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T, C
°
!, kg/m3
", N & s/m2
#, m2/s
T, F
°
!, slug/ft3
", lb & s/ft2
#, ft2/s
0
10
20
30
40
50
60
70
80
90
100
1000
1000
998
996
992
988
983
978
972
965
958
1.788 E"3
1.307 E"3
1.003 E"3
0.799 E"3
0.657 E"3
0.548 E"3
0.467 E"3
0.405 E"3
0.355 E"3
0.316 E"3
0.283 E"3
1.788 E"6
1.307 E"6
1.005 E"6
0.802 E"6
0.662 E"6
0.555 E"6
0.475 E"6
0.414 E"6
0.365 E"6
0.327 E"6
0.295 E"6
32
50
68
86
104
122
140
158
176
194
212
1.940
1.940
1.937
1.932
1.925
1.917
1.908
1.897
1.886
1.873
1.859
3.73 E"5
2.73 E"5
2.09 E"5
1.67 E"5
1.37 E"5
1.14 E"5
0.975 E"5
0.846 E"5
0.741 E"5
0.660 E"5
0.591 E"5
1.925 E"5
1.407 E"5
1.082 E"5
0.864 E"5
0.713 E"5
0.597 E"5
0.511 E"5
0.446 E"5
0.393 E"5
0.352 E"5
0.318 E"5
Appendix A
Table A.1 Viscosity and Density of
Water at 1 atm
Suggested curve fits for water in the range 0 ! T ! 100°C:
!(kg/m3) ! 1000 " 0.0178 " T°C " 4°C " 1.7 # 0.2%
ln
z$
Table A.2 Viscosity and Density of
Air at 1 atm
"
! "1.704 " 5.306z % 7.003z2
"0
273 K
TK
"0 $ 1.788 E"3 kg/(m ! s)
T, C
°
!, kg/m3
", N & s/m2
#, m2/s
T, F
°
!, slug/ft3
", lb & s/ft2
#, ft2/s
"40
0
20
50
100
150
200
250
300
400
500
1.52
1.29
1.20
1.09
0.946
0.835
0.746
0.675
0.616
0.525
0.457
1.51 E"5
1.71 E"5
1.80 E"5
1.95 E"5
2.17 E"5
2.38 E"5
2.57 E"5
2.75 E"5
2.93 E"5
3.25 E"5
3.55 E"5
0.99 E"5
1.33 E"5
1.50 E"5
1.79 E"5
2.30 E"5
2.85 E"5
3.45 E"5
4.08 E"5
4.75 E"5
6.20 E"5
7.77 E"5
"40
32
68
122
212
302
392
482
572
752
932
2.94 E"3
2.51 E"3
2.34 E"3
2.12 E"3
1.84 E"3
1.62 E"3
1.45 E"3
1.31 E"3
1.20 E"3
1.02 E"3
0.89 E"3
3.16 E"7
3.58 E"7
3.76 E"7
4.08 E"7
4.54 E"7
4.97 E"7
5.37 E"7
5.75 E"7
6.11 E"7
6.79 E"7
7.41 E"7
1.07 E"4
1.43 E"4
1.61 E"4
1.93 E"4
2.47 E"4
3.07 E"4
3.71 E"4
4.39 E"4
5.12 E"4
6.67 E"4
8.37 E"4
Suggested curve fits for air:
!$
Power law:
Sutherland law:
p
RT
"
T 0.7
!a b
"0
T0
Rair ! 287 J/(kg ! K)
T 3/2 T0 % S
"
!a b a
b
"0
T0
T%S
Sair ! 110.4 K
with T0 $ 273 K, "0 $ 1.71 E"5 kg/(m & s), and T in kelvins.
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Physical Properties of Fluids 827
Table A.3 Properties of Common
Liquids at 1 atm and 20°C (68°F)
Liquid
Ammonia
Benzene
Carbon tetrachloride
Ethanol
Ethylene glycol
Freon 12
Gasoline
Glycerin
Kerosene
Mercury
Methanol
SAE 10W oil
SAE 10W30 oil
SAE 30W oil
SAE 50W oil
Water
Seawater (30 ‰)
!, kg/m3 ", kg/(m ! s)
", N/m*
p# , N/m2
13,608
13,881
31590
13,789
31117
31327
13,680
31260
13,804
13,550
13,791
13,870
13,876
13,891
13,902
13,998
31025
2.13 E!2
2.88 E!2
2.70 E!2
2.28 E!2
4.84 E!2
—
2.16 E!2
6.33 E!2
2.83 E!2
4.84 E!1
2.25 E!2
3.63 E!2
—
3.53 E!2
—
7.28 E!2
7.28 E!2
9.10 E"5
1.01 E"4
1.20 E"4
5.73 E"3
1.23 E"1
—
5.51 E"4
1.43 E!2
3.11 E"3
1.13 E!3
1.34 E"4
—
—
—
—
2.34 E"3
2.34 E"3
2.20 E!4
6.51 E!4
9.67 E!4
1.20 E!3
2.14 E!2
2.62 E!4
2.92 E!4
1.49
1.92 E!3
1.56 E!3
5.98 E!4
1.04 E!1‡
1.7 E!1‡
2.9 E!1‡
8.6 E!1‡
1.00 E!3
1.07 E!3
Bulk modulus K, Viscosity
N/m2
parameter C†
1.82 E"9
1.47 E"9
1.32 E"9
1.09 E"9
3.05 E"9
7.95 E"8
1.3 E"90
4.35 E"90
1.41 E"90
2.85 E"10
1.03 E"90
1.31 E"90
—
1.38 E"90
—
2.19 E"90
2.33 E"90
1.05
4.34
4.45
5.72
11.7
1.76
3.68
28.0
5.56
1.07
4.63
15.7
14.0
18.3
20.2
Table A.1
7.28
*
In contact with air.
The viscosity–temperature variation of these liquids may be fitted to the empirical expression
†
293 K
!
! 1b d
! exp c C a
!20%C
TK
with accuracy of #6 percent in the range 0 $ T $ 100°C.
‡
Representative values. The SAE oil classifications allow a viscosity variation of up to #50 percent, especially at lower
temperatures.
Table A.4 Properties of Common
Gases at 1 atm and 20°C (68°F)
Gas
Molecular
weight
R, m2/(s2 ! K)
!g, N/m3
", N ! s/m2
Specifi
c-heat
ratio
Power-law
exponent n*
H2
He
H2O
Ar
Dry air
CO2
CO
N2
O2
NO
N2O
Cl2
CH4
2.016
4.003
18.020
39.944
28.960
44.010
28.010
28.020
32.000
30.010
44.020
70.910
16.040
4124
2077
0461
0208
0287
0189
0297
0297
0260
0277
0189
0117
0518
00.822
01.630
07.350
16.300
11.800
17.900
11.400
11.400
13.100
12.100
17.900
28.900
06.540
9.05 E!6
1.97 E!5
1.02 E!5
2.24 E!5
1.80 E!5
1.48 E!5
1.82 E!5
1.76 E!5
2.00 E!5
1.90 E!5
1.45 E!5
1.03 E!5
1.34 E!5
1.41
1.66
1.33
1.67
1.40
1.30
1.40
1.40
1.40
1.40
1.31
1.34
1.32
0.68
0.67
1.15
0.72
0.67
0.79
0.71
0.67
0.69
0.78
0.89
1.00
0.87
*
The power-law curve fit, Eq. (1.27), !/!293K ! (T/293)n, fits these gases to within #4 percent in the range 250 $ T $
1000 K. The temperature must be in kelvins.
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Appendix A
Table A.5 Surface
Tension, Vapor
Pressure, and Sound
Speed of Water
T, C
°
!, N/m
0
10
20
30
40
50
60
70
80
90
100
0.0756
0.0742
0.0728
0.0712
0.0696
0.0679
0.0662
0.0644
0.0626
0.0608
0.0589
120
140
160
180
200
220
240
260
280
300
320
340
360
374*
0.0550
0.0509
0.0466
0.0422
0.0377
0.0331
0.0284
0.0237
0.0190
0.0144
0.0099
0.0056
0.0019
0.0*19
*Critical point.
p! , kPa
0.611
1.227
2.337
4.242
7.375
12.34
19.92
31.16
47.35
70.11
101.3
198.5
361.3
617.8
1002
1554
2318
3344
4688
6412
8581
11,274
14,586
18,651
22,090*
a, m/s
1402
1447
1482
1509
1529
1542
1551
1553
1554
1550
1543
1518
1483
1440
1389
1334
1268
1192
1110
1022
920
800
630
370
0*
Table A.6
Properties of
the Standard
Atmosphere
z, m
T, K
p, Pa
", kg/m3
a, m/s
!500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10,000
10,500
11,000
11,500
12,000
12,500
13,000
13,500
14,000
14,500
15,000
15,500
16,000
16,500
17,000
17,500
18,000
18,500
19,000
19,500
20,000
22,000
24,000
26,000
28,000
30,000
40,000
50,000
60,000
70,000
291.41
288.16
284.91
281.66
278.41
275.16
271.91
268.66
265.41
262.16
258.91
255.66
252.41
249.16
245.91
242.66
239.41
236.16
232.91
229.66
226.41
223.16
219.91
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
216.66
218.60
220.60
222.50
224.50
226.50
250.40
270.70
255.70
219.70
107,508
101,350
095,480
089,889
084,565
079,500
074,684
070,107
065,759
061,633
057,718
054,008
050,493
047,166
044,018
041,043
038,233
035,581
033,080
030,723
028,504
026,416
024,455
022,612
020,897
019,312
017,847
016,494
015,243
014,087
013,018
012,031
011,118
010,275
009496
008775
008110
007495
006926
006401
005915
005467
004048
002972
002189
001616
001197
000,287
000,080
000,022
000,006
1.2854
1.2255
1.1677
1.1120
1.0583
1.0067
0.9570
0.9092
0.8633
0.8191
0.7768
0.7361
0.6970
0.6596
0.6237
0.5893
0.5564
0.5250
0.4949
0.4661
0.4387
0.4125
0.3875
0.3637
0.3361
0.3106
0.2870
0.2652
0.2451
0.2265
0.2094
0.1935
0.1788
0.1652
0.1527
0.1411
0.1304
0.1205
0.1114
0.1029
0.0951
0.0879
0.0645
0.0469
0.0343
0.0251
0.0184
0.0040
0.0010
0.0003
0.0001
342.2
340.3
338.4
336.5
334.5
332.6
330.6
328.6
326.6
324.6
322.6
320.6
318.5
316.5
314.4
312.3
310.2
308.1
306.0
303.8
301.7
299.5
297.3
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
295.1
296.4
297.8
299.1
300.4
301.7
317.2
329.9
320.6
297.2
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Appendix B
Compressible Flow Tables
Table B.1
Isentropic Flow
of a Perfect Gas,
k " 1.4
Ma
p/p0
!/!0
T/T0
A/A*
Ma
p/p0
!/!0
T/T0
A/A*
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
1.0000
0.9930
0.9725
0.9395
0.8956
0.8430
0.7840
0.7209
0.6560
0.5913
0.5283
0.4684
0.4124
0.3609
0.3142
0.2724
0.2353
0.2026
0.1740
0.1492
0.1278
1.0000
0.9950
0.9803
0.9564
0.9243
0.8852
0.8405
0.7916
0.7400
0.6870
0.6339
0.5817
0.5311
0.4829
0.4374
0.3950
0.3557
0.3197
0.2868
0.2570
0.2300
1.0000
0.9980
0.9921
0.9823
0.9690
0.9524
0.9328
0.9107
0.8865
0.8606
0.8333
0.8052
0.7764
0.7474
0.7184
0.6897
0.6614
0.6337
0.6068
0.5807
0.5556
!
5.8218
2.9635
2.0351
1.5901
1.3398
1.1882
1.0944
1.0382
1.0089
1.0000
1.0079
1.0304
1.0663
1.1149
1.1762
1.2502
1.3376
1.4390
1.5553
1.6875
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
0.1094
0.0935
0.0800
0.0684
0.0585
0.0501
0.0430
0.0368
0.0317
0.0272
0.0234
0.0202
0.0175
0.0151
0.0131
0.0114
0.0099
0.0086
0.0075
0.0066
0.2058
0.1841
0.1646
0.1472
0.1317
0.1179
0.1056
0.0946
0.0849
0.0762
0.0685
0.0617
0.0555
0.0501
0.0452
0.0409
0.0370
0.0335
0.0304
0.0277
0.5313
0.5081
0.4859
0.4647
0.4444
0.4252
0.4068
0.3894
0.3729
0.3571
0.3422
0.3281
0.3147
0.3019
0.2899
0.2784
0.2675
0.2572
0.2474
0.2381
1.8369
2.0050
2.1931
2.4031
2.6367
2.8960
3.1830
3.5001
3.8498
4.2346
4.6573
5.1210
5.6286
6.1837
6.7896
7.4501
8.1691
8.9506
9.7990
10.7188
829