cen72367_appx1.qxd 11/17/04 4:34 PM Page 885
APPENDIX
P R O P E R T Y TA B L E S A N D
CHARTS (SI UNITS)*
1
TABLE A–1
Molar Mass, Gas Constant, and Ideal-Gas Specfic Heats
of Some Substances 886
TABLE A–2
Boiling and Freezing Point
Properties 887
TABLE A–3
Properties of Saturated Water 888
TABLE A–4
Properties of Saturated Refrigerant-134a 889
TABLE A–5
Properties of Saturated Ammonia 890
TABLE A–6
Properties of Saturated Propane 891
TABLE A–7
Properties of Liquids 892
TABLE A–8
Properties of Liquid Metals 893
TABLE A–9
Properties of Air at 1 atm Pressure 894
TABLE A–10 Properties of Gases at 1 atm Pressure 895
TABLE A–11 Properties of the Atmosphere at High Altitude 897
FIGURE A–12 The Moody Chart for the Friction Factor for Fully
Developed Flow in Circular Pipes 898
TABLE A–13 One-dimensional isentropic compressible flow functions for
an ideal gas with k 1.4 899
TABLE A–14 One-dimensional normal shock functions for an ideal gas
with k 1.4 900
TABLE A–15 Rayleigh flow functions for an ideal gas with k 1.4 901
TABLE A–16 Fanno flow functions for an ideal gas with k 1.4 902
* Most properties in the tables are obtained from the property database of EES, and the
original sources are listed under the tables. Properties are often listed to more significant
digits than the claimed accuracy for the purpose of minimizing accumulated round-off error
in hand calculations and ensuring a close match with the results obtained with EES.
885
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886
FLUID MECHANICS
TABLE A–1
Molar mass, gas constant, and ideal-gas specfic heats of some substances
Substance
Air
Ammonia, NH3
Argon, Ar
Bromine, Br2
Isobutane, C4H10
n-Butane, C4H10
Carbon dioxide, CO2
Carbon monoxide, CO
Chlorine, Cl2
Chlorodifluoromethane (R-22), CHClF2
Ethane, C2H6
Ethylene, C2H4
Fluorine, F2
Helium, He
n-Heptane, C7H16
n-Hexane, C6H14
Hydrogen, H2
Krypton, Kr
Methane, CH4
Neon, Ne
Nitrogen, N2
Nitric oxide, NO
Nitrogen dioxide, NO2
Oxygen, O2
n-Pentane, C5H12
Propane, C3H8
Propylene, C3H6
Steam, H2O
Sulfur dioxide, SO2
Tetrachloromethane, CCl4
Tetrafluoroethane (R-134a), C2H2F4
Trifluoroethane (R-143a), C2H3F3
Xenon, Xe
Specific Heat Data at 25°C
Molar Mass
M, kg/kmol
Gas Constant
R, kJ/kg · K*
cp, kJ/kg · K
28.97
17.03
39.95
159.81
58.12
58.12
44.01
28.01
70.905
86.47
30.070
28.054
38.00
4.003
100.20
86.18
2.016
83.80
16.04
20.183
28.01
30.006
46.006
32.00
72.15
44.097
42.08
18.015
64.06
153.82
102.03
84.04
131.30
0.2870
0.4882
0.2081
0.05202
0.1430
0.1430
0.1889
0.2968
0.1173
0.09615
0.2765
0.2964
0.2187
2.077
0.08297
0.09647
4.124
0.09921
0.5182
0.4119
0.2968
0.2771
0.1889
0.2598
0.1152
0.1885
0.1976
0.4615
0.1298
0.05405
0.08149
0.09893
0.06332
1.005
2.093
0.5203
0.2253
1.663
1.694
0.8439
1.039
0.4781
0.6496
1.744
1.527
0.8237
5.193
1.649
1.654
14.30
0.2480
2.226
1.030
1.040
0.9992
0.8060
0.9180
1.664
1.669
1.531
1.865
0.6228
0.5415
0.8334
0.9291
0.1583
cv, kJ/kg · K
0.7180
1.605
0.3122
0.1732
1.520
1.551
0.6550
0.7417
0.3608
0.5535
1.468
1.231
0.6050
3.116
1.566
1.558
10.18
0.1488
1.708
0.6180
0.7429
0.7221
0.6171
0.6582
1.549
1.480
1.333
1.403
0.4930
0.4875
0.7519
0.8302
0.09499
k cp /cv
1.400
1.304
1.667
1.300
1.094
1.092
1.288
1.400
1.325
1.174
1.188
1.241
1.362
1.667
1.053
1.062
1.405
1.667
1.303
1.667
1.400
1.384
1.306
1.395
1.074
1.127
1.148
1.329
1.263
1.111
1.108
1.119
1.667
* The unit kJ/kg · K is equivalent to kPa · m3/kg · K. The gas constant is calculated from R Ru /M, where Ru 8.31447 kJ/kmol · K is the universal gas
constant and M is the molar mass.
Source: Specific heat values are obtained primarily from the property routines prepared by The National Institute of Standards and Technology (NIST),
Gaithersburg, MD.
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APPENDIX 1
TABLE A–2
Boiling and freezing point properties
Boiling Data at 1 atm
Substance
Normal
Boiling
Point, °C
Ammonia
33.3
185.9
80.2
Latent Heat of
Vaporization
hfg , kJ/kg
1357
Freezing
Point, °C
77.7
189.3
5.5
Latent Heat
of Fusion
hif , kJ/kg
322.4
Argon
Benzene
Brine (20% sodium
chloride by mass)
n-Butane
Carbon dioxide
Ethanol
Ethyl alcohol
Ethylene glycol
Glycerine
Helium
Hydrogen
Isobutane
Kerosene
Mercury
Methane
103.9
0.5
78.4*
78.2
78.6
198.1
179.9
268.9
252.8
11.7
204–293
356.7
161.5
—
385.2
230.5 (at 0°C)
838.3
855
800.1
974
22.8
445.7
367.1
251
294.7
510.4
17.4
138.5
56.6
114.2
156
10.8
18.9
—
259.2
160
24.9
38.9
182.2
109
108
181.1
200.6
—
59.5
105.7
—
11.4
58.4
Methanol
Nitrogen
64.5
195.8
1100
198.6
97.7
210
99.2
25.3
124.8
306.3
57.5
180.7
218.8
13.7
187.7
80.0
Octane
Oil (light)
Oxygen
Petroleum
Propane
183
—
42.1
Refrigerant-134a
26.1
Water
100
161.6
394
Freezing Data
212.7
230–384
427.8
216.8
2257
96.6
0.0
28
126
—
80.3
—
333.7
Liquid Properties
Temperature,
°C
Density
r, kg/m3
Specific
Heat
cp, kJ/kg · K
33.3
20
0
25
185.6
20
682
665
639
602
1394
879
4.43
4.52
4.60
4.80
1.14
1.72
20
0.5
0
25
20
20
20
268.9
252.8
11.7
20
25
161.5
100
25
195.8
160
20
25
183
20
42.1
0
50
50
26.1
0
25
0
25
50
75
100
1150
601
298
783
789
1109
1261
146.2
70.7
593.8
820
13,560
423
301
787
809
596
703
910
1141
640
581
529
449
1443
1374
1295
1207
1000
997
988
975
958
3.11
2.31
0.59
2.46
2.84
2.84
2.32
22.8
10.0
2.28
2.00
0.139
3.49
5.79
2.55
2.06
2.97
2.10
1.80
1.71
2.0
2.25
2.53
3.13
1.23
1.27
1.34
1.43
4.22
4.18
4.18
4.19
4.22
* Sublimation temperature. (At pressures below the triple-point pressure of 518 kPa, carbon dioxide exists as a solid or gas. Also, the freezing-point temperature
of carbon dioxide is the triple-point temperature of 56.5°C.)
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FLUID MECHANICS
TABLE A–3
Properties of saturated water
Temp.
T, °C
Saturation
Pressure
Psat, kPa
Density
r, kg/m3
Enthalpy
of
Vaporization
hfg, kJ/kg
Specific
Heat
cp, J/kg · K
Liquid
Vapor
Thermal
Conductivity
k, W/m · K
Prandtl
Number
Pr
Dynamic Viscosity
m, kg/m · s
Liquid
Vapor
Volume
Expansion
Coefficient
b, 1/K
Liquid
Liquid
Vapor
Liquid
Vapor
Liquid
Vapor
0.01
5
10
15
20
0.6113
0.8721
1.2276
1.7051
2.339
999.8
999.9
999.7
999.1
998.0
0.0048
0.0068
0.0094
0.0128
0.0173
2501
2490
2478
2466
2454
4217
4205
4194
4186
4182
1854
1857
1862
1863
1867
0.561
0.571
0.580
0.589
0.598
0.0171
0.0173
0.0176
0.0179
0.0182
1.792
1.519
1.307
1.138
1.002
103
103
103
103
103
0.922
0.934
0.946
0.959
0.973
105
105
105
105
105
13.5
11.2
9.45
8.09
7.01
1.00
1.00
1.00
1.00
1.00
0.068
0.015
0.733
0.138
0.195
103
103
103
103
103
25
30
35
40
45
3.169
4.246
5.628
7.384
9.593
997.0
996.0
994.0
992.1
990.1
0.0231
0.0304
0.0397
0.0512
0.0655
2442
2431
2419
2407
2395
4180
4178
4178
4179
4180
1870
1875
1880
1885
1892
0.607
0.615
0.623
0.631
0.637
0.0186
0.0189
0.0192
0.0196
0.0200
0.891
0.798
0.720
0.653
0.596
103
103
103
103
103
0.987
1.001
1.016
1.031
1.046
105
105
105
105
105
6.14
5.42
4.83
4.32
3.91
1.00
1.00
1.00
1.00
1.00
0.247
0.294
0.337
0.377
0.415
103
103
103
103
103
50
55
60
65
70
12.35
15.76
19.94
25.03
31.19
988.1
985.2
983.3
980.4
977.5
0.0831
0.1045
0.1304
0.1614
0.1983
2383
2371
2359
2346
2334
4181
4183
4185
4187
4190
1900
1908
1916
1926
1936
0.644
0.649
0.654
0.659
0.663
0.0204
0.0208
0.0212
0.0216
0.0221
0.547
0.504
0.467
0.433
0.404
103
103
103
103
103
1.062
1.077
1.093
1.110
1.126
105
105
105
105
105
3.55
3.25
2.99
2.75
2.55
1.00
1.00
1.00
1.00
1.00
0.451
0.484
0.517
0.548
0.578
103
103
103
103
103
75
80
85
90
95
38.58
47.39
57.83
70.14
84.55
974.7
971.8
968.1
965.3
961.5
0.2421
0.2935
0.3536
0.4235
0.5045
2321
2309
2296
2283
2270
4193
4197
4201
4206
4212
1948
1962
1977
1993
2010
0.667
0.670
0.673
0.675
0.677
0.0225
0.0230
0.0235
0.0240
0.0246
0.378
0.355
0.333
0.315
0.297
103
103
103
103
103
1.142
1.159
1.176
1.193
1.210
105
105
105
105
105
2.38
2.22
2.08
1.96
1.85
1.00
1.00
1.00
1.00
1.00
0.607
0.653
0.670
0.702
0.716
103
103
103
103
103
100
110
120
130
140
101.33
143.27
198.53
270.1
361.3
957.9
950.6
943.4
934.6
921.7
0.5978
0.8263
1.121
1.496
1.965
2257
2230
2203
2174
2145
4217
4229
4244
4263
4286
2029
2071
2120
2177
2244
0.679
0.682
0.683
0.684
0.683
0.0251
0.0262
0.0275
0.0288
0.0301
0.282
0.255
0.232
0.213
0.197
103
103
103
103
103
1.227
1.261
1.296
1.330
1.365
105
105
105
105
105
1.75
1.58
1.44
1.33
1.24
1.00
1.00
1.00
1.01
1.02
0.750
0.798
0.858
0.913
0.970
103
103
103
103
103
150
160
170
180
190
475.8
617.8
791.7
1,002.1
1,254.4
916.6
907.4
897.7
887.3
876.4
2.546
3.256
4.119
5.153
6.388
2114
2083
2050
2015
1979
4311
4340
4370
4410
4460
2314
2420
2490
2590
2710
0.682
0.680
0.677
0.673
0.669
0.0316
0.0331
0.0347
0.0364
0.0382
0.183
0.170
0.160
0.150
0.142
103
103
103
103
103
1.399
1.434
1.468
1.502
1.537
105
105
105
105
105
1.16
1.09
1.03
0.983
0.947
1.02
1.05
1.05
1.07
1.09
1.025
1.145
1.178
1.210
1.280
103
103
103
103
103
200
220
240
260
280
1,553.8
2,318
3,344
4,688
6,412
864.3
840.3
813.7
783.7
750.8
7.852
11.60
16.73
23.69
33.15
1941
1859
1767
1663
1544
4500
4610
4760
4970
5280
2840
3110
3520
4070
4835
0.663
0.650
0.632
0.609
0.581
0.0401
0.0442
0.0487
0.0540
0.0605
0.134
0.122
0.111
0.102
0.094
103
103
103
103
103
1.571
1.641
1.712
1.788
1.870
105
105
105
105
105
0.910
0.865
0.836
0.832
0.854
1.11
1.15
1.24
1.35
1.49
1.350
1.520
1.720
2.000
2.380
103
103
103
103
103
1405
1239
1028
720
0
5750
6540
8240
14,690
—
5980
7900
11,870
25,800
—
0.548
0.509
0.469
0.427
—
0.0695
0.0836
0.110
0.178
—
0.086
0.078
0.070
0.060
0.043
103
103
103
103
103
1.965
2.084
2.255
2.571
4.313
105
105
105
105
105
0.902
1.00
1.23
2.06
1.69
1.97
2.43
3.73
2.950 103
300
320
340
360
374.14
8,581
11,274
14,586
18,651
22,090
713.8
667.1
610.5
528.3
317.0
46.15
64.57
92.62
144.0
317.0
Note 1: Kinematic viscosity n and thermal diffusivity a can be calculated from their definitions, n m/r and a k/rcp n/Pr. The temperatures 0.01°C,
100°C, and 374.14°C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can
be used at any pressure with negligible error except at temperatures near the critical-point value.
Note 2: The unit kJ/kg · °C for specific heat is equivalent to kJ/kg · K, and the unit W/m · °C for thermal conductivity is equivalent to W/m · K.
Source: Viscosity and thermal conductivity data are from J. V. Sengers and J. T. R. Watson, Journal of Physical and Chemical Reference Data 15 (1986), pp.
1291–1322. Other data are obtained from various sources or calculated.
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APPENDIX 1
TABLE A–4
Properties of saturated refrigerant-134a
Temp.
T, °C
Saturation
Pressure
P, kPa
Liquid
Vapor
Liquid
Vapor
Vapor
Volume
Expansion
Coefficient
b, 1/K
Liquid
40
35
30
25
20
51.2
66.2
84.4
106.5
132.8
1418
1403
1389
1374
1359
2.773
3.524
4.429
5.509
6.787
225.9
222.7
219.5
216.3
213.0
1254
1264
1273
1283
1294
748.6
764.1
780.2
797.2
814.9
0.1101
0.1084
0.1066
0.1047
0.1028
0.00811
0.00862
0.00913
0.00963
0.01013
4.878
4.509
4.178
3.882
3.614
104
104
104
104
104
2.550
3.003
3.504
4.054
4.651
106
106
106
106
106
5.558
5.257
4.992
4.757
4.548
0.235
0.266
0.299
0.335
0.374
0.00205
0.00209
0.00215
0.00220
0.00227
0.01760
0.01682
0.01604
0.01527
0.01451
15
10
5
0
5
164.0
200.7
243.5
293.0
349.9
1343
1327
1311
1295
1278
8.288
10.04
12.07
14.42
17.12
209.5
206.0
202.4
198.7
194.8
1306
1318
1330
1344
1358
833.5
853.1
873.8
895.6
918.7
0.1009
0.0989
0.0968
0.0947
0.0925
0.01063
0.01112
0.01161
0.01210
0.01259
3.371
3.150
2.947
2.761
2.589
104
104
104
104
104
5.295
5.982
6.709
7.471
8.264
106
106
106
106
106
4.363
4.198
4.051
3.919
3.802
0.415
0.459
0.505
0.553
0.603
0.00233
0.00241
0.00249
0.00258
0.00269
0.01376
0.01302
0.01229
0.01156
0.01084
10
15
20
25
30
414.9
488.7
572.1
665.8
770.6
1261
1244
1226
1207
1188
20.22
23.75
27.77
32.34
37.53
190.8
186.6
182.3
177.8
173.1
1374
1390
1408
1427
1448
943.2
969.4
997.6
1028
1061
0.0903
0.0880
0.0856
0.0833
0.0808
0.01308
0.01357
0.01406
0.01456
0.01507
2.430
2.281
2.142
2.012
1.888
104
104
104
104
104
9.081
9.915
1.075
1.160
1.244
106
106
105
105
105
3.697
3.604
3.521
3.448
3.383
0.655
0.708
0.763
0.819
0.877
0.00280
0.00293
0.00307
0.00324
0.00342
0.01014
0.00944
0.00876
0.00808
0.00742
35
40
45
50
55
887.5
1017.1
1160.5
1318.6
1492.3
1168
1147
1125
1102
1078
43.41
50.08
57.66
66.27
76.11
168.2
163.0
157.6
151.8
145.7
1471
1498
1529
1566
1608
1098
1138
1184
1237
1298
0.0783
0.0757
0.0731
0.0704
0.0676
0.01558
0.01610
0.01664
0.01720
0.01777
1.772
1.660
1.554
1.453
1.355
104
104
104
104
104
1.327
1.408
1.486
1.562
1.634
105
105
105
105
105
3.328
3.285
3.253
3.231
3.223
0.935
0.995
1.058
1.123
1.193
0.00364
0.00390
0.00420
0.00456
0.00500
0.00677
0.00613
0.00550
0.00489
0.00429
60
65
70
75
80
1682.8
1891.0
2118.2
2365.8
2635.2
1053
1026
996.2
964
928.2
87.38
100.4
115.6
133.6
155.3
139.1
132.1
124.4
115.9
106.4
1659
1722
1801
1907
2056
1372
1462
1577
1731
1948
0.0647
0.0618
0.0587
0.0555
0.0521
0.01838
0.01902
0.01972
0.02048
0.02133
1.260
1.167
1.077
9.891
9.011
104
104
104
105
105
1.704
1.771
1.839
1.908
1.982
105
105
105
105
105
3.229
3.255
3.307
3.400
3.558
1.272
1.362
1.471
1.612
1.810
0.00554
0.00624
0.00716
0.00843
0.01031
0.00372
0.00315
0.00261
0.00209
0.00160
85
90
95
100
2928.2
3246.9
3594.1
3975.1
887.1
837.7
772.5
651.7
95.4
82.2
64.9
33.9
2287
2701
3675
7959
2281
2865
4144
8785
0.0484
0.0444
0.0396
0.0322
0.02233
0.02357
0.02544
0.02989
8.124
7.203
6.190
4.765
105
105
105
105
2.071
2.187
2.370
2.833
105
105
105
105
3.837
4.385
5.746
11.77
2.116
2.658
3.862
8.326
0.01336
0.01911
0.03343
0.10047
0.00114
0.00071
0.00033
0.00004
Density
r, kg/m3
Liquid
Vapor
182.3
217.8
269.3
376.3
Enthalpy
of
Vaporization
hfg, kJ/kg
Specific
Heat
cp, J/kg · K
Thermal
Conductivity
k, W/m · K
Prandtl
Number
Pr
Dynamic Viscosity
m, kg/m · s
Liquid
Vapor
Liquid
Surface
Tension,
N/m
Note 1: Kinematic viscosity n and thermal diffusivity a can be calculated from their definitions, n m/r and a k/rcp n/Pr. The properties listed here (except
the vapor density) can be used at any pressures with negligible error except at temperatures near the critical-point value.
Note 2: The unit kJ/kg · °C for specific heat is equivalent to kJ/kg · K, and the unit W/m · °C for thermal conductivity is equivalent to W/m · K.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: R. Tillner-Roth and H. D. Baehr, “An International
Standard Formulation for the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 K to 455 K and Pressures up to
70 MPa,” J. Phys. Chem, Ref. Data, Vol. 23, No. 5, 1994; M. J. Assael, N. K. Dalaouti, A. A. Griva, and J. H. Dymond, “Viscosity and Thermal Conductivity of
Halogenated Methane and Ethane Refrigerants,” IJR, Vol. 22, pp. 525–535, 1999; NIST REFPROP 6 program (M. O. McLinden, S. A. Klein, E. W. Lemmon,
and A. P. Peskin, Physical and Chemical Properties Division, National Institute of Standards and Technology, Boulder, CO 80303, 1995).
cen72367_appx1.qxd 11/17/04 4:34 PM Page 890
890
FLUID MECHANICS
TABLE A–5
Properties of saturated ammonia
Saturation
Pressure
P, kPa
Liquid
Liquid
Vapor
Liquid
Vapor
Volume
Expansion
Coefficient
b, 1/K
Liquid
40
30
25
20
15
71.66
119.4
151.5
190.1
236.2
690.2
677.8
671.5
665.1
658.6
0.6435
1.037
1.296
1.603
1.966
1389
1360
1345
1329
1313
4414
4465
4489
4514
4538
2242
2322
2369
2420
2476
—
—
0.5968
0.5853
0.5737
0.01792
0.01898
0.01957
0.02015
0.02075
2.926
2.630
2.492
2.361
2.236
104
104
104
104
104
7.957
8.311
8.490
8.669
8.851
106
106
106
106
106
—
—
1.875
1.821
1.769
0.9955
1.017
1.028
1.041
1.056
0.00176
0.00185
0.00190
0.00194
0.00199
0.03565
0.03341
0.03229
0.03118
0.03007
10
5
0
5
10
290.8
354.9
429.6
516
615.3
652.1
645.4
638.6
631.7
624.6
2.391
2.886
3.458
4.116
4.870
1297
1280
1262
1244
1226
4564
4589
4617
4645
4676
2536
2601
2672
2749
2831
0.5621
0.5505
0.5390
0.5274
0.5158
0.02138
0.02203
0.02270
0.02341
0.02415
2.117
2.003
1.896
1.794
1.697
104
104
104
104
104
9.034
9.218
9.405
9.593
9.784
106
106
106
106
106
1.718
1.670
1.624
1.580
1.539
1.072
1.089
1.107
1.126
1.147
0.00205
0.00210
0.00216
0.00223
0.00230
0.02896
0.02786
0.02676
0.02566
0.02457
15
20
25
30
35
728.8
857.8
1003
1167
1351
617.5
610.2
602.8
595.2
587.4
5.729
6.705
7.809
9.055
10.46
1206
1186
1166
1144
1122
4709
4745
4784
4828
4877
2920
3016
3120
3232
3354
0.5042
0.4927
0.4811
0.4695
0.4579
0.02492
0.02573
0.02658
0.02748
0.02843
1.606
1.519
1.438
1.361
1.288
104
104
104
104
104
9.978
1.017
1.037
1.057
1.078
106
105
105
105
105
1.500
1.463
1.430
1.399
1.372
1.169
1.193
1.218
1.244
1.272
0.00237
0.00245
0.00254
0.00264
0.00275
0.02348
0.02240
0.02132
0.02024
0.01917
40
45
50
55
60
1555
1782
2033
2310
2614
579.4
571.3
562.9
554.2
545.2
12.03
13.8
15.78
18.00
20.48
1099
1075
1051
1025
997.4
4932
4993
5063
5143
5234
3486
3631
3790
3967
4163
0.4464
0.4348
0.4232
0.4116
0.4001
0.02943
0.03049
0.03162
0.03283
0.03412
1.219
1.155
1.094
1.037
9.846
104
104
104
104
105
1.099
1.121
1.143
1.166
1.189
105
105
105
105
105
1.347
1.327
1.310
1.297
1.288
1.303
1.335
1.371
1.409
1.452
0.00287
0.00301
0.00316
0.00334
0.00354
0.01810
0.01704
0.01598
0.01493
0.01389
65
70
75
80
85
2948
3312
3709
4141
4609
536.0
526.3
516.2
505.7
494.5
23.26
26.39
29.90
33.87
38.36
968.9
939.0
907.5
874.1
838.6
5340
5463
5608
5780
5988
4384
4634
4923
5260
5659
0.3885
0.3769
0.3653
0.3538
0.3422
0.03550
0.03700
0.03862
0.04038
0.04232
9.347
8.879
8.440
8.030
7.645
105
105
105
105
105
1.213
1.238
1.264
1.292
1.322
105
105
105
105
105
1.285
1.287
1.296
1.312
1.338
1.499
1.551
1.612
1.683
1.768
0.00377
0.00404
0.00436
0.00474
0.00521
0.01285
0.01181
0.01079
0.00977
0.00876
90
95
100
5116
5665
6257
482.8
470.2
456.6
43.48
49.35
56.15
800.6
759.8
715.5
6242
6561
6972
6142
6740
7503
0.3306
0.3190
0.3075
0.04447
0.04687
0.04958
7.284 105
6.946 105
6.628 105
1.354 105
1.389 105
1.429 105
1.375
1.429
1.503
1.871
1.999
2.163
0.00579
0.00652
0.00749
0.00776
0.00677
0.00579
Temp.
T, °C
Density
r, kg/m3
Vapor
Enthalpy
of
Vaporization
hfg, kJ/kg
Specific
Heat
cp, J/kg · K
Liquid
Vapor
Thermal
Conductivity
k, W/m · K
Prandtl
Number
Pr
Dynamic Viscosity
m, kg/m · s
Liquid
Vapor
Surface
Tension,
N/m
Note 1: Kinematic viscosity n and thermal diffusivity a can be calculated from their definitions, n m/r and a k/rcp n/Pr. The properties listed here (except
the vapor density) can be used at any pressures with negligible error except at temperatures near the critical-point value.
Note 2: The unit kJ/kg · °C for specific heat is equivalent to kJ/kg · K, and the unit W/m · °C for thermal conductivity is equivalent to W/m · K.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Tillner-Roth, Harms-Watzenberg, and Baehr, “Eine
neue Fundamentalgleichung fur Ammoniak,” DKV-Tagungsbericht 20:167–181, 1993; Liley and Desai, “Thermophysical Properties of Refrigerants,” ASHRAE,
1993, ISBN 1-1883413-10-9.
cen72367_appx1.qxd 11/17/04 4:34 PM Page 891
891
APPENDIX 1
TABLE A–6
Properties of saturated propane
Temp.
T, °C
120
110
100
90
80
Saturation
Pressure
P, kPa
0.4053
1.157
2.881
6.406
12.97
Liquid
Vapor
Liquid
Vapor
Vapor
Volume
Expansion
Coefficient
b, 1/K
Liquid
664.7
654.5
644.2
633.8
623.2
0.01408
0.03776
0.08872
0.1870
0.3602
498.3
489.3
480.4
471.5
462.4
2003
2021
2044
2070
2100
1115
1148
1183
1221
1263
0.1802
0.1738
0.1672
0.1606
0.1539
0.00589
0.00645
0.00705
0.00769
0.00836
6.136
5.054
4.252
3.635
3.149
104
104
104
104
104
4.372
4.625
4.881
5.143
5.409
106
106
106
106
106
6.820
5.878
5.195
4.686
4.297
0.827
0.822
0.819
0.817
0.817
0.00153
0.00157
0.00161
0.00166
0.00171
0.02630
0.02486
0.02344
0.02202
0.02062
0.6439
1.081
1.724
2.629
3.864
453.1
443.5
433.6
423.1
412.1
2134
2173
2217
2258
2310
1308
1358
1412
1471
1535
0.1472
0.1407
0.1343
0.1281
0.1221
0.00908
0.00985
0.01067
0.01155
0.01250
2.755
2.430
2.158
1.926
1.726
104
104
104
104
104
5.680
5.956
6.239
6.529
6.827
106
106
106
106
106
3.994
3.755
3.563
3.395
3.266
0.818
0.821
0.825
0.831
0.839
0.00177
0.00184
0.00192
0.00201
0.00213
0.01923
0.01785
0.01649
0.01515
0.01382
Density
r, kg/m3
Liquid
Vapor
Enthalpy
of
Vaporization
hfg, kJ/kg
Specific
Heat
cp, J/kg · K
Thermal
Conductivity
k, W/m · K
Prandtl
Number
Pr
Dynamic Viscosity
m, kg/m · s
Liquid
Vapor
Liquid
Surface
Tension,
N/m
70
60
50
40
30
24.26
42.46
70.24
110.7
167.3
612.5
601.5
590.3
578.8
567.0
20
10
0
5
10
243.8
344.4
473.3
549.8
635.1
554.7
542.0
528.7
521.8
514.7
5.503
7.635
10.36
11.99
13.81
400.3
387.8
374.2
367.0
359.5
2368
2433
2507
2547
2590
1605
1682
1768
1814
1864
0.1163
0.1107
0.1054
0.1028
0.1002
0.01351
0.01459
0.01576
0.01637
0.01701
1.551
1.397
1.259
1.195
1.135
104
104
104
104
104
7.136
7.457
7.794
7.970
8.151
106
106
106
106
106
3.158
3.069
2.996
2.964
2.935
0.848
0.860
0.875
0.883
0.893
0.00226
0.00242
0.00262
0.00273
0.00286
0.01251
0.01122
0.00996
0.00934
0.00872
15
20
25
30
35
729.8
834.4
949.7
1076
1215
507.5
500.0
492.2
484.2
475.8
15.85
18.13
20.68
23.53
26.72
351.7
343.4
334.8
325.8
316.2
2637
2688
2742
2802
2869
1917
1974
2036
2104
2179
0.0977
0.0952
0.0928
0.0904
0.0881
0.01767
0.01836
0.01908
0.01982
0.02061
1.077
1.022
9.702
9.197
8.710
104
104
105
105
105
8.339
8.534
8.738
8.952
9.178
106
106
106
106
106
2.909
2.886
2.866
2.850
2.837
0.905
0.918
0.933
0.950
0.971
0.00301
0.00318
0.00337
0.00358
0.00384
0.00811
0.00751
0.00691
0.00633
0.00575
40
45
50
60
70
1366
1530
1708
2110
2580
467.1
458.0
448.5
427.5
403.2
30.29
34.29
38.79
49.66
64.02
306.1
295.3
283.9
258.4
228.0
2943
3026
3122
3283
3595
2264
2361
2473
2769
3241
0.0857
0.0834
0.0811
0.0765
0.0717
0.02142
0.02228
0.02319
0.02517
0.02746
8.240
7.785
7.343
6.487
5.649
105
105
105
105
105
9.417
9.674
9.950
1.058
1.138
106
106
106
105
105
2.828
2.824
2.826
2.784
2.834
0.995
1.025
1.061
1.164
1.343
0.00413
0.00448
0.00491
0.00609
0.00811
0.00518
0.00463
0.00408
0.00303
0.00204
80
90
3127
3769
373.0
329.1
84.28
118.6
189.7
133.2
4501
6977
4173
7239
0.0663
0.0595
0.03029
0.03441
4.790 105
3.807 105
1.249 105
1.448 105
3.251
4.465
1.722
3.047
0.01248
0.02847
0.00114
0.00037
Note 1: Kinematic viscosity n and thermal diffusivity a can be calculated from their definitions, n m/r and a k/rcp n/Pr. The properties listed here (except
the vapor density) can be used at any pressures with negligible error except at temperatures near the critical-point value.
Note 2: The unit kJ/kg · °C for specific heat is equivalent to kJ/kg · K, and the unit W/m · °C for thermal conductivity is equivalent to W/m · K.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Reiner Tillner-Roth, “Fundamental Equations of
State,” Shaker, Verlag, Aachan, 1998; B. A. Younglove and J. F. Ely, “Thermophysical Properties of Fluids. II Methane, Ethane, Propane, Isobutane, and Normal
Butane,” J. Phys. Chem. Ref. Data, Vol. 16, No. 4, 1987; G.R. Somayajulu, “A Generalized Equation for Surface Tension from the Triple-Point to the CriticalPoint,” International Journal of Thermophysics, Vol. 9, No. 4, 1988.
cen72367_appx1.qxd 11/17/04 4:34 PM Page 892
892
FLUID MECHANICS
TABLE A–7
Properties of liquids
Temp.
T, °C
Density
r, kg/m3
Specific
Heat cp,
J/kg · K
Thermal
Conductivity
k, W/m · K
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m · s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
Volume
Expansion
Coeff.
b, 1/K
Methane (CH4)
160
150
140
130
120
110
100
90
420.2
405.0
388.8
371.1
351.4
328.8
301.0
261.7
3492
3580
3700
3875
4146
4611
5578
8902
0.1863
0.1703
0.1550
0.1402
0.1258
0.1115
0.0967
0.0797
1.270
1.174
1.077
9.749
8.634
7.356
5.761
3.423
107
107
107
108
108
108
108
108
1.133
9.169
7.551
6.288
5.257
4.377
3.577
2.761
104
105
105
105
105
105
105
105
2.699
2.264
1.942
1.694
1.496
1.331
1.188
1.055
107
107
107
107
107
107
107
107
2.126
1.927
1.803
1.738
1.732
1.810
2.063
3.082
0.00352
0.00391
0.00444
0.00520
0.00637
0.00841
0.01282
0.02922
104
104
104
104
104
104
7.429
6.531
5.795
5.185
4.677
4.250
107
107
107
107
107
107
7.414
6.622
5.980
5.453
5.018
4.655
0.00118
0.00120
0.00123
0.00127
0.00132
0.00137
104
104
104
104
104
104
104
105
105
1.360
8.531
5.942
4.420
3.432
2.743
2.233
1.836
1.509
106
107
107
107
107
107
107
107
107
12.65
8.167
6.079
4.963
4.304
3.880
3.582
3.363
3.256
0.00142
0.00150
0.00161
0.00177
0.00199
0.00232
0.00286
0.00385
0.00628
8.219
5.287
3.339
1.970
1.201
7.878
5.232
3.464
2.455
103
103
103
103
103
104
104
104
104
84,101
54,327
34,561
20,570
12,671
8,392
5,631
3,767
2,697
4.242
9.429
2.485
8.565
3.794
2.046
1.241
8.029
6.595
103
104
104
105
105
105
105
106
106
46,636
10,863
2,962
1,080
499.3
279.1
176.3
118.1
98.31
Methanol [CH3(OH)]
20
30
40
50
60
70
788.4
779.1
769.6
760.1
750.4
740.4
2515
2577
2644
2718
2798
2885
0.1987
0.1980
0.1972
0.1965
0.1957
0.1950
1.002
9.862
9.690
9.509
9.320
9.128
107
108
108
108
108
108
5.857
5.088
4.460
3.942
3.510
3.146
Isobutane (R600a)
100
75
50
25
0
25
50
75
100
683.8
659.3
634.3
608.2
580.6
550.7
517.3
478.5
429.6
1881
1970
2069
2180
2306
2455
2640
2896
3361
0.1383
0.1357
0.1283
0.1181
0.1068
0.0956
0.0851
0.0757
0.0669
1.075
1.044
9.773
8.906
7.974
7.069
6.233
5.460
4.634
107
107
108
108
108
108
108
108
108
108
9.305
5.624
3.769
2.688
1.993
1.510
1.155
8.785
6.483
Glycerin
0
5
10
15
20
25
30
35
40
1276
1273
1270
1267
1264
1261
1258
1255
1252
2262
2288
2320
2354
2386
2416
2447
2478
2513
0.2820
0.2835
0.2846
0.2856
0.2860
0.2860
0.2860
0.2860
0.2863
9.773
9.732
9.662
9.576
9.484
9.388
9.291
9.195
9.101
108
108
108
108
108
108
108
108
10.49
6.730
4.241
2.496
1.519
0.9934
0.6582
0.4347
0.3073
Engine Oil (unused)
0
20
40
60
80
100
120
140
150
899.0
888.1
876.0
863.9
852.0
840.0
828.9
816.8
810.3
1797
1881
1964
2048
2132
2220
2308
2395
2441
0.1469
0.1450
0.1444
0.1404
0.1380
0.1367
0.1347
0.1330
0.1327
9.097
8.680
8.391
7.934
7.599
7.330
7.042
6.798
6.708
108
108
108
108
108
108
108
108
108
3.814
0.8374
0.2177
0.07399
0.03232
0.01718
0.01029
0.006558
0.005344
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Originally based on various sources.
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
cen72367_appx1.qxd 11/17/04 4:34 PM Page 893
893
APPENDIX 1
TABLE A–8
Properties of liquid metals
Temp.
T, °C
Density
r, kg/m3
Specific
Heat cp,
J/kg · K
Thermal
Conductivity
k, W/m · K
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m · s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
Volume
Expansion
Coeff.
b, 1/K
Mercury (Hg) Melting Point: 39°C
0
25
50
75
100
150
200
250
300
13595
13534
13473
13412
13351
13231
13112
12993
12873
140.4
139.4
138.6
137.8
137.1
136.1
135.5
135.3
135.3
8.18200
8.51533
8.83632
9.15632
9.46706
10.07780
10.65465
11.18150
11.68150
4.287
4.514
4.734
4.956
5.170
5.595
5.996
6.363
6.705
106
106
106
106
106
106
106
106
106
1.687
1.534
1.423
1.316
1.245
1.126
1.043
9.820
9.336
103
103
103
103
103
103
103
104
104
1.241
1.133
1.056
9.819
9.326
8.514
7.959
7.558
7.252
107
107
107
108
108
108
108
108
108
0.0289
0.0251
0.0223
0.0198
0.0180
0.0152
0.0133
0.0119
0.0108
1.545
1.436
1.215
1.048
9.157
107
107
107
107
108
0.01381
0.01310
0.01154
0.01022
0.00906
2.167
1.976
1.814
1.702
1.589
1.475
1.360
107
107
107
107
107
107
107
0.02252
0.02048
0.01879
0.01771
0.01661
0.01549
0.01434
7.432
5.967
4.418
3.188
2.909
2.614
107
107
107
107
107
107
0.01106
0.008987
0.006751
0.004953
0.004593
0.004202
4.213
3.456
2.652
2.304
2.126
107
107
107
107
107
0.006023
0.004906
0.00374
0.003309
0.003143
107
107
107
107
107
107
0.02102
0.01611
0.01161
0.00753
0.00665
0.00579
Bismuth (Bi) Melting Point: 271°C
350
400
500
600
700
9969
9908
9785
9663
9540
146.0
148.2
152.8
157.3
161.8
16.28
16.10
15.74
15.60
15.60
1.118
1.096
1.052
1.026
1.010
105
105
105
105
105
1.540
1.422
1.188
1.013
8.736
103
103
103
103
104
Lead (Pb) Melting Point: 327°C
400
450
500
550
600
650
700
10506
10449
10390
10329
10267
10206
10145
158
156
155
155
155
155
155
15.97
15.74
15.54
15.39
15.23
15.07
14.91
9.623
9.649
9.651
9.610
9.568
9.526
9.483
106
106
106
106
106
106
106
2.277
2.065
1.884
1.758
1.632
1.505
1.379
103
103
103
103
103
103
103
Sodium (Na) Melting Point: 98°C
100
200
300
400
500
600
927.3
902.5
877.8
853.0
828.5
804.0
1378
1349
1320
1296
1284
1272
85.84
80.84
75.84
71.20
67.41
63.63
6.718
6.639
6.544
6.437
6.335
6.220
105
105
105
105
105
105
6.892
5.385
3.878
2.720
2.411
2.101
104
104
104
104
104
104
Potassium (K) Melting Point: 64°C
200
300
400
500
600
795.2
771.6
748.0
723.9
699.6
790.8
772.8
754.8
750.0
750.0
43.99
42.01
40.03
37.81
35.50
6.995
7.045
7.090
6.964
6.765
105
105
105
105
105
3.350
2.667
1.984
1.668
1.487
104
104
104
104
104
Sodium–Potassium (%22Na-%78K) Melting Point: 11°C
100
200
300
400
500
600
847.3
823.2
799.1
775.0
751.5
728.0
944.4
922.5
900.6
879.0
880.1
881.2
25.64
26.27
26.89
27.50
27.89
28.28
3.205
3.459
3.736
4.037
4.217
4.408
105
105
105
105
105
105
5.707
4.587
3.467
2.357
2.108
1.859
104
104
104
104
104
104
6.736
5.572
4.339
3.041
2.805
2.553
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Originally based on various sources.
1.810
1.810
1.810
1.810
1.810
1.810
1.815
1.829
1.854
104
104
104
104
104
104
104
104
104
cen72367_appx1.qxd 11/17/04 4:34 PM Page 894
894
FLUID MECHANICS
TABLE A–9
Properties of air at 1 atm pressure
Temp.
T, °C
Density
r, kg/m3
Specific
Heat cp
J/kg · K
Thermal
Conductivity
k, W/m · K
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m · s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
150
100
50
40
30
2.866
2.038
1.582
1.514
1.451
983
966
999
1002
1004
0.01171
0.01582
0.01979
0.02057
0.02134
4.158
8.036
1.252
1.356
1.465
106
106
105
105
105
8.636
1.189
1.474
1.527
1.579
106
106
105
105
105
3.013
5.837
9.319
1.008
1.087
106
106
106
105
105
0.7246
0.7263
0.7440
0.7436
0.7425
20
10
0
5
10
1.394
1.341
1.292
1.269
1.246
1005
1006
1006
1006
1006
0.02211
0.02288
0.02364
0.02401
0.02439
1.578
1.696
1.818
1.880
1.944
105
105
105
105
105
1.630
1.680
1.729
1.754
1.778
105
105
105
105
105
1.169
1.252
1.338
1.382
1.426
105
105
105
105
105
0.7408
0.7387
0.7362
0.7350
0.7336
15
20
25
30
35
1.225
1.204
1.184
1.164
1.145
1007
1007
1007
1007
1007
0.02476
0.02514
0.02551
0.02588
0.02625
2.009
2.074
2.141
2.208
2.277
105
105
105
105
105
1.802
1.825
1.849
1.872
1.895
105
105
105
105
105
1.470
1.516
1.562
1.608
1.655
105
105
105
105
105
0.7323
0.7309
0.7296
0.7282
0.7268
40
45
50
60
70
1.127
1.109
1.092
1.059
1.028
1007
1007
1007
1007
1007
0.02662
0.02699
0.02735
0.02808
0.02881
2.346
2.416
2.487
2.632
2.780
105
105
105
105
105
1.918
1.941
1.963
2.008
2.052
105
105
105
105
105
1.702
1.750
1.798
1.896
1.995
105
105
105
105
105
0.7255
0.7241
0.7228
0.7202
0.7177
80
90
100
120
140
0.9994
0.9718
0.9458
0.8977
0.8542
1008
1008
1009
1011
1013
0.02953
0.03024
0.03095
0.03235
0.03374
2.931
3.086
3.243
3.565
3.898
105
105
105
105
105
2.096
2.139
2.181
2.264
2.345
105
105
105
105
105
2.097
2.201
2.306
2.522
2.745
105
105
105
105
105
0.7154
0.7132
0.7111
0.7073
0.7041
160
180
200
250
300
0.8148
0.7788
0.7459
0.6746
0.6158
1016
1019
1023
1033
1044
0.03511
0.03646
0.03779
0.04104
0.04418
4.241
4.593
4.954
5.890
6.871
105
105
105
105
105
2.420
2.504
2.577
2.760
2.934
105
105
105
105
105
2.975
3.212
3.455
4.091
4.765
105
105
105
105
105
0.7014
0.6992
0.6974
0.6946
0.6935
350
400
450
500
600
0.5664
0.5243
0.4880
0.4565
0.4042
1056
1069
1081
1093
1115
0.04721
0.05015
0.05298
0.05572
0.06093
7.892
8.951
1.004
1.117
1.352
105
105
104
104
104
3.101
3.261
3.415
3.563
3.846
105
105
105
105
105
5.475
6.219
6.997
7.806
9.515
105
105
105
105
105
0.6937
0.6948
0.6965
0.6986
0.7037
700
800
900
1000
1500
2000
0.3627
0.3289
0.3008
0.2772
0.1990
0.1553
1135
1153
1169
1184
1234
1264
0.06581
0.07037
0.07465
0.07868
0.09599
0.11113
1.598
1.855
2.122
2.398
3.908
5.664
104
104
104
104
104
104
4.111
4.362
4.600
4.826
5.817
6.630
105
105
105
105
105
105
1.133
1.326
1.529
1.741
2.922
4.270
104
104
104
104
104
104
0.7092
0.7149
0.7206
0.7260
0.7478
0.7539
Note: For ideal gases, the properties cp, k, m, and Pr are independent of pressure. The properties r, n, and a at a pressure P (in atm) other than 1 atm are
determined by multiplying the values of r at the given temperature by P and by dividing n and a by P.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Keenan, Chao, Keyes, Gas Tables, Wiley, 198; and
Thermophysical Properties of Matter, Vol. 3: Thermal Conductivity, Y. S. Touloukian, P. E. Liley, S. C. Saxena, Vol. 11: Viscosity, Y. S. Touloukian, S. C. Saxena,
and P. Hestermans, IFI/Plenun, NY, 1970, ISBN 0-306067020-8.
cen72367_appx1.qxd 11/17/04 4:34 PM Page 895
895
APPENDIX 1
TABLE A–10
Properties of gases at 1 atm pressure
Temp.
T, °C
Density
r, kg/m3
Specific
Heat cp
J/kg · K
Thermal
Conductivity
k, W/m · K
50
0
50
100
150
200
300
400
500
1000
1500
2000
2.4035
1.9635
1.6597
1.4373
1.2675
1.1336
0.9358
0.7968
0.6937
0.4213
0.3025
0.2359
746
811
866.6
914.8
957.4
995.2
1060
1112
1156
1292
1356
1387
0.01051
0.01456
0.01858
0.02257
0.02652
0.03044
0.03814
0.04565
0.05293
0.08491
0.10688
0.11522
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m · s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
Carbon Dioxide, CO2
5.860
9.141
1.291
1.716
2.186
2.698
3.847
5.151
6.600
1.560
2.606
3.521
106
106
105
105
105
105
105
105
105
104
104
104
1.129
1.375
1.612
1.841
2.063
2.276
2.682
3.061
3.416
4.898
6.106
7.322
105
105
105
105
105
105
105
105
105
105
105
105
4.699
7.003
9.714
1.281
1.627
2.008
2.866
3.842
4.924
1.162
2.019
3.103
106
106
106
105
105
105
105
105
105
104
104
104
0.8019
0.7661
0.7520
0.7464
0.7445
0.7442
0.7450
0.7458
0.7460
0.7455
0.7745
0.8815
1.378
1.629
1.863
2.080
2.283
2.472
2.812
3.111
3.379
4.557
6.321
9.826
105
105
105
105
105
105
105
105
105
105
105
105
9.012
1.303
1.764
2.274
2.830
3.426
4.722
6.136
7.653
1.700
3.284
6.543
106
105
105
105
105
105
105
105
105
104
104
104
0.7840
0.7499
0.7328
0.7239
0.7191
0.7164
0.7134
0.7111
0.7087
0.7080
0.7733
0.9302
8.564
1.028
1.191
1.345
1.491
1.630
1.886
2.119
2.334
3.281
4.434
6.360
106
105
105
105
105
105
105
105
105
105
105
105
9.774
1.436
1.969
2.567
3.227
3.944
5.529
7.297
9.228
2.136
4.022
7.395
106
105
105
105
105
105
105
105
105
104
104
104
0.8116
0.7494
0.7282
0.7247
0.7284
0.7344
0.7450
0.7501
0.7502
0.7331
0.7936
1.0386
7.293
8.391
9.427
1.041
1.136
1.228
1.403
1.570
1.730
2.455
3.099
3.690
106
106
106
105
105
105
105
105
105
105
105
105
6.624
9.329
1.240
1.582
1.957
2.365
3.274
4.302
5.443
1.272
2.237
3.414
105
105
104
104
104
104
104
104
104
103
103
103
0.6562
0.7071
0.7191
0.7196
0.7174
0.7155
0.7149
0.7179
0.7224
0.7345
0.7795
1.1717
Carbon Monoxide, CO
50
0
50
100
150
200
300
400
500
1000
1500
2000
1.5297
1.2497
1.0563
0.9148
0.8067
0.7214
0.5956
0.5071
0.4415
0.2681
0.1925
0.1502
1081
1048
1039
1041
1049
1060
1085
1111
1135
1226
1279
1309
0.01901
0.02278
0.02641
0.02992
0.03330
0.03656
0.04277
0.04860
0.05412
0.07894
0.10458
0.13833
1.149
1.739
2.407
3.142
3.936
4.782
6.619
8.628
1.079
2.401
4.246
7.034
105
105
105
105
105
105
105
105
104
104
104
104
Methane, CH4
50
0
50
100
150
200
300
400
500
1000
1500
2000
0.8761
0.7158
0.6050
0.5240
0.4620
0.4132
0.3411
0.2904
0.2529
0.1536
0.1103
0.0860
50
0
50
100
150
200
300
400
500
1000
1500
2000
0.11010
0.08995
0.07603
0.06584
0.05806
0.05193
0.04287
0.03650
0.03178
0.01930
0.01386
0.01081
2243
2217
2302
2443
2611
2791
3158
3510
3836
5042
5701
6001
0.02367
0.03042
0.03766
0.04534
0.05344
0.06194
0.07996
0.09918
0.11933
0.22562
0.31857
0.36750
1.204
1.917
2.704
3.543
4.431
5.370
7.422
9.727
1.230
2.914
5.068
7.120
105
105
105
105
105
105
105
105
104
104
104
104
Hydrogen, H2
12635
13920
14349
14473
14492
14482
14481
14540
14653
15577
16553
17400
0.1404
0.1652
0.1881
0.2095
0.2296
0.2486
0.2843
0.3180
0.3509
0.5206
0.6581
0.5480
1.009
1.319
1.724
2.199
2.729
3.306
4.580
5.992
7.535
1.732
2.869
2.914
104
104
104
104
104
104
104
104
104
103
103
103
(Continued)
cen72367_appx1.qxd 11/17/04 4:34 PM Page 896
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FLUID MECHANICS
TABLE A–10
Properties of gases at 1 atm pressure (Continued)
Temp.
T, °C
Density
r, kg/m3
Specific
Heat cp
J/kg · K
Thermal
Conductivity
k, W/m · K
Thermal
Diffusivity
a, m2/s
50
0
50
100
150
200
300
400
500
1000
1500
2000
1.5299
1.2498
1.0564
0.9149
0.8068
0.7215
0.5956
0.5072
0.4416
0.2681
0.1925
0.1502
957.3
1035
1042
1041
1043
1050
1070
1095
1120
1213
1266
1297
0.02001
0.02384
0.02746
0.03090
0.03416
0.03727
0.04309
0.04848
0.05358
0.07938
0.11793
0.18590
1.366
1.843
2.494
3.244
4.058
4.921
6.758
8.727
1.083
2.440
4.839
9.543
50
0
50
100
150
200
300
400
500
1000
1500
2000
1.7475
1.4277
1.2068
1.0451
0.9216
0.8242
0.6804
0.5793
0.5044
0.3063
0.2199
0.1716
984.4
928.7
921.7
931.8
947.6
964.7
997.1
1025
1048
1121
1165
1201
0.02067
0.02472
0.02867
0.03254
0.03637
0.04014
0.04751
0.05463
0.06148
0.09198
0.11901
0.14705
1.201
1.865
2.577
3.342
4.164
5.048
7.003
9.204
1.163
2.678
4.643
7.139
Dynamic
Viscosity
m, kg/m · s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
Nitrogen, N2
105
105
105
105
105
105
105
105
104
104
104
104
1.390
1.640
1.874
2.094
2.300
2.494
2.849
3.166
3.451
4.594
5.562
6.426
105
105
105
105
105
105
105
105
105
105
105
105
9.091
1.312
1.774
2.289
2.851
3.457
4.783
6.242
7.816
1.713
2.889
4.278
106
105
105
105
105
105
105
105
105
104
104
104
0.6655
0.7121
0.7114
0.7056
0.7025
0.7025
0.7078
0.7153
0.7215
0.7022
0.5969
0.4483
1.616
1.916
2.194
2.451
2.694
2.923
3.350
3.744
4.114
5.732
7.133
8.417
105
105
105
105
105
105
105
105
105
105
105
105
9.246
1.342
1.818
2.346
2.923
3.546
4.923
6.463
8.156
1.871
3.243
4.907
106
105
105
105
105
105
105
105
105
104
104
104
0.7694
0.7198
0.7053
0.7019
0.7019
0.7025
0.7030
0.7023
0.7010
0.6986
0.6985
0.6873
7.187
8.956
1.078
1.265
1.456
1.650
2.045
2.446
2.847
4.762
6.411
7.808
106
106
105
105
105
105
105
105
105
105
105
105
7.305
1.114
1.587
2.150
2.806
3.556
5.340
7.498
1.002
2.761
5.177
8.084
106
105
105
105
105
105
105
105
104
104
104
104
1.0047
1.0033
0.9944
0.9830
0.9712
0.9599
0.9401
0.9240
0.9108
0.8639
0.8233
0.7833
Oxygen, O2
105
105
105
105
105
105
105
105
104
104
104
104
Water Vapor, H2O
50
0
50
100
150
200
300
400
500
1000
1500
2000
0.9839
0.8038
0.6794
0.5884
0.5189
0.4640
0.3831
0.3262
0.2840
0.1725
0.1238
0.0966
1892
1874
1874
1887
1908
1935
1997
2066
2137
2471
2736
2928
0.01353
0.01673
0.02032
0.02429
0.02861
0.03326
0.04345
0.05467
0.06677
0.13623
0.21301
0.29183
7.271
1.110
1.596
2.187
2.890
3.705
5.680
8.114
1.100
3.196
6.288
1.032
106
105
105
105
105
105
105
105
104
104
104
103
Note: For ideal gases, the properties cp, k, m, and Pr are independent of pressure. The properties r, n, and a at a pressure P (in atm) other than 1 atm are
determined by multiplying the values of r at the given temperature by P and by dividing n and a by P.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Originally based on various sources.
cen72367_appx1.qxd 11/17/04 4:34 PM Page 897
897
APPENDIX 1
TABLE A–11
Properties of the atmosphere at high altitude
Altitude,
m
Temperature,
°C
Pressure,
kPa
Gravity
g, m/s2
Speed of
Sound,
m/s
Density,
kg/m3
Viscosity
m, kg/m · s
Thermal
Conductivity,
W/m · K
0
200
400
600
800
15.00
13.70
12.40
11.10
9.80
101.33
98.95
96.61
94.32
92.08
9.807
9.806
9.805
9.805
9.804
340.3
339.5
338.8
338.0
337.2
1.225
1.202
1.179
1.156
1.134
1.789
1.783
1.777
1.771
1.764
105
105
105
105
105
0.0253
0.0252
0.0252
0.0251
0.0250
1000
1200
1400
1600
1800
8.50
7.20
5.90
4.60
3.30
89.88
87.72
85.60
83.53
81.49
9.804
9.803
9.802
9.802
9.801
336.4
335.7
334.9
334.1
333.3
1.112
1.090
1.069
1.048
1.027
1.758
1.752
1.745
1.739
1.732
105
105
105
105
105
0.0249
0.0248
0.0247
0.0245
0.0244
2000
2200
2400
2600
2800
2.00
0.70
0.59
1.89
3.19
79.50
77.55
75.63
73.76
71.92
9.800
9.800
9.799
9.799
9.798
332.5
331.7
331.0
330.2
329.4
1.007
0.987
0.967
0.947
0.928
1.726
1.720
1.713
1.707
1.700
105
105
105
105
105
0.0243
0.0242
0.0241
0.0240
0.0239
3000
3200
3400
3600
3800
4.49
5.79
7.09
8.39
9.69
70.12
68.36
66.63
64.94
63.28
9.797
9.797
9.796
9.796
9.795
328.6
327.8
327.0
326.2
325.4
0.909
0.891
0.872
0.854
0.837
1.694
1.687
1.681
1.674
1.668
105
105
105
105
105
0.0238
0.0237
0.0236
0.0235
0.0234
4000
4200
4400
4600
4800
10.98
12.3
13.6
14.9
16.2
61.66
60.07
58.52
57.00
55.51
9.794
9.794
9.793
9.793
9.792
324.6
323.8
323.0
322.2
321.4
0.819
0.802
0.785
0.769
0.752
1.661
1.655
1.648
1.642
1.635
105
105
105
105
105
0.0233
0.0232
0.0231
0.0230
0.0229
5000
5200
5400
5600
5800
17.5
18.8
20.1
21.4
22.7
54.05
52.62
51.23
49.86
48.52
9.791
9.791
9.790
9.789
9.785
320.5
319.7
318.9
318.1
317.3
0.736
0.721
0.705
0.690
0.675
1.628
1.622
1.615
1.608
1.602
105
105
105
105
105
0.0228
0.0227
0.0226
0.0224
0.0223
6000
6200
6400
6600
6800
24.0
25.3
26.6
27.9
29.2
47.22
45.94
44.69
43.47
42.27
9.788
9.788
9.787
9.786
9.785
316.5
315.6
314.8
314.0
313.1
0.660
0.646
0.631
0.617
0.604
1.595
1.588
1.582
1.575
1.568
105
105
105
105
105
0.0222
0.0221
0.0220
0.0219
0.0218
7000
8000
9000
30.5
36.9
43.4
41.11
35.65
30.80
9.785
9.782
9.779
312.3
308.1
303.8
0.590
0.526
0.467
1.561 105
1.527 105
1.493 105
0.0217
0.0212
0.0206
10,000
12,000
14,000
16,000
18,000
49.9
56.5
56.5
56.5
56.5
26.50
19.40
14.17
10.53
7.57
9.776
9.770
9.764
9.758
9.751
299.5
295.1
295.1
295.1
295.1
0.414
0.312
0.228
0.166
0.122
1.458
1.422
1.422
1.422
1.422
105
105
105
105
105
0.0201
0.0195
0.0195
0.0195
0.0195
Source: U.S. Standard Atmosphere Supplements, U.S. Government Printing Office, 1966. Based on year-round mean conditions at 45° latitude and varies with
the time of the year and the weather patterns. The conditions at sea level (z 0) are taken to be P 101.325 kPa, T 15°C, r 1.2250 kg/m3,
g 9.80665 m2/s.
0.008
0.009
f
0
0.003–0.03
0.0016
0.000033
0.000005
0.00085
0.0005
0.00015
0.000007
0.00015
0
0.9–9
0.5
0.01
0.0015
0.26
0.15
0.046
0.002
0.045
mm
Roughness, e
Smooth pipes
e/D = 0
e/D = 0.000001
Fully rough turbulent flow ( f levels off )
e/D = 0.000005
0.00005
0.0001
0.0002
0.001
0.0008
0.0006
0.0004
0.002
0.004
0.01
0.008
0.006
0.015
0.02
0.03
0.05
0.04
L V2
. Friction factors in the
The Moody chart for the friction factor for fully developed flow in circular pipes for use in the head loss relation hL f
D 2g
1
e/D
2.51
2 log10 a
b.
turbulent flow are evaluated from the Colebrook equation
3.7 Re 1f
1f
Reynolds number, Re
0.00001
3
4
5
6
7
103 2(10 ) 3 4 5 6 8 104 2(10 ) 3 4 5 6 8 105 2(10 ) 3 4 5 6 8 106 2(10 ) 3 4 5 6 8 107 2(10 ) 3 4 5 6 8 108
ft
Material
Glass, plastic
Concrete
Wood stave
Rubber, smoothed
Copper or brass tubing
Cast iron
Galvanized iron
Wrought iron
Stainless steel
Commercial steel
e
0.01
64/R
0.015
0.02
0.025
inar
0.03
0.04
0.05
0.06
0.07
0.08
Laminar Transitional Turbulent
flow
flow
flow
Lam
f=
low,
FIGURE A–12
Darcy friction factor, f
0.1
0.09
cen72367_appx1.qxd 11/17/04 4:34 PM Page 898
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FLUID MECHANICS
Relative roughness, e/D
cen72367_appx1.qxd 11/17/04 4:34 PM Page 899
899
APPENDIX 1
k1
Ma* Ma
B 2 (k 1)Ma2
0.5(k1)(k1)
A
1
2
k1
ca
b a1 Ma2bd
A* Ma k 1
2
k(k1)
P
k1
a1 Ma2b
P0
2
1(k1)
r
k1
a1 Ma2b
r0
2
1
T
k1
a1 Ma2b
T0
2
TABLE A–13
One-dimensional isentropic compressible flow functions for an ideal
gas with k 1.4
Ma
Ma*
A/A*
P/P0
r/r0
T/T0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
5.0
0
0.1094
0.2182
0.3257
0.4313
0.5345
0.6348
0.7318
0.8251
0.9146
1.0000
1.1583
1.2999
1.4254
1.5360
1.6330
1.7179
1.7922
1.8571
1.9140
1.9640
2.2361
2.2495
5.8218
2.9635
2.0351
1.5901
1.3398
1.1882
1.0944
1.0382
1.0089
1.0000
1.0304
1.1149
1.2502
1.4390
1.6875
2.0050
2.4031
2.8960
3.5001
4.2346
25.000
1.0000
0.9930
0.9725
0.9395
0.8956
0.8430
0.7840
0.7209
0.6560
0.5913
0.5283
0.4124
0.3142
0.2353
0.1740
0.1278
0.0935
0.0684
0.0501
0.0368
0.0272
0.0019
0
1.0000
0.9950
0.9803
0.9564
0.9243
0.8852
0.8405
0.7916
0.7400
0.6870
0.6339
0.5311
0.4374
0.3557
0.2868
0.2300
0.1841
0.1472
0.1179
0.0946
0.0760
0.0113
0
1.0000
0.9980
0.9921
0.9823
0.9690
0.9524
0.9328
0.9107
0.8865
0.8606
0.8333
0.7764
0.7184
0.6614
0.6068
0.5556
0.5081
0.4647
0.4252
0.3894
0.3571
0.1667
0
3.0
A/A*
Compressible flow functions
2.5
2.0
Ma*
1.5
1.0
T/T0
0.5
r/r*
P/P0
0
0
0.5
1.0
1.5
Ma
2.0
2.5
3.0
cen72367_appx1.qxd 11/17/04 4:34 PM Page 900
900
FLUID MECHANICS
T01 T02
TABLE A–14
(k 1)Ma21 2
Ma2 B 2kMa21 k 1
One-dimensional normal shock functions for an ideal gas with k 1.4
P 2 1 kMa21 2kMa21 k 1
P 1 1 kMa22
k1
r 2 P 2P 1
(k 1)Ma21
V1
r1
T2T1
2 (k 1)Ma21 V2
T2 2 Ma21(k 1)
T1 2 Ma22(k 1)
P 02 Ma1 1 Ma22(k 1)2 (k 1)/[2(k 1)]
c
d
P 01 Ma2 1 Ma21(k 1)2
P 02 (1 kMa21)[1 Ma22(k 1)2]k(k1)
P1
1 kMa22
Ma1
Ma2
P2/P1
r2/r1
T2/T1
P02/P01
P02/P1
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
4.0
5.0
1.0000
0.9118
0.8422
0.7860
0.7397
0.7011
0.6684
0.6405
0.6165
0.5956
0.5774
0.5613
0.5471
0.5344
0.5231
0.5130
0.5039
0.4956
0.4882
0.4814
0.4752
0.4350
0.4152
0.3780
1.0000
1.2450
1.5133
1.8050
2.1200
2.4583
2.8200
3.2050
3.6133
4.0450
4.5000
4.9783
5.4800
6.0050
6.5533
7.1250
7.7200
8.3383
8.9800
9.6450
10.3333
18.5000
29.000
1.0000
1.1691
1.3416
1.5157
1.6897
1.8621
2.0317
2.1977
2.3592
2.5157
2.6667
2.8119
2.9512
3.0845
3.2119
3.3333
3.4490
3.5590
3.6636
3.7629
3.8571
4.5714
5.0000
6.0000
1.0000
1.0649
1.1280
1.1909
1.2547
1.3202
1.3880
1.4583
1.5316
1.6079
1.6875
1.7705
1.8569
1.9468
2.0403
2.1375
2.2383
2.3429
2.4512
2.5632
2.6790
4.0469
5.8000
1.0000
0.9989
0.9928
0.9794
0.9582
0.9298
0.8952
0.8557
0.8127
0.7674
0.7209
0.6742
0.6281
0.5833
0.5401
0.4990
0.4601
0.4236
0.3895
0.3577
0.3283
0.1388
0.0617
0
1.8929
2.1328
2.4075
2.7136
3.0492
3.4133
3.8050
4.2238
4.6695
5.1418
5.6404
6.1654
6.7165
7.2937
7.8969
8.5261
9.1813
9.8624
10.5694
11.3022
12.0610
21.0681
32.6335
5.0
P02 /P1
P2 /P1
Normal shock functions
4.0
r2 /r1
3.0
T2/T1
2.0
1.0
Ma2
P02/P01
0
1.0
1.5
2.0
Ma1
2.5
3.0
cen72367_appx1.qxd 11/17/04 4:34 PM Page 901
901
APPENDIX 1
T0
(k 1)Ma2[2 (k 1)Ma2]
T 0*
(1 kMa2)2
TABLE A–15
P0
2 (k 1)Ma2 k(k1)
k1
a
b
2
P*0 1 kMa
k1
Ma
T0/T 0*
P0/P 0*
T/T*
P/P*
V/V*
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0.0000
0.0468
0.1736
0.3469
0.5290
0.6914
0.8189
0.9085
0.9639
0.9921
1.0000
0.9787
0.9343
0.8842
0.8363
0.7934
0.7561
0.7242
0.6970
0.6738
0.6540
1.2679
1.2591
1.2346
1.1985
1.1566
1.1141
1.0753
1.0431
1.0193
1.0049
1.0000
1.0194
1.0777
1.1756
1.3159
1.5031
1.7434
2.0451
2.4177
2.8731
3.4245
0.0000
0.0560
0.2066
0.4089
0.6151
0.7901
0.9167
0.9929
1.0255
1.0245
1.0000
0.9118
0.8054
0.7017
0.6089
0.5289
0.4611
0.4038
0.3556
0.3149
0.2803
2.4000
2.3669
2.2727
2.1314
1.9608
1.7778
1.5957
1.4235
1.2658
1.1246
1.0000
0.7958
0.6410
0.5236
0.4335
0.3636
0.3086
0.2648
0.2294
0.2004
0.1765
0.0000
0.0237
0.0909
0.1918
0.3137
0.4444
0.5745
0.6975
0.8101
0.9110
1.0000
1.1459
1.2564
1.3403
1.4046
1.4545
1.4938
1.5252
1.5505
1.5711
1.5882
1k
P
P* 1 kMa2
r* (1 k)Ma2
V
r
V*
1 kMa2
3.5
P0 /P0*
3.0
2.5
Rayleigh flow functions
Ma(1 k) 2
T
a
b
T*
1 kMa2
Rayleigh flow functions for an ideal gas with k 1.4
2.0
V/V*
1.5
1.0
T0 /T 0*
0.5
T/T *
P/P*
0
0
0.5
1.0
1.5
Ma
2.0
2.5
3.0
cen72367_appx1.qxd 11/17/04 4:34 PM Page 902
902
FLUID MECHANICS
T0 T *0
TABLE A–16
r0
P0
1 2 (k 1)Ma2 (k1)/2(k 1)
a
b
P*
r*
Ma
k1
0
0
Fanno flow functions for an ideal gas with k 1.4
k1
T
T* 2 (k 1)Ma2
1/2
1
k1
P
a
b
2
P* Ma 2 (k 1)Ma
1/2
r*
V
k1
b
Ma a
r
V*
2 (k 1)Ma2
fL* 1 Ma2 k 1
(k 1)Ma2
ln
D
2k
kMa2
2 (k 1)Ma2
Ma
P0/P 0*
T/T*
P/P*
V/V*
fL*/D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
5.8218
2.9635
2.0351
1.5901
1.3398
1.1882
1.0944
1.0382
1.0089
1.0000
1.0304
1.1149
1.2502
1.4390
1.6875
2.0050
2.4031
2.8960
3.5001
4.2346
1.2000
1.1976
1.1905
1.1788
1.1628
1.1429
1.1194
1.0929
1.0638
1.0327
1.0000
0.9317
0.8621
0.7937
0.7282
0.6667
0.6098
0.5576
0.5102
0.4673
0.4286
10.9435
5.4554
3.6191
2.6958
2.1381
1.7634
1.4935
1.2893
1.1291
1.0000
0.8044
0.6632
0.5568
0.4741
0.4082
0.3549
0.3111
0.2747
0.2441
0.2182
0.0000
0.1094
0.2182
0.3257
0.4313
0.5345
0.6348
0.7318
0.8251
0.9146
1.0000
1.1583
1.2999
1.4254
1.5360
1.6330
1.7179
1.7922
1.8571
1.9140
1.9640
66.9216
14.5333
5.2993
2.3085
1.0691
0.4908
0.2081
0.0723
0.0145
0.0000
0.0336
0.0997
0.1724
0.2419
0.3050
0.3609
0.4099
0.4526
0.4898
0.5222
3.0
P0 /P 0*
Fanno flow functions
2.5
2.0
V/V *
1.5
1.0
T/T *
0.5
fL*/D
P/P*
0
0
0.5
1.0
1.5
Ma
2.0
2.5
3.0