.80
1.099
1.310
1.035
1.016
0.056
0.82
1.089
1.273
1.028
1.012
0.043
0.84
1.079
1.237
1.022
1.009
0.033
0.86
1.070
1.203
1.016
1.007
0.024
0.88
1.060
1.170
1.012
1.005
0.017
0.90
1.050
1.138
1.008
1.003
0.011
0.92
1.040
1.108
1.005
1.002
0.007
0.94
1.030
1.080
1.003
1.001
0.004
0.96
1.020
1.052
1.001
1.000
0.002
0.98
1.010
1.025
1.000
1.000
0.000
150
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS
g M
Τ Τ*
=
1.667
I
4fL
ro ,. r ,.
t,.
1.000
1.000
1.000
0.000
~ ,.
o
max
D
1.00
1.000
1.02
0.990
0.975
1.000
1.000
0.000
1.04
0.980
0.952
1.001
1.000
0.001
1.06
0.970
0.929
1.003
1.001
0.003
1.08
0.960
0.907
1.005
1.002
0.005
1.10
0.950
0.886
1.007
1.002
0.007
1.12
0.940
0.866
1.010
1.003
0.010
1.14
0.930
0.846
1.014
1.005
0.014
1.16
0.920
0.827
1.017
1.006
0.017
1.18
0.911
0.809
1.022
1.007
0.021
1.20
0.901
0.791
1.027
1.008
0.025 0.029
1.22
0.891
0.774
1.032
1.010
1.24
0.881
0.757
1.038
1.012
0.034
1.26
0.872
0.741
1.044
1.013
0.038
1.28
0.862
0.725
1.051
1.015
0.043
1.30
0.853
0.710
1.057
1.017
0.047
1.32
0.843
0.696
1.065
1.019
0.052
1.34
0.834
0.682
1.073
1.020
0.057
1.36
0.825
0.668
1.081
1.022
0.062
1.38
0.816
0.654
1.089
1.024
0.067
1.40
0.806
0.641
1.098
1.026
0.072
1.028
0.077
1.42
0.797
0.629
1.108
1.44
0.788
0.617
1.117
1.030
0.083
1.46
0.779
0.605
1.127
1.032
0.088
1.48
0.771
0.593
1.138
1.034
0.093
Table 3
151
FANNO FLOW OF A PERFECT GAS g = M
T
1..
r,.
1.667 R
R
o
,_
;, o
I 1*
4f1,
ax
D
1.50
0.762
0.582
1.148
1.037
0.098
1.52
0.753
0.571
1.160
1.039
0.103
1.171
1.041
0.108
1.54
0.745
0.560
1.56
0.736
0.550
1.183
1.043
0.113
1.58
0. 728
0.540
1.195
1.045
0.118
1.60
0. 719
0.530
1.208
1.047
0.123
1.62
0.711
0.521
1.220
1.049
0.128
1.64
0.703
0.511
1.234
1.051
0.133
1.66
0.695
0.502
1.247
1.053
0.137
1.68
0.687
0.493
1.261
1.055
0.142
1.70
0.679
0.485
1.275
1.057
0.147
1.72
0.671
0.476
1.290
1.059
0.152
1.74
0.664
0.468
1.305
1.061
0.156
1.76
0.656
0.460
1.320
1.063
0.161
1.78
0.648
0.452
1.336
1.065
0.165
1.80
0.641
0.445
1.352
1.067
0.170
1.82
0.634
0.437
1.368
1.069
0.174
1.84
0.626
0.430
1.385
1.071
0.179
1.86
0.619
0.423
1.402
1.073
0.183
1.88
0.612
0.416
1.419
1.075
0.187
1.90
0.605
0.409
1.437
1.077
0.191
1.92
0.598
0.403
1.455
1.079
0.195
1.94
0.591
0.396
1.474
1.081
0.199
1.96
0.585
0.390
1.492
1.083
0.203
1.98
0.578
0.384
1.512
1.085
0.207
152
One-dimensional Compressible Flow
FANNO FLOW OF A PERFECT GAS g = M
T
.
E, ~.
1.667 r
p
p
o
;,,.
o
I I :,,.
4f
max
, D
2.00
0.571
0.378
1.531
1.087
0.211
2.02
0.565
0.372
1.551
1.088
0.215
2.04
0.558
0.366
1.571
1.090
0.219
2.06
0.552
0.361
1.592
1.092
0.223
2.08
0.546
0.355
1.613
1.094
0.226
2.10
0.540
0.350
1.634
1.095
0.230
2.12
0.534
0.345
1.656
1.097
0.233
2.14
0.528
0.339
1.678
1.099
0.237
2.16
0.522
0.334
1.700
1.101
0.240
2.18
0.516
0.329
1.723
1.102
0.244
2.20
0.510
0.325
1.746
1.104
0.247 0.250
2.22
0.504
0.320
1.769
1.105
2.24
0.499
0.315
1.793
1.107
0.254
2.26
0.493
0.311
1.818
1.109
0.257
2.28
0.488
0.306
1.842
1.110
0.260
2.30
0.482
0.302
1.867
1.112
0.263
2.32
0.477
0.298
1.893
1.113
0.266
2.34
0.472
0.294
1.918
1.115
0.269
2.36
0.467
0.289
1.945
1.116
0.272
2.38
0.462
0.285
1.971
1.118
0.275
2.40
0.457
0.282
1.998
1.119
0.278 0.280
2.42
0.452
0.278
2.025
1.121
2.44
0.447
0.274
2.053
1.122
0.283
2.46
0.442
0.270
2.081
1.123
0.286
2.48
0.437
0.267
2.110
1.125
0.289
Table 3
153
FAul FLOW OF A PERFECT GAS g
Μ
Ρ
Τ Τ*
Ρ*
2.5
0.432
0.263
2.6
0.410
0.246
2.7
0.389
0.231
2.8
0.369
0.217
=
1.667
Ρ ο
I I*
4fL max D
2.139
1.126
0.291
2.289
1.133
0.304
2.450
1.139
0.315
2.622
1.144
0.326 0.336
V
2.9
0.350
0.204
2.805
1.150
3.0
0.333
0.192
2.999
1.155
0.345
3.1
0.317
0.182
3.205
1.159
0.354
3.2
0.302
0.172
3.422
1.164
0.362
3.3
0.288
0.163
3.553
1.168
0.369 0.376
3.4
0.275
0.154
3.895
1.172
3.5
0.262
0.146
4.151
1.175
0.383
3.6
0.251
0.139
4.420
1.178
0.389
3.7
0.240
0.132
4. 703
1.182
0.394
3.8
0.229
0.126
5.000
1.185
0.399
3.9
P. 220
0.120
5.311
1.187
0.404
4.0
0.210
0.115
5.6
1.190
0.409
4.5
0.172
0.092
7.5
1.201
0.428
5.0
0.143
0.076
9.8
1.209
0.442
5.5
0.120
0.063
12.6
1.216
0.453
6.0
0.103
0.053
15.8
1.221
0.461
6.5
0.088
0.046
19.7
1.225
0.468
7.0
0.077
0.040
24.1
1.228
0.474
7.5
0.067
0.035
29.2
1.231
0.478
8.0
0.060
0.031
35.0
1.233
0.482
8.5
0.053
0.027
41.6
1.235
0.485
9.0
0.048
0.024
48.9
1.236
0.487
9.5
0.043
0.022
57.1
1.238
0.489
0
0
1.250
0.509
f
f