-
Table A1
4
Properties of water
P (kglm3)
Dynamic
Viscosity
P (Pa4
Surface
Tension
o (Nlm)
Vapor
Pressure
(Pa)
0
999,9
1,787~10"
75,6 x105
O,6105x1O3
5
1000,O
1,519 xlo"
74,9 xlo"
0,8722 xlo3
10
999,7
1,307 xlo-'
74,2 xl0"
1,228 xlo3
20
998,2
1,002 xlo5
72,8 xlo"
2,338 xlo3
30
995,7
7,975 x10"1
71,2 X I O - ~
4,243 xlo3
40
992,2
6,529 xlo"
69,6 x10"
7,376 xlo3
50
988,l
5,468 x ~ o - ~ 67,9 x10"
12,33 xlo3
60
983,2
4,665 x10"
66 2 xlo"
19,92 xlo3
70
977,8
4,042 x10-~" 64,4 &lo-'
31,16 xlo3
80
971,8
3,547 xlo"
62,6 x10"
47,34 xlo3
90
965,3
3,147 xlo"
60,8 x10"
70,lO xlo3
100
958,4
2,818 xlo5
58,9 x10"
101,3 xlo3
Temperature
Density
("c)
I
IS(
.
-
-
-- -
Table A2 Wroperties of Air at standard
atmospheric pressure
Temperature
Density
("C)
P (kg/m3)
-40
-20
1,514
1,395
0
5
10
15
1,292
1,269
1,247
1,225
20
25
30
40
50
60
70
80
90
100
200
300
400
500
1000
1,204
1,184
1,165
1,127
1,109
1,060
1,029
0,9996
0,9721
0,9461
0,7461
0,6159
0,5243
0,4565
0,2772
Dynamic
Viscosity
P (Pa.s)
Specific heat
ratio
15,7x104
16,3x104
17,lxlod
17,3xl0"
17,6x10"
18,Ox10"
1,401
1,401
1,401
1,401
1,401
1,401
18,2x10"
18,5xl0"
18,6xlo4
18,7x10-~
19,5x10"
19,7xl0'
20,3xlod
20,7xl0"
21,4xlo4
1,401
1,401
1,400
1,400
1,400
1,399
1.399
1,399
1,398
1,397
1,390
1.379
1,368
1,357
1,321
21,7x10'
25,3x10"
29,8xl0"
33,2x10"
36,4x10"
50,4xlod
-
A
I
-
Table A3 The International standard'Atmosphere
Altitude
Pressure
Temperature
Density
(m)
-1000
(Pa)
113,9x103
("C)
21,5
P (kg/m3)
1,35
Dynamic
Viscosity
P (Pas)
18,2x1O4
0
101,3 xlo3
15,O
1,23
18,9x104
1000
89,88
83
1,11
17,6x104
2000
79,50
2,o
1,Ol
17,3x104
3000
70,12 xlo3
-43
0,909
16,9x104
4000
61,66 xlo3
-11,O
0,8 19
16,6x104
5000
54,05 xlo3
-17,5
0,736
16,3x106
6000
47,22 xlo3
-24,O
0,660
16,0x10"
7000
41,ll xlo3
-30,5
0,590
15,6x104
8000
35,65 xlo3
-36,9
0,526
15,2x104
9000
30,80 xlo3
-43,4
0,467
14,9x104
10 000
26,50 xlo3
-49,9
0,4 14
14,6 x10"
15 000
12,l 1 X
-56,5
0,195
14,2 x10"
20 000
55,29 xlo3
-56,s
0,0889
14,2 xl0"
25 000
25,49 xlo3
-51,6
0,0401
14,5 x10"
30 000
11,97 xlo3
-46,6
0,0184
14,8 x10"
40 000
0,287 xlo3
-22,8
0,00400
16,O xlo4
50 000
0,0798 xlo3
-2,5
0,00103
17,O xlo"
60 000
0,0220 XI o3
-26,l
0,000310
15,8 X I 0"
70 000
0,00522 x1 o3
-53,6
0,0000828
14,4 x10"
80 000
0,00105 x103
-743
0,0000185
13,2 x10"
~
O
~
Table A4 Physical properties of common
liquids at specified temperatures
Liquid and temperature
Density
Dynamic
Viscosity
P (kgfm3) P (Pass)
Surface
Tension
o (Nlm)
Benzene 20 'C
879
0,65 x
28,9 x10'~
Ethyl alcohol 20 'C
799
1 , 2 ~o1 - ~
22x10~~
0,96x 1o - ~
26x10~~
Carbon tetrachloride 20 'C 1590
Glycerin 20 'C
1260
620x1o5
63x10'~
Kerosene 20 'C
814
1,9x104
29x 1 o5
Mercury 20 'C
13 550
1,5x10"
480x10"
Meriam red oil 20 'C
Sea water 10 'C
Oils 38 'C
SAE 1OW
SAE 1OW -30
-SAE OW
1
-
-.Iable A5
-
--
.I
- I
---
rn
Ph
rys
at standard atmospheric pressure
(101,3 kPa) and temperature (15'C)
1
Gas
Density
Kinematic' R Gas
Viscosity constant
Cp
Y
(J1kg.K) ( J 4 . K )
P (kg/m3)
v (m2/s)
Air
1,22
14,6x104
287
1004
1.40
Carbon
dioxide
1,85
7,84x104
189
841
1,3
Helium
0,169
114x10"
2077
5187
1,66
Hydrogen
0,085
101x10"
4127
14223
I ,41
Methane
0,678
15,9x104
518
2208
1,31
Nitrogen
1,18
14,5x104
297
1041
1,40
Oxygen
1,35
15,0x10"
260
916
1,40
-
Table A6
Isentropic flow for gas with y = 1,4
(cont)
Table A6
Ma
P~PO
TITO
isentropic
AIA*
0.27
0.9506
0.9856
2.2385
0.28
0.9470
0.9846
2.1656
0.29
0.9433
0.9835
2.0979
0.30
0.9395
0.9823
2.0351
0.31
0.9355
0.9811
1.9765
0.32
0.9315
0.9799
1.9219
0.33
0.9274
0.9787
1.8707
0.34
0.9231
0.9774
1.8229
0.35
0.9188
0.9761
1.7780
0.36
0.9143
0.9747
1.7358
0.37
0.9098
0.9733
1.6961
0.38
0.9052
0.9719
1.6587
0.39
0.9004
0.9705
1.6234
0.40
0,8956
0.9690
1.5901
0.41
0.8907
0.9675
1.5587
0.42
0.8857
0.9659
1.5289
0.43
0.8807
0.9643
1.5007
0.44
0.8755
0.9627
1.4740
0.45
0.8703
0.9611
1.4487
0.46
0.8650
0.9594
1.4246
0.47
0.8596
0.9577
1.4018
0.49
0.8486
0.9542
1.3595
0.51
0.8374
0.9506
1.3212
0.53
0.8259
0.9468
1.2865
0.55
0.8142
0.9430
1.2549
0.57
0.8022
0.9390
1.2263
0.59
0.7901
0.9349
1.2003
0.61
0.7778
0.9307
1.I767
Table A6
Ma
(cont) isentropic
P~PO
TITO
AIA*
1.12
1.14
1.16
0.4568
0.4455
0.4343
0.7994
0.7937
0.7879
1.0113
1 .0153
1.0198
1.18
0.4232
0.7822
1.0248
1.20
1.22
1.24
0.4124
0.4017
0.3912
0.7764
1.0304
0.7706
0.7648
1.0366
1.0432
1.26
0.3809
0.7590
1.0504
1.28
1.30
1.32
1.34
1.36
1.38
1.40
0.3708
0.36091
0.35119
0.34166
0.7532
0.7474
0.7416
1.0581
1.0663
1.0750
0.7358
0.7300
0.7242
0.7184
1.0842
1.0940
1.1042
1.1149
1.42
1.44
1.46
1.48
0.7126
0.7069
0.7011
0.6954
1.1262
1.1379
1.1501
1.1629
1.50
1.52
1.54
1.56
0.30549
0.29693
0.28856
0.28039
0.27240
0.26461
0.25700
0.24957
0.6897
0.6840
0.6783
0.6726
1.1762
1.1899
1.2042
1.2190
1.58
0.24233
0.6670
1.2344
1.60
1.62
1.64
0.23527
0.22839
0.22168
0.6614
0.6558
0.6502
1.2502
1.2666
1.2836
1.66
0.21515
0.6447
1.3010
0.33233
0.32319
0.31424
Table A6
Ma
(cont)
PIPO
isentropic
T ~ o
AIA*
1.68
1.70
0.20879
0.20259
0.6392
1.3190
0.6337
1.3376
1.72
1.74
1.76
1.78
1.80
0.19656
0.19070
0.18499
0.17944
0.17404
0.6283
0.6229
0.6175
0.6121
0.6068
1.3567
1.3764
1.3967
1.4175
1.4390
1.82
1.84
1.86
1.88
0.16879
0.16369
0.15873
0.15392
0.6015
0.5963
0.5910
0.5859
1.4610
1.4836
1.5069
1.5308
1.90
1.92
1.94
1.96
1.98
2.00
2.05
2.10
2.15
2.20
0.14924
0.14470
0.5807
1.5553
0.14028
0.13600
0.13184
0.12780
0.11823
0.10935
0.10113
0.09352
0.5756
0.5705
0.5655
0.5605
0.5556
0.5433
0.5313
0.5196
0.5081
1.5804
1.6062
1.6326
1.6597
1.6875
1.7600
1.8369
1.9185
2.0050
2.25
2.30
0.08648
0.07997
0.4969
0.4859
2.0964
2.1931
2.35
0.07396
0.4752
2.2953
2.40
2.45
2.50
0.06840
0.06327
0.05853
0.4647
0.4544
0.4444
2.4031
2.5168
2.6367
2.55
0.05415
0.4347
2.7630
(cont)
Table A6
Ma
PIPO
isentropic
T ~ o
AIA*
2.60
0.05012
0.4252
2.65
2.70
0.04639
0.04295
0.4159
0.4068
3.0359
3.1830
2.75
0.3980
3.3377
2.80
0.03978
0.03685
0.3894
3.5001
2.85
0.03415
0.3810
3.6707
2.90
2.95
0.03165
0.3729
3.8498
0.02935
0.02722
0.02023
0.01880
0.01748
0.01625
0.01512
0.3649
0.3571
4.0376
4.2346
0.3281
0.3213
5.1210
5.3691
0.3147
0.3082
0.3019
0.2958
5.6286
5.9000
6.1837
6.4801
0.01062
0.00990
0.00924
0.2899
0.2841
0.2784
0.2729
0.2675
0.2623
6.7896
7.1128
7.4501
7.8020
8.1691
8.5517
3.85
0.00863
0.00806
0.2572
0.2522
8.9506
9.3661
3.90
0.00753
0.2474
9.7990
3.95
4.00
0.00704
0.00659
0.00616
0.00577
0.2427
0.2381
10.2496
10.7188
0.2336
0.2293
11.2069
11.7147
3.00
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
4.05
4.10
0.01408
0.01311
0.01221
0.01138
2.8960
(cont)
Table A6
Ma
PIPO
7.20
7.40
0.00020
0.00017
0.0880
0.0837
7.60
0.00014
0.0797
1 18.0799
133.5200
150.5849
7.80
8.00
0.00012
0.00010
0.0759
0.0725
169.4030
190.1094
8.20
0.00009
0.00007
0.0692
0.0662
212.8461
237.7622
0.00006
0.00005
0.00005
0.00004
0.00004
0.00003
0.00003
0.00002
0.0633
0.0607
0.0581
0.0558
0.0536
265.0142
294.7661
327.1893
362.4632
400.7753
0.0515
0.0495
0.0476
442.3210
487.3042
535.9375
8.40
8.60
8.80
9.00
9.20
9.40
9.60
9.80
10.00
Tmo
isentropic
AIA*
Table A7 Normal Shock Tables for a Gas with v=1.4
Ma1
Ma2
pap1
TZT1
pap1
1.OO
1.OOOO
1.OOOO
1.OOOO
1.OOOO
1.OOOO
0.5283
1.01
0.9901
1.0235
1.0066
1.0167
1.0000
0.5221
1.02
0.9805
1.0471
1.0132
1.0334
1.0000
0.5160
1.03
0.9712
1.0711
1.0198
1.0502
1.0000
0.5100
1.04
0.9620
1.0952
1.0263
1.0671
0.9999
0.5039
1.05
0.9531
1. I 196
1.0328
1.0840
0.9999
0.4979
1.06
0.9444
1.1442
1.0393
1.1009
0.9998
0.4920
1.07
0.9360
1.1691
1.0458
1.1179
0.9996
0.4861
1.08
0.9277
1.1941
1.0522
1.1349
0.9994
0.4803
1.09
0.9196
1.2195
1.0586
1.1520
0.9992
0.4746
1.1
0.9118
1.2450
1.0649
1.1691
0.9989
0.4689
1.I
1
0.9041
1.2708
1.0713
1.1862
0.9986
0.4632
1.12
0.8966
1.2968
1.0776
1.2034
0.9982
0.4576
1.I3
0.8892
1.3231
1.0840
1.2206
0.9978
0.4521
1.14
0.8820
1.3495
1.0903
1.2378
0.9973
0.4467
1.15
0.8750
1.3763
1.0966
1.2550
0.9967
0.4413
1.16
0.8682
1.4032
1.1029
1.2723
0.9961
0.4360
1.17
0.8615
1.4304
1.1092
1.2896
0.9953
0.4307
1.I8
0.8549
1.4578
1. I 154
1.3069
0.9946
0.4255
1.I9
0.8485
1.4855
1.I217
1.3243
0.9937
0.4204
1.2
0.8422
1.5133
1.1280
1.3416
0.9928
0.4154
1.21
0.8360
1.5415
1.1343
1.3590
0.9918
0.4104
1.22
0.8300
1.5698
1,1405
1.3764
0.9907
0.4055
p02lp01
pllp02
Table
normal shock
Ma1
T2lT1
~21~1
1.24
1.1531
1.4112
1.25
1.1594
1.4286
1.26
1.1657
1.4460
1.27
1.1720
1.4634
1.28
1.1783
1.4808
1.29
1.I846
1.4983
1.3
1.1909
1.5157
1.31
972
1.I
1.5331
1.32
1.2035
15505
1.33
1.2099
1.5680
1.34
1.2162
1.5854
1.35
1.2226
1.6028
1.36
1.2290
1.6202
1.37
1.2354
1.6376
1.38
1.2418
1.6549
1.39
1.2482
1.6723
1.4
1.2547
1.6897
1.41
1.2612
1.7070
1.42
1.2676
1.7243
1.43
1.2741
1.7416
1.44
1.2807
1.7589
1.45
1.2872
1.7761
1.46
1.2938
1.7934
1.47
1.3003
1.8106
1.48
1.3069
1.a278
Table
normal shock
Ma1
T21T1
1.49
1.5
1.51
1.52
1.53
1.3136
1.3202
1.3269
1.54
1 3470
1.3538
13 0 6
1.3674
1.3742
1.3811
1.3880
1.3949
1.4018
1.4088
1.4158
1.4228
1.4299
1.4369
1.4440
1.4512
1.4583
1.4655
1.4727
1.4800
1.4873
1.4946
1.5019
1.55
1.56
1.57
1.58
1.59
1.6
1.61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.7
1.71
1.72
1.73
1.74
1.75
1.76
1.3336
1.3403
~21~1
1.8449
1.8621
1.8792
1 ,8963
1.9133
1.9303
1.9473
1.9643
1.9812
1.9981
2.0149
2.0317
2.0485
2.0653
2.0820
2.0986
2.1152
2.1318
2.1484
2.1649
2.1813
2.1977
2.2141
2.2304
2.2467
2.2629
2.2791
2.2952
Table
normal shock
TWTl
1.5093
1.5167
1.5241
1.5316
1.5391
1.5466
1.5541
1.5617
1 5693
1.5770
1.5847
1.5924
1.6001
1.6079
1.6157
1.6236
1.6314
1.6394
1.6473
1.6553
1.6633
1.6713
1.6794
1.6875
1.7038
1.7203
1.7369
1.7536
P2/~1
2.3113
2.3273
2.3433
2.3592
2.3751
2.3909
2.4067
2.4224
2.4381
2.4537
2.4693
2.4848
2.5003
2.5157
2.5310
2.5463
2.5616
2.5767
2.5919
2.6069
2.6220
2.6369
2.6518
2.6667
2.6962
2.7255
2.7545
2.7833
Table
(cont) normal shock
~ 2 1 ~ 1 T21T1
4.9783
5.0768
1.7705
5.1762
1.8046
~21~1
2.8119
2.8402
2.8683
5.2765
5.3778
5.4800
5.5831
5.6872
5.7922
1.8219
1 ,8393
1 .a569
1 .a746
1 .a924
1.9104
2.8962
2.9238
2.9512
2.9784
3.0053
3.0319
5.8981
6.0050
1.9285
1.9468
3.0584
3.0845
6.1128
1.9652
3.1105
6.2215
6.3312
6.4418
1.9838
3.1362
3.1617
1.7875
2.0025
2.0213
3.1869
2.0403
2.0595
2.0788
3.2119
3.2367
3.2612
7.2421
7.3602
2.0982
2.1178
2.1375
2.1574
2.1774
3.2855
3.3095
3.3333
3.3569
3.3803
7.4792
7.5991
2.1976
2.2179
7.7200
7.8418
2.2383
2.2590
3.4034
3.4263
3.4490
7.9645
2.2797
6.5533
6.6658
6.7792
6.8935
7.0088
7.1250
3.4714
3.4937
Table
(cont)
normal shock
Table
(cont)
Ma1
pap1
T21T1
3.44
13.6392
3.2337
3.48
3.52
13.9621
14.2888
3.2878
3.3425
3.56
3.6
3.3978
3.4537
3.64
14.6192
14.9533
15.2912
3.68
15.6328
3.72
3.76
3.8
3.84
15.9781
16.3272
16.6800
17.0365
3.5674
3.6252
3.6836
3.7426
3.88
3.92
17.3968
17.7608
3.96
4
18.1285
18.5000
4.04
4.08
4.12
4.16
4.2
4.24
4.28
4.32
18.8752
19.2541
19.6368
20.0232
20.4133
20.8072
21.2048
21.6061
4.1096
4.1729
4.2368
4.3014
4.3666
4.4324
4.36
4.4
4.44
22.0112
22.4200
22.8325
4.6334
4.7017
4.7706
4.48
23.2488
4.8401
4.52
23.6688
4.9102
normal shock
3.5103
3.8022
3.8625
3.9233
3.9848
4.0469
4.4988
4.5658
~ 2 1 ~ 1
4.2179
4.2467
4.2749
4.3026
4.3296
4.3561
4.3821
4.4075
4.4324
4.4568
4.4807
4.5041
4.5270
4.5494
4.5714
4.5930
4.6141
4.6348
4.6550
4.6749
4.6944
4.7135
4.7322
4.7505
4.7685
4.7861
4.8034
4.8203
Table
normal
shock
Ma1
T2lTl
~2/Pl
4.56
4.9810
4.6
5.0523
4.8369
4.8532
4.64
5.1243
4.8692
4.68
4.72
5.1969
5.2701
4.8849
4.9002
4.76
5.3440
4.9153
4.9301
4.8
5.4184
4.84
4.88
4.92
4.96
5
5.4935
5.5692
5.6455
5.7224
4.9446
5.8000
5.0000
5.1
5.2
5.3
5.4
5.9966
6.1971
5.0326
5.5
6.8218
5.1489
5.6
5.7
5.8
7.0378
7.2577
5.1749
5.1998
7.4814
7.7091
7.9406
5.2236
5.2464
5.2683
6.1
8.1760
5.2893
6.2
6.3
8.4153
8.6584
5.3094
5.3287
6.4
6.5
8.9055
5.3473
5.3651
5.9
6
6.6
6.4014
6.6097
9.1564
9.4113
4.9589
4.9728
4.9865
5.0637
5.0934
5.1218
5.3822
Table
(cont)
normal shock
Ma1
T21T1
6.7
6.8
9.6700
9.9326
6.9
7
10.1990
7.1
10.7436
11.0218
11.3038
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9
9.1
9.2
9.3
9.4
10.4694
1 1 ,5897
1 1.8795
12.1732
12.4707
12.7722
13.0775
13.3867
13.6998
14.0168
14.3377
14.6625
14.9911
15.3237
15.6601
16.0004
16.3446
16.6927
17.0447
17.4006
17.7603
18.1240
~21~1
5.3987
5.4145
5.4298
5.4444
5.4586
5.4722
5.4853
5.4980
5.5102
5.5220
5.5334
5.5443
5.5550
5.5652
5.5751
5.5847
5.5940
5.6030
5.6117
5.6201
5.6282
5.6361
5.6437
5.6512
5.6584
5.6653
5.6721
5.6787
Table
A7
(cant) normal shock
Table A8
Ma
-
TIT*
Fanno flow friction flow for gases with y = 1.4
VW
4fL*ID
pOlpO*
@P*
w
0
00
109.5434
57.8738
0.01 10
7134.4045
1.1999
54.7701
28.9421
0.0219
1778.4499
1.1998
36.5116
19.3005
0.0329
787.0814
0.04
1.1996
27.3817
14.4815
0.0438
440.3522
0.05
1.1994
21,9034
11.5914
0.0548
280.0203
0.06
1.1991
18.2508
9.6659
0.0657
193.0311
0.07
1.1988
15.6416
8.2915
0.0766
140.6550
0.08
1.1985
13.6843
7.2616
0.0876
106.7182
0.09
1.1981
12.1618
6.4613
0.0985
83.4961
0
1.2
m
0.01
1.2000
0.02
0.03
0.1
1.1976
10.9435
5.8218
0.1094
66.9216
0.11
1.I971
9.9466
5.2992
0.1204
54.6879
0.12
1.1966
9.1156
4.8643
0.1313
45.4080
38.2070
0.13
1.1960
8.4123
4.4969
0.1422
0.14
1.1953
7.8093
4.1824
0.1531
32.5113
0.1639
27.9320
0.15
1.I946
7.2866
3.9103
0.16
1.1939
6.8291
3.6727
0.1748
24.1978
21.1152
0.17
1.1931
6.4253
3.4635
0.1857
0.18
1.1923
6.0662
3.2779
0.1965
18.5427
0.19
1.1914
5.7448
3.1123
0.2074
16.3752
0.2
1.1905
5.4554
2.9635
0.2182
14.5333
0.21
1.1895
5.1936
2.8293
0.2290
12.9560
0.22
1.1885
4.9554
2.7076
0.2398
11.5961
0.23
1.1874
4.7378
2.5968
0.2506
10.4161
0.24
1.1863
4.5383
2.4956
0.2614
9.3865
0.25
1.1852
4.3546
2.4027
0.2722
8.4834
0.26
1.I840
4.1851
2.3173
0.2829
7.6876
0.27
1.1828
4.0279
2.2385
0.2936
6.9832
0.28
1.1815
3.8820
2.1656
0.3043
6.3572
0.29
1.1801
3.7460
2.0979
0.3150
5.7989
h
Table AB(cont.)
s Fanno
with
friction
PIP*
vw
3.6191
3.5002
3.3887
3.2840
3.1853
3.0922
3.0042
2.9209
2.8420
2.7671
2.6958
2.6280
2.5634
2.5017
2.4428
2.3865
2.3326
2.2809
2.2313
2.1838
2.1381
2.0942
2.0519
2.0112
1.9719
1.9341
1.8975
1 .a623
1 .a282
1.7952
0.3257
0.3364
0.3470
0.3576
0.3682
0.3788
0.3893
0.3999
0.4104
0.4209
0.4313
0.4418
0.4522
0.4626
0.4729
0.4833
0.4936
0.5038
0.5141
0.5243
0.5345
0.5447
0.5548
0.5649
0.5750
0.5851
0.5951
0.6051
0.6150
0.6249
-
Table 'A8(cont.)
Fanno
TIT.
plp*
-
Ma
=
+ith
friction
y = 1,4
L
pOIpO*
0.6348
0.6447
0.6545
0.6643
0.6740
0.6837
0.6934
0.7031
0.7127
0.7223
0.7318
0.7413
0.7508
0.7602
0.7696
0.7789
0.7883
0.7975
0.8068
0.8160
0.8251
0.8343
0.8433
0.8524
0.8614
0.8704
0.8793
0.8882
0.8970
0.9058
0.4908
0.4527
0.4172
0.3841
0.3533
0.3246
0.2979
0.2730
0.2498
0.2282
0.2081
0.1895
0.1721
0.1561
0.1411
0.1273
0.1145
0.1026
0.0917
0.0816
0.0723
0.0638
0.0559
0.0488
0.0423
0.0363
0.0310
0.0261
0.0218
0.0179
9
m
.
A
.
-
Table A8(cont.)
-
Fanno m
with
friction
Ma
Tn"
PIP*
pOIpO*
VW
0.9
1.0327
1.1291
1.0089
0.9146
0.91
1.0295
1.1150
1.0071
0.9233
0.92
1.0263
1.1011
1.0056
0.9320
0.93
1.0230
1.0876
1.0043
0.9407
0.94
1.0198
1.0743
1.0031
0.9493
0.95
1.0165
1.0613
1.0021
0.9578
0.9663
0.96
1.0132
1.0485
1.0014
0.97
1.0099
1.0360
1.0008
0.9748
0.98
1.0066
1.0238
1.0003
0.9833
0.99
I.0033
1.0118
1.0001
0.9916
1
1.oooo
1.moo
1.0000
1.oooo
1.01
0.9967
0.9884
1.0001
1.0083
1.02
0.9933
0.9771
1.0003
1.0166
1.03
0.9900
0.9660
1.0007
1.0248
1.04
0.9866
0.9551
1.0013
1.0330
1.05
0.9832
0.9443
1.0020
1.0411
1.06
0.9798
0.9338
1.0029
1.0492
1.07
0.9764
0.9235
1.0039
1.0573
1.08
0.9730
0.9133
1.0051
1.0653
1.0733
1.0812
I.09
0.9696
0.9034
1.0064
I. I
0.9662
0.8936
1.0079
1.12
0.9593
0.8745
1.0113
1.0970
1.14
0.9524
0.8561
1,0153
1.1126
1.16
0.9455
0.8383
1.0198
1.1280
1.18
0.9386
0.8210
1.0248
1.1432
1.2
0.9317
0.8044
1.0304
1.1583
1.22
0.9247
0.7882
1.0366
1.1732
1.24
0.9178
0.7726
1.0432
1.1879
1.2025
1.2169
1.26
0.9108
0.7574
1.0504
1.28
0.9038
0.7427
1.0581
- A8(cont.)--
- -
Fanno 'with
friction
-
y = I,4
plp*
pOIpO*
V W
4fL*ID
0.8969
0.7285
1.0663
1.2311
0.0648
Tn"
1.32
0.8899
0.7147
1.0750
1.2452
0.0716
1.34
0.8829
0.7012
1.0842
1.2591
0.0785
1.36
0.8760
0.6882
1.0940
1.2729
0.0855
1.38
0.8690
0.6755
1.1042
1.2864
0.0926
1.4
0.8621
0.6632
1. I 149
1.2999
0.0997
1.42
0.8551
0.6512
1.1262
1.3131
0.1069
1.44
0.8482
0.6396
1.1379
1.3262
0.1142
1.46
0.8413
0.6282
1.1501
1.3392
0.1215
1.48
0.8344
0.6172
1.1629
1.3520
0.1288
1.5
0.8276
0.6065
1.1762
1.3646
0.1361
1.52
0.8207
0.5960
1.1899
1.3770
0.1433
1.54
0.8139
0.5858
1.2042
1.3894
0.1506
1.56
0.8071
0.5759
1.2190
1.4015
0.1579
1.58
0.8004
0.5662
1.2344
1.4135
0.1651
1.6
1.62
0.7937
0.7869
0.5568
0.5476
1.2502
1.2666
1.4254
1.4371
0.1724
0.1795
1.64
0.7803
0.5386
1.2836
1.4487
0.1867
1.66
0.7736
0.5299
1.3010
1.4601
0.1938
1.68
0.7670
0.5213
1.3190
1.4713
0.2008
1.7
0.7605
0.5130
1.3376
1.4825
0.2078
1.72
0.7539
0.5048
1.3567
1.4935
0.2147
1.74
0.7474
0.4969
1.3764
1.5043
0.2216
1.76
0.7410
0.4891
1.3967
1.5150
0.2284
1.78
0.7345
0.4815
1.4175
1.5256
0.2352
1.8
0.7282
0.4741
1.4390
1.5360
0.2419
1.82
0.7218
0.4668
1.4610
1.5463
0.2485
1.84
0.7155
0.4597
1.4836
1.5564
0.2551
1.86
0.7093
0.4528
1.5069
1,5664
0.2616
1.88
0.7030
0.4460
1.5308
1.5763
0.2680
Fanno
with
friction
PIP*
pOIpO*
VN"
0.4394
1.5553
1.5861
0.4329
1,5804
1.5957
0.4265
1.6062
1.6052
0.4203
I,6326
1.6146
0.4142
1.6597
1.6239
0.4082
1.6875
1.6330
0.3939
1.7600
1.6553
0.3802
1,8369
1.6769
0.3673
1.9185
1.6977
0.3549
2.0050
1.7179
0.3432
2.0964
1.7374
0.3320
2.1931
1.7563
0.3213
2.2953
1.7745
0.3111
2.4031
1.7922
0.3014
2.5168
1,8092
0.2921
2.6367
1.8257
0.2832
2.7630
1.8417
0.2747
2.8960
1.8571
0.2666
3.0359
1.8721
0.2588
3.1830
1.8865
0.2513
3.3377
1.go05
0.2441
3.5001
1.9140
0.2373
3.6707
1.9271
0.2307
3.8498
1.9398
0.2243
4.0376
1.9521
0.2182
4.2346
1.9640
0.1961
5.1210
2.0079
0.1770
6.1837
2.0466
0.1606
7.4501
2.0808
0.1462
8.9506
2.1111
Table A8(cont.)
Ma
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Fanno
TIT*
PIP*
0.2857
0.2376
0.2000
0.1702
0.1463
0.1270
0.1111
0.0980
0.0870
0.0777
0.0698
0.0630
0.0571
0.1336
0.1083
0.0894
0.0750
0.0638
0.0548
0.0476
0.0417
0.0369
0.0328
0.0293
0.0264
0.0239
with
pOIpO*
10.719
16.562
25.000
36.869
53.180
75.134
104.14
141.84
190.11
251.09
327.19
421.13
535.94
friction
VN"
2.1381
2.1936
2.2361
2.2691
2.2953
2.3163
2.3333
2.3474
2.3591
2.3689
2.3772
2.3843
2.3905
-
Table A9 Rayleiah flow frictionless with heat transfer v = 1.4
Ma
0
0.01
TIT"
0.0000
0.0006
TOITO*
0.0000
0.0005
plp*
2.4000
2.3997
pOIpO*
VN"
1.2679
1.2678
0.0000
0.0002
Table A9 (cont.) frictionless
TIT*
TOITO*
Ma
with heat
transfer
poipo*
1.2177
0.25
0.3044
0.2568
PIP*
2.2069
0.26
0.3250
0.2745
2.1925
1.2140
0.27
0.3457
0.2923
2.1 777
1.2102
0.28
0.3667
0.3104
2.1626
1.2064
0.29
0.3877
0.3285
2.1472
1.2025
0.3
0.4089
0.3469
2.1314
1.I985
0.31
0.4300
0.3653
2.1 154
1.1945
0.32
0.4512
0.3837
2.0991
1.1904
0.33
0.4723
0.4021
2.0825
1.A863
0.34
0.4933
0.4206
2.0657
1.1822
0.35
0.5141
0.4389
2.0487
1.1779
0.36
0.5348
0.4572
2.0314
1.1737
0.37
0.5553
0.4754
2.0140
1.1695
0.38
0.5755
0.4935
1.9964
1.1652
0.39
0.5955
0.51 13
1.9787
1.1609
0.4
0.6151
0.5290
1.9608
1.I566
0.41
0.6345
0.5465
1.9428
1.1523
0.42
0.6535
0.5638
1.9247
1.I480
0.43
0.6721
0.5808
1.go65
1.1437
1.8882
1.I394
1.8699
1.1351
1.8515
1.I308
1.8331
1.1266
1.8147
1.I224
1.7962
1.1182
Table A9 (cont.) frictionless
with heat
transfer
pOIpO*
Ma
TIT*
TOITO*
0.5
0.7901
0.6914
PIP*
1.7778
0.51
0.8051
0.7058
1.7594
1.lo99
0.52
0.8196
0.7199
1.7409
1.1059
0.53
0.8335
0.7336
1.7226
1.1019
0.54
0.8469
0.7470
1.7043
1.0979
0.55
0.8599
0.7599
1.6860
1.0940
0.56
0.8723
0.7725
1.6678
1.0901
0.57
0.8842
0.7847
1.6496
1.0863
0.58
0.8955
0.7965
1.6316
1.0826
0.59
0.9064
0.8079
1.6136
1.0789
0.6
0.9167
0.8189
1.5957
1.0753
0.61
0.9265
0.8296
1.5780
1.0717
0.62
0.9358
0.8398
1.5603
1.0682
0.63
0.9447
0.8497
15428
1.0648
0.64
0.9530
0.8592
1.5253
1.0615
1.1141
-- -
-
1 J".'
Table A9 (cont.) frictionless
TIT*
TOITO*
0.9401
0.9455
0.9505
0.9553
0.9598
0.9639
0.9679
0.9715
0.9749
0.9781
0.9810
0.9836
0.9861
0.9883
0.9903
0.9921
0.9937
0.9951
0.9963
0.9973
0.9981
0.9988
0.9993
0.9997
0.9999
with heat
transfer
Table A9 (cont.) frictionless
with heal
transfer
Ma
TIT
TOITO"
PIP*
pOIpO*
1
1.oooo
1.oooo
1.oooo
1.oooo
1.02
0.9930
0.9997
0.9770
1.0002
1.04
0.9855
0.9989
0.9546
1.0008
1.06
0.9776
0.9977
0.9327
1.0017
1.08
0.9691
0.9960
0.91 15
1.0031
1.1
0.9603
0.9939
0.8909
1.0049
1.12
0.9512
0.991 5
0.8708
1.0070
1.14
0.9417
0.9887
0.8512
1.0095
1.16
0.9320
0.9856
0.8322
1.0124
1.18
0.9220
0.9823
0.8137
1.0157
1.2
0.9118
0.9787
0.7958
1.0194
1.22
0.901 5
0.9749
0.7783
1.0235
1.24
0.891 1
0.9709
0.7613
1.0279
1.26
0.8805
0.9668
0.7447
1.0328
1.28
0.8699
0.9624
0.7287
1.0380
1.3
0.8592
0.9580
0.7130
1.0437
1.32
0.8484
0.9534
0.6978
1.0497
1.34
0.8377
0.9487
0.6830
1.0561
1.36
0.8269
0.9440
0.6686
1.0629
1.38
0.8161
0.9391
0.6546
1.0701
1.4
0.8054
0.9343
0.641 0
1.0777
1.42
0.7947
0.9293
0.6278
1.0856
1.44
0.7840
0.9243
0.6149
1.0940
1.46
0.7735
0.9193
0.6024
1.lo28
1.48
0.7629
0.9143
0.5902
1.1120
I!
I
I
j
I
1
i
I
I
I
i
!
-
Table A9 (cont.) frictionless
with heat
transfer
PIP*
0.5783
pOIpO*
1.1215
Ma
1.5
0.7525
TORO*
0.9093
1.52
1.54
0.7422
0.7319
0.9042
0.8992
0.5668
1.1315
0.5555
1.1419
1.56
1.58
0.7217
0.7117
0.8942
0.8892
0.5446
1.1527
0.5339
1.1640
1.6
1.62
0.7017
0.691 9
0.8842
0.8792
0.5236
1.64
0.6822
0.8743
0.5036
1.66
0.6726
0.8694
0.4940
1.68
0.6631
0.8645
0.4847
1.7
0.6538
0.8597
0.4756
1.72
0.6445
0.8549
0.4668
1.74
0.6355
0.8502
0.4581
1.76
0.6265
0.8455
0.4497
1.78
0.6176
0.8409
0.4415
1.8
0.6089
0.8363
0.4335
1.82
0.6004
0.8317
0.4257
1.84
0.5919
0.8273
0.4181
1.86
0.5836
0.8228
0.4107
1.88
0.5754
0.8185
0.4035
1.9
0.5673
0.8141
0.3964
1.92
0.5594
0.8099
0.3895
1.94
0.5516
0.8057
0.3828
1.96
0.5439
0.8015
0.3763
2
0.5289
0.7934
0.3636
TTT*
0.5135
Table A9 (cont.) frictionless
with heat
transfer
pOlpO*
Ma
TIT"
TOITO*
2.05
0.5109
0.7835
PIP*
0.3487
2.1
0.4936
0.7741
0.3345
1.6162
2.15
0.4770
0.7649
0.3212
1.6780
2.2
0.4611
0.7561
0.3086
1.7434
2.25
0.4458
0.7477
0.2968
1.8128
2.3
0.4312
0.7395
0.2855
1.8860
2.35
0.4172
0.7317
0.2749
1.9634
2.4
0.4038
0.7242
0.2648
20451
2.45
0.3910
0.7170
0.2552
2.1311
2.5
0.3787
0.7101
0.2462
2.221 8
2.55
0.3669
0.7034
0.2375
2.3173
2.6
0.3556
0.6970
0.2294
2.4177
2.65
0.3448
0.6908
0.2216
2.5233
2.7
0.3344
0.6849
0.2142
2.6343
2.75
0.3244
0.6793
0.2071
2.7508
2.8
0.3149
0.6738
0.2004
2.8731
2.85
0.3057
0.6685
0.1940
3.0014
2.9
0.2969
0.6635
0.1 879
3.1359
2.95
0.2884
0.6586
0.1820
3.2768
3
0.2803
0.6540
0.1765
3.4245
3.2
0.2508
0.6370
0.1 565
4.0871
3.4
0.2255
0.6224
0.1397
4.8783
3.6
0.2037
0.6097
0.1 254
5.8173
3.8
0.1848
0.5987
0.1 131
6.9256
4
0.1683
0.5891
0.1026
8.2268
1.5579
Table A9 (cont.) frictionless
with heat
transfer
pOlpO*
4.2
TIT"
0.1539
TOITO*
0.5807
PIP*
0.0934
9.7473
4.4
0.1412
0.5732
0.0854
11.5155
4.6
0.1300
0.5666
0.0784
13.5629
4.8
0.1200
0.5608
0.0722
15.9234
5
0.1111
0.5556
0.0667
18.6339
5.2
0.1032
0.5509
0.0618
21.7344
5.4
0.0960
0.5467
0.0574
25.2679
5.6
0.0896
0.5429
0.0534
29.2806
5.8
0.0838
0.5394
0.0499
33.8223
6
0.0785
0.5363
0.0467
38.9459
6.2
0.0737
0.5335
0.0438
44.7084
6.4
0.0693
0.5309
0.041 1
51.1700
6.6
0.0653
0.5285
0.0387
58.3953
6.8
0.0616
0.5264
0.0365
66.4524
7
0.0583
0.5244
0.0345
75.4138
7.2
0.0552
0.5225
0.0326
85.3562
7.4
0.0523
0.5208
0.0309
96.3605
7.6
0.0496
0.5193
0.0293
108.5124
7.8
0.0472
0.5178
0.0278
121.go17
8
0.0449
0.5165
0.0265
136.6235
8.2
0.0428
0.5152
0.0252
152.7774
8.4
0.0408
0.5140
0.0241
170.4680
8.6
0.0390
0.51 30
0.0230
189.8050
8.8
0.0373
0.51 19
0.0219
210.9036
9
0.0356
0.51 10
0.0210
233.8840
Ma
Table A9 (cont.) frictionless
Ma
TIT"
9.2
with heat
transfer
plp*
pOIpO*
VN*
0.0341
TOITO*
0.5101
0.0201
258.8719
1.6999
9.4
0.0327
0.5092
0.0192
285.9989
1.7005
9.6
0.0314
0.5085
0.0185
315.4021
1.7011
9.8
0.0301
0.5077
0.0177
347.2245
1.7016
10
0.0290
0.5070
0.0170
381.6149
1.7021