Using Superheat Tables
Water at the rate of 50 kg/s is to be heated, vaporized, and superheated in a pressurized boiler from 20°C to 150°C at a pressure of 0.3 MPa. If the boiler efficiency is 90%, determine the amount of heat input to the boiler?
Given: T_{i} = 20°C (subcooled), T_{o} = 150°C (superheated), \eta = 0.9
Assumptions: The enthalpy of subcooled liquid is equal to that of the saturated liquid at the same temperature.
Lookup values: From Table A4 (p = 0.3 MPa and T = 150°C), enthalpy h_{o} = 2761.0 kJ/kg and from Table A3 (saturated steam table for T = 20°C), h_{i} = 10.42 kJ/kg (interpolated).
Find: Q_{in}
TABLE A.3 (IP Units) Properties of Saturated Steam | ||||||||||||
Pressure (psia) | Saturation Temp. (°F) | Specific Volume (ft³/lb_{m}) |
Internal Energy (Btu/lb_{m}) | Enthalpy (Btu/lb_{m}) | Entropy (Btu/(lb_{m} · °R)) | |||||||
Sat. Liquid | Sat. Vapor | Sat. Liquid | Evap. | Sat. Vapor | Sat. Liquid | Evap. | Sat. Vapor | Sat. Liquid | Evap. | Sat. Vapor | ||
p | Tsat | vf | vg | uf | ufg | ug | hf | hfg | hg | sf | sfg | sg |
0.08866 | 32.02 | 0.016022 | 3302 | 0.00 | 1021.2 | 1021.2 | 0.01 | 1075.4 | 1075.4 | 0.00000 | 2.1869 | 2.1869 |
0.09992 | 35.00 | 0.016021 | 2948 | 2.99 | 1019.2 | 1022.2 | 3.00 | 1073.7 | 1076.7 | 0.00607 | 2.1704 | 2.1764 |
0.12166 | 40.00 | 0.016020 | 2445 | 8.02 | 1015.8 | 1023.9 | 8.02 | 1070.9 | 1078.9 | 0.01617 | 2.1430 | 2.1592 |
0.14748 | 45.00 | 0.016021 | 2037 | 13.04 | 1012.5 | 1025.5 | 13.04 | 1068.1 | 1081.1 | 0.02618 | 2.1162 | 2.1423 |
0.17803 | 50.00 | 0.016024 | 1704.2 | 18.06 | 1009.1 | 1027.2 | 18.06 | 1065.2 | 1083.3 | 0.03607 | 2.0899 | 2.1259 |
0.2563 | 60.00 | 0.016035 | 1206.9 | 28.08 | 1002.4 | 1030.4 | 28.08 | 1059.6 | 1087.7 | 0.05555 | 2.0388 | 2.0943 |
0.3632 | 70.00 | 0.016051 | 867.7 | 38.09 | 995.6 | 1033.7 | 38.09 | 1054.0 | 1092.0 | 0.07463 | 1.9896 | 2.0642 |
0.5073 | 80.00 | 0.016073 | 632.8 | 48.08 | 988.9 | 1037.0 | 48.09 | 1048.3 | 1096.4 | 0.09332 | 1.9423 | 2.0356 |
0.6988 | 90.00 | 0.016099 | 467.7 | 58.07 | 982.2 | 1040.2 | 58.07 | 1042.7 | 1100.7 | 0.11165 | 1.8966 | 2.0083 |
0.9503 | 100.00 | 0.016130 | 350.0 | 68.04 | 975.4 | 1043.5 | 68.05 | 1037.0 | 1105.0 | 0.12963 | 1.8526 | 1.9822 |
1 | 101.70 | 0.016136 | 333.6 | 69.74 | 974.3 | 1044.0 | 69.74 | 1036.0 | 1105.8 | 0.13266 | 1.8453 | 1.9779 |
2 | 126.04 | 0.016230 | 173.75 | 94.02 | 957.8 | 1051.8 | 94.02 | 1022.1 | 1116.1 | 0.17499 | 1.7448 | 1.9198 |
3 | 141.43 | 0.016300 | 118.72 | 109.38 | 947.2 | 1056.6 | 109.39 | 1013.1 | 1122.5 | 0.20089 | 1.6852 | 1.8861 |
4 | 152.93 | 0.016358 | 90.64 | 120.88 | 939.3 | 1060.2 | 120.89 | 1006.4 | 1127.3 | 0.21983 | 1.6426 | 1.8624 |
5 | 162.21 | 0.016407 | 73.53 | 130.15 | 932.9 | 1063.0 | 130.17 | 1000.9 | 1131.0 | 0.23486 | 1.6093 | 1.8441 |
6 | 170.03 | 0.016451 | 61.98 | 137.98 | 927.4 | 1065.4 | 138.00 | 996.2 | 1134.2 | 0.24736 | 1.5819 | 1.8292 |
8 | 192.84 | 0.016526 | 47.35 | 150.81 | 918.4 | 1069.2 | 150.84 | 988.4 | 1139.3 | 0.26754 | 1.5383 | 1.8058 |
10 | 193.19 | 0.016590 | 38.42 | 161.20 | 911.0 | 1072.2 | 161.23 | 982.1 | 1143.3 | 0.28358 | 1.5041 | 1.7877 |
14.696 | 211.99 | 0.016715 | 26.80 | 180.10 | 897.5 | 1077.6 | 180.15 | 970.4 | 1150.5 | 0.31212 | 1.4446 | 1.7567 |
15 | 213.03 | 0.016723 | 26.29 | 181.14 | 896.8 | 1077.9 | 181.19 | 969.7 | 1150.9 | 0.31367 | 1.4414 | 1.7551 |
20 | 227.96 | 0.016830 | 20.09 | 196.19 | 885.8 | 1082.0 | 196.26 | 960.1 | 1156.4 | 0.33580 | 1.3962 | 1.7320 |
25 | 240.08 | 0.016922 | 16.306 | 208.44 | 876.9 | 1085.3 | 208.52 | 952.2 | 1160.7 | 0.35345 | 1.3607 | 1.7142 |
30 | 250.34 | 0.017004 | 13.748 | 218.84 | 869.2 | 1088.0 | 218.93 | 945.4 | 1164.3 | 0.36821 | 1.3314 | 1.6996 |
35 | 259.30 | 0.017073 | 11.900 | 227.93 | 862.4 | 1090.3 | 228.04 | 939.3 | 1167.4 | 0.38093 | 1.3064 | 1.6873 |
40 | 267.26 | 0.017146 | 10.501 | 236.03 | 856.2 | 1092.3 | 236.16 | 933.8 | 1170.0 | 0.39214 | 1.2845 | 1.6767 |
45 | 274.46 | 0.017209 | 9.403 | 243.37 | 850.7 | 1094.0 | 243.51 | 928.8 | 1172.3 | 0.40218 | 1.2651 | 1.6673 |
50 | 281.03 | 0.017269 | 8.518 | 250.08 | 845.5 | 1095.6 | 250.24 | 924.2 | 1174.4 | 0.41129 | 1.2476 | 1.6589 |
55 | 287.10 | 0.017325 | 7.789 | 256.28 | 840.8 | 1097.0 | 256.46 | 919.9 | 1176.3 | 0.41963 | 1.2317 | 1.6513 |
60 | 292.73 | 0.017378 | 7.177 | 262.06 | 836.3 | 1098.3 | 262.25 | 915.8 | 1178.0 | 0.42733 | 1.2170 | 1.6444 |
65 | 298.00 | 0.017429 | 6.657 | 267.46 | 832.1 | 1099.5 | 267.67 | 911.9 | 1179.6 | 0.43450 | 1.2035 | 1.6380 |
70 | 302.96 | 0.017478 | 6.209 | 272.56 | 828.1 | 1100.6 | 272.79 | 908.3 | 1181.0 | 0.44120 | 1.1909 | 1.6321 |
75 | 307.63 | 0.017524 | 5.818 | 277.37 | 824.3 | 1101.6 | 277.61 | 904.8 | 1182.4 | 0.44749 | 1.1790 | 1.6265 |
80 | 312.07 | 0.017570 | 5.474 | 281.95 | 820.6 | 1102.6 | 282.21 | 901.4 | 1183.6 | 0.45344 | 1.1679 | 1.6214 |
85 | 316.29 | 0.017613 | 5.17 | 286.3 | 817.1 | 1103.5 | 286.58 | 898.2 | 1184.8 | 0.45907 | 1.1574 | 1.6165 |
90 | 320.31 | 0.017655 | 4.898 | 290.46 | 813.8 | 1104.3 | 290.76 | 895.1 | 1185.9 | 0.46442 | 1.1475 | 1.6119 |
95 | 324.16 | 0.017696 | 4.654 | 294.45 | 810.6 | 1105.0 | 294.76 | 892.1 | 1186.9 | 0.46952 | 1.1380 | 1.6076 |
100 | 327.86 | 0.017736 | 4.434 | 298.28 | 807.5 | 1105.8 | 298.61 | 889.2 | 1187.8 | 0.47439 | 1.1290 | 1.6034 |
110 | 334.82 | 0.017813 | 4.051 | 305.52 | 801.6 | 1107.1 | 305.88 | 883.7 | 1189.6 | 0.48355 | 1.1122 | 1.5957 |
120 | 341.30 | 0.017886 | 3.73 | 312.27 | 796 | 1108.3 | 312.67 | 878.5 | 1191.1 | 0.49201 | 1.0966 | 1.5886 |
130 | 347.37 | 0.017957 | 3.457 | 318.61 | 790.7 | 1109.4 | 319.04 | 873.5 | 1192.5 | 0.49989 | 1.0822 | 1.5821 |
140 | 353.08 | 0.018024 | 3.221 | 324.58 | 785.7 | 1110.3 | 325.05 | 868.7 | 1193.8 | 0.50727 | 1.0688 | 1.5761 |
150 | 358.48 | 0.018089 | 3.016 | 330.24 | 781 | 1111.2 | 330.75 | 864.2 | 1194.9 | 0.51422 | 1.0562 | 1.5704 |
0.6113 | 0.01 | 0.001 | 206.14 | 0 | 2375.3 | 2375.3 | 0.01 | 2501.3 | 2501.4 | 0 | 9.1562 | 9.1562 |
1.0 | 6.98 | 0.001 | 129.21 | 29.30 | 2355.7 | 2385.0 | 29.30 | 2484.9 | 2514.2 | 0.1059 | 8.8697 | 8.9756 |
1.5 | 13.03 | 0.001001 | 87.98 | 54.71 | 2338.6 | 2393.3 | 54.71 | 2470.6 | 2525.3 | 0.1957 | 8.6322 | 8.8279 |
2.0 | 17.50 | 0.001001 | 67.00 | 73.48 | 2326.0 | 2399.5 | 73.48 | 2460.0 | 2533.5 | 0.2607 | 8.4629 | 8.7237 |
2.5 | 21.08 | 0.001002 | 54.25 | 88.48 | 2315.9 | 2404.4 | 88.49 | 2451.6 | 2540.4 | 0.3120 | 8.3311 | 8.6432 |
3.0 | 24.08 | 0.001003 | 45.67 | 101.04 | 2307.5 | 2408.5 | 101.05 | 2444.5 | 2545.5 | 0.3545 | 8.2231 | 8.5776 |
4.0 | 28.96 | 0.001004 | 34.80 | 121.45 | 2293.7 | 2415.2 | 121.46 | 2432.9 | 2554.4 | 0.4226 | 8.0520 | 8.4746 |
5.0 | 32.88 | 0.001005 | 28.19 | 137.81 | 2282.7 | 2420.5 | 137.82 | 2423.7 | 2561.5 | 0.4764 | 7.9187 | 8.3951 |
7.5 | 40.29 | 0.001008 | 19.24 | 168.78 | 2261.7 | 2430.5 | 168.79 | 2406.0 | 2574.8 | 0.5764 | 7.6750 | 8.2515 |
10 | 45.81 | 0.001010 | 14.67 | 191.82 | 2246.1 | 2437.9 | 191.83 | 2392.8 | 2584.7 | 0.6493 | 7.5009 | 8.1502 |
15 | 53.97 | 0.001014 | 10.02 | 225.92 | 2222.8 | 2448.7 | 225.94 | 2373.1 | 2599.1 | 0.7549 | 7.2536 | 8.0085 |
20 | 60.06 | 0.001017 | 7.649 | 251.38 | 2205.4 | 2456.7 | 251.40 | 2358.3 | 2609.7 | 0.8320 | 7.0766 | 7.9085 |
25 | 64.97 | 0.001020 | 6.204 | 271.90 | 2191.2 | 2463.1 | 271.93 | 2346.3 | 2618.2 | 0.8931 | 6.9383 | 7.8314 |
30 | 69.10 | 0.001022 | 5.229 | 289.20 | 2179.2 | 2468.4 | 289.23 | 2336.1 | 2625.3 | 0.9439 | 6.8247 | 7.7686 |
40 | 75.87 | 0.001027 | 3.993 | 317.53 | 2159.5 | 2477.0 | 317.58 | 2319.2 | 2636.8 | 1.0259 | 6.6441 | 7.6700 |
50 | 81.33 | 0.001030 | 3.240 | 340.44 | 2143.4 | 2483.9 | 340.49 | 2305.4 | 2645.9 | 1.0910 | 6.5029 | 7.5939 |
75 | 91.78 | 0.001037 | 2.217 | 384.31 | 2112.4 | 2496.7 | 384.39 | 2278.6 | 2663.0 | 1.2130 | 6.2434 | 7.4564 |
100 | 99.63 | 0.001043 | 1.6940 | 417.36 | 2088.7 | 2506.1 | 417.46 | 2258.0 | 2675.5 | 1.3026 | 6.0568 | 7.3594 |
125 | 105.99 | 0.001048 | 1.3749 | 444.19 | 2069.3 | 2513.5 | 444.32 | 2241.0 | 2685.4 | 1.3740 | 5.9104 | 7.2844 |
150 | 111.37 | 0.001053 | 1.1593 | 466.94 | 2052.7 | 2519.7 | 467.11 | 2226.5 | 2693.6 | 1.4336 | 5.7897 | 7.2233 |
175 | 116.06 | 0.001057 | 1.0036 | 486.8 | 2038.1 | 2524.9 | 486.99 | 2213.6 | 2700.6 | 1.4849 | 5.6868 | 7.1717 |
200 | 120.23 | 0.001061 | 0.8857 | 504.49 | 2025.0 | 2529.5 | 504.70 | 2201.9 | 2706.7 | 1.5301 | 5.5970 | 7.1271 |
225 | 124 | 0.001064 | 0.7933 | 520.47 | 2013.1 | 2533.6 | 520.72 | 2191.3 | 2712.1 | 1.5706 | 5.5173 | 7.0878 |
250 | 127.44 | 0.001067 | 0.7187 | 535.10 | 2002.1 | 2537.2 | 535.37 | 2181.5 | 2716.9 | 1.6072 | 5.4455 | 7.0527 |
275 | 130.6 | 0.001070 | 0.6573 | 548.59 | 1991.9 | 2540.5 | 548.89 | 2172.4 | 2721.3 | 1.6408 | 5.3801 | 7.0209 |
300 | 133.55 | 0.001073 | 0.6058 | 561.15 | 1982.4 | 2543.6 | 561.47 | 2163.8 | 2725.3 | 1.6718 | 5.3201 | 6.9919 |
325 | 136.3 | 0.001076 | 0.5620 | 572.90 | 1973.5 | 2546.4 | 573.25 | 2155.8 | 2729.0 | 1.7006 | 5.2646 | 6.9652 |
350 | 138.88 | 0.001079 | 0.5243 | 583.95 | 1965.0 | 2548.9 | 584.33 | 2148.1 | 2732.4 | 1.7275 | 5.2130 | 6.9405 |
375 | 141.32 | 0.001081 | 0.4914 | 594.40 | 1956.9 | 2551.3 | 594.81 | 2140.8 | 2735.6 | 1.7528 | 5.1647 | 6.9175 |
400 | 143.63 | 0.001084 | 0.4625 | 604.31 | 1949.3 | 2553.6 | 604.74 | 2133.8 | 2738.6 | 1.7766 | 5.1193 | 6.8959 |
450 | 147.93 | 0.001088 | 0.4140 | 622.77 | 1934.9 | 2557.6 | 623.25 | 2120.7 | 2743.9 | 1.8207 | 5.0359 | 6.8565 |
500 | 151.86 | 0.001093 | 0.3749 | 639.68 | 1921.6 | 2561.2 | 640.23 | 2108.5 | 2748.7 | 1.8607 | 4.9606 | 6.8213 |
550 | 155.48 | 0.001097 | 0.3427 | 655.32 | 1909.2 | 2564.5 | 655.93 | 2097.0 | 2753.0 | 1.8973 | 4.8920 | 6.7893 |
600 | 158.85 | 0.001101 | 0.3157 | 669.90 | 1897.5 | 2567.4 | 670.56 | 2086.3 | 2756.8 | 1.9312 | 4.8288 | 6.7600 |
650 | 162.01 | 0.001104 | 0.2927 | 683.56 | 1886.5 | 2570.1 | 684.28 | 2076.0 | 2760.3 | 1.9627 | 4.7703 | 6.7331 |
700 | 164.97 | 0.001108 | 0.2729 | 696.44 | 1876.1 | 2572.5 | 697.22 | 2066.3 | 2763.5 | 1.9922 | 4.7158 | 6.7080 |
750 | 167.78 | 0.001112 | 0.2556 | 708.64 | 1866.1 | 2574.7 | 709.47 | 2057.0 | 2766.4 | 2.0200 | 4.6647 | 6.6847 |
800 | 170.43 | 0.001115 | 0.2404 | 720.22 | 1856.6 | 2576.8 | 721.11 | 2048.0 | 2769.1 | 2.0462 | 4.6166 | 6.6628 |
850 | 172.96 | 0.001118 | 0.2270 | 731.27 | 1847.4 | 2578.7 | 732.22 | 2039.4 | 2771.6 | 2.0710 | 4.5711 | 6.6421 |
900 | 175.38 | 0.001121 | 0.2150 | 741.83 | 1838.6 | 2580.5 | 742.83 | 2031.1 | 2773.9 | 2.0946 | 4.5280 | 6.6226 |
950 | 177.69 | 0.001124 | 0.2042 | 751.95 | 1830.2 | 2582.1 | 753.02 | 2023.1 | 2776.1 | 2.1172 | 4.4869 | 6.6041 |
1000 | 179.91 | 0.001127 | 0.19444 | 761.68 | 1822.0 | 2583.6 | 762.81 | 2015.3 | 2778.1 | 2.1387 | 4.4478 | 6.5865 |
1100 | 184.09 | 0.001133 | 0.17753 | 780.09 | 1806.3 | 2586.4 | 781.34 | 2000.4 | 2781.7 | 2.1792 | 4.3744 | 6.5536 |
1200 | 187.99 | 0.001139 | 0.16333 | 797.29 | 1791.5 | 2588.8 | 798.65 | 1986.2 | 2784.8 | 2.2166 | 4.3067 | 6.5233 |
1300 | 191.64 | 0.001144 | 0.15125 | 813.44 | 1777.5 | 2591.0 | 814.93 | 1972.7 | 2787.6 | 2.2515 | 4.2438 | 6.4953 |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. |
TABLE A.4 (IP Units) Properties of Superheated Steam |
|||||
Pressure (psia) | Temperature (°F) | v (ft3/lbm) | u (Btu/lbm) | h (Btu/lbm) | s (Btu/lbm · °R) |
1.0 | Sat. | 333.6 | 1044.0 | 1105.8 | 1.9779 |
(101.70°F) | 200 | 392.5 | 1077.5 | 1150.1 | 2.0508 |
240 | 416.4 | 1091.2 | 1168.3 | 2.0775 | |
280 | 440.3 | 1105.0 | 1186.5 | 2.1028 | |
320 | 464.2 | 1118.9 | 1204.8 | 2.1269 | |
360 | 488.1 | 1132.9 | 1223.2 | 2.1500 | |
400 | 511.9 | 1147.0 | 1241.8 | 2.1720 | |
440 | 535.8 | 1161.2 | 1260.4 | 2.1932 | |
500 | 571.5 | 1182.8 | 1288.5 | 2.2235 | |
600 | 631.1 | 1219.3 | 1336.1 | 2.2706 | |
700 | 690.7 | 1256.7 | 1384.5 | 2.3142 | |
800 | 750.3 | 1294.9 | 1433.7 | 2.3550 | |
1000 | 869.5 | 1373.9 | 1534.8 | 2.4294 | |
1200 | 988.6 | 1456.7 | 1639.6 | 2.4967 | |
1400 | 1107.7 | 1543.1 | 1748.1 | 2.5584 | |
5 | Sat. | 73.53 | 1063.0 | 1131.0 | 1.8441 |
(162.21°F) | 200 | 78.15 | 1076.3 | 1148.6 | 1.8715 |
240 | 83.00 | 1090.3 | 1167.1 | 1.8987 | |
280 | 81.83 | 1104.3 | 1185.5 | 1.9244 | |
320 | 92.64 | 1118.3 | 1204.0 | 1.9487 | |
360 | 97.45 | 1132.4 | 1222.6 | 1.9719 | |
400 | 102.24 | 1146.6 | 1241.2 | 1.9941 | |
440 | 107.03 | 1160.9 | 1259.9 | 2.0154 | |
500 | 114.20 | 1182.5 | 1288.2 | 2.0458 | |
600 | 126.15 | 1219.1 | 1335.8 | 2.0930 | |
700 | 138.08 | 1256.5 | 1384.3 | 2.1367 | |
800 | 150.01 | 1294.7 | 1433.5 | 2.1775 | |
1000 | 173.86 | 1373.9 | 1534.7 | 2.2520 | |
1200 | 197.70 | 1456.6 | 1639.5 | 2.3192 | |
1400 | 221.54 | 1543.1 | 1748.1 | 2.3810 | |
14.696 | Sat. | 26.80 | 1077.6 | 1150.5 | 1.7567 |
(211.99°F) | 240 | 28.00 | 1087.9 | 1164.0 | 1.7764 |
280 | 29.69 | 1102.4 | 1183.1 | 1.8030 | |
320 | 31.36 | 1116.8 | 1202.1 | 1.8280 | |
360 | 33.02 | 1131.2 | 1221.0 | 1.8516 | |
400 | 34.67 | 1145.6 | 1239.9 | 1.8741 | |
440 | 36.31 | 1160.1 | 1258.8 | 1.8956 | |
500 | 38.77 | 1181.8 | 1287.3 | 1.9263 | |
600 | 42.86 | 1218.6 | 1335.2 | 1.9737 | |
700 | 46.93 | 1256.1 | 1383.8 | 2.0175 | |
800 | 51.00 | 1294.4 | 1433.1 | 2.0584 | |
1000 | 59.13 | 1373.7 | 1534.5 | 2.1330 | |
1200 | 67.25 | 1456.5 | 1639.3 | 2.2003 | |
1400 | 75.36 | 1543.0 | 1747.9 | 2.2621 | |
1600 | 83.47 | 1633.2 | 1860.2 | 2.3194 | |
20 | Sat. | 20.09 | 1082.0 | 1156.4 | 1.7320 |
(227.96°F) | 240 | 20.47 | 1086.5 | 1162.3 | 1.7405 |
280 | 21.73 | 1101.4 | 1181.8 | 1.7676 | |
320 | 22.98 | 1116.0 | 1201.0 | 1.7930 | |
360 | 24.21 | 1130.6 | 1220.1 | 1.8168 | |
400 | 25.43 | 1145.1 | 1239.2 | 1.8395 | |
440 | 26.64 | 1159.6 | 1258.2 | 1.8611 | |
500 | 28.46 | 1181.5 | 1286.8 | 1.8919 | |
600 | 31.47 | 1218.4 | 1334.8 | 1.9395 | |
700 | 34.47 | 1255.9 | 1383.5 | 1.9834 | |
800 | 37.46 | 1294.3 | 1432.9 | 2.0243 | |
1000 | 43.44 | 1373.5 | 1534.3 | 2.0989 | |
1200 | 49.41 | 1456.4 | 1639.2 | 2.1663 | |
1400 | 55.37 | 1542.9 | 1747.9 | 2.2281 | |
1600 | 61.33 | 1633.2 | 1860.1 | 2.2854 | |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air- Conditioning Engineers, Atlanta, GA, 1997. With permission. |
TABLE A.4 (SI Units) Properties of Superheated Steam |
|||||
Pressure (MPa) | Temperature (°C) | v (m3/kg) | u (kJ/kg) | h (kJ/kg) | s (kJ/kg · K) |
0.01 | Sat. | 14.674 | 2437.9 | 2584.7 | 8.1502 |
50 | 14.869 | 2443.9 | 2592.6 | 8.1749 | |
100 | 17.196 | 2515.5 | 2687.5 | 8.4479 | |
150 | 19.512 | 2587.9 | 2783.0 | 8.6882 | |
200 | 21.825 | 2661.3 | 2879.5 | 8.9038 | |
250 | 24.136 | 2736.0 | 2977.3 | 9.1002 | |
300 | 26.445 | 2812.1 | 3076.5 | 9.2813 | |
400 | 31.063 | 2968.9 | 3279.6 | 9.6077 | |
500 | 35.679 | 3132.3 | 3489.1 | 9.8978 | |
600 | 40.295 | 3302.5 | 3705.4 | 10.1608 | |
700 | 44.911 | 3479.6 | 3928.7 | 10.4028 | |
800 | 49.526 | 3663.8 | 4159.0 | 10.6281 | |
900 | 54.141 | 3855.0 | 4396.4 | 10.8396 | |
1000 | 58.757 | 4053.0 | 4640.6 | 11.0393 | |
1100 | 63.372 | 4257.5 | 4891.2 | 11.2287 | |
1200 | 67.987 | 4467.9 | 5147.8 | 11.4091 | |
1300 | 72.602 | 4683.7 | 5409.7 | 11.5811 | |
0.05 | Sat. | 3.240 | 2483.9 | 2645.9 | 7.5939 |
100 | 3.418 | 2511.6 | 2682.5 | 7.6947 | |
150 | 3.889 | 2585.6 | 2780.1 | 7.9401 | |
200 | 4.356 | 2659.9 | 2877.7 | 8.1580 | |
250 | 4.820 | 2735.0 | 2976.0 | 8.3556 | |
300 | 5.284 | 2811.3 | 3075.5 | 8.5373 | |
400 | 6.209 | 2968.5 | 3278.9 | 8.8642 | |
500 | 7.134 | 3132.0 | 3488.7 | 9.1546 | |
600 | 8.057 | 3302.2 | 3705.1 | 9.4178 | |
700 | 8.981 | 3479.4 | 3928.5 | 9.6599 | |
800 | 9.904 | 3663.6 | 4158.9 | 9.8852 | |
900 | 10.828 | 3854.9 | 4396.3 | 10.0967 | |
1000 | 11.751 | 4052.9 | 4640.5 | 10.2964 | |
1100 | 12.674 | 4257.4 | 4891.1 | 10.4859 | |
1200 | 13.597 | 4467.8 | 5147.7 | 10.6662 | |
1300 | 14.521 | 4683.6 | 5409.6 | 10.8382 | |
0.2 | Sat. | 0.8857 | 2529.5 | 2706.7 | 7.1272 |
150 | 0.9596 | 2576.9 | 2768.8 | 7.2795 | |
200 | 1.0803 | 2654.4 | 2870.5 | 7.5066 | |
250 | 1.1988 | 2731.2 | 2971.0 | 7.7086 | |
300 | 1.3162 | 2808.6 | 3071.8 | 7.8926 | |
400 | 1.5493 | 2966.7 | 3276.6 | 8.2218 | |
500 | 1.7814 | 3130.8 | 3487.1 | 8.5133 | |
600 | 2.013 | 3301.4 | 3704.0 | 8.7770 | |
700 | 2.244 | 3478.8 | 3927.6 | 9.0194 | |
800 | 2.475 | 3663.1 | 4158.2 | 9.2449 | |
900 | 2.705 | 3854.5 | 4395.8 | 9.4566 | |
1000 | 2.937 | 4052.5 | 4640.0 | 9.6563 | |
1100 | 3.168 | 4257.0 | 4890.7 | 9.8458 | |
1200 | 3.399 | 4467.5 | 5147.5 | 10.0262 | |
1300 | 3.630 | 4683.2 | 5409.3 | 10.1982 | |
0.3 | Sat. | 0.6058 | 2543.6 | 2725.3 | 6.9919 |
150 | 0.6339 | 2570.8 | 2761.0 | 7.0778 | |
200 | 0.7163 | 2650.7 | 2865.6 | 7.3115 | |
250 | 0.7964 | 2728.7 | 2967.6 | 7.5166 | |
300 | 0.8753 | 2806.7 | 3069.3 | 7.7022 | |
400 | 1.0315 | 2965.6 | 3275.0 | 8.0330 | |
500 | 1.1867 | 3130.0 | 3486.0 | 8.3251 | |
600 | 1.3414 | 3300.8 | 3703.2 | 8.5892 | |
700 | 1.4957 | 3478.4 | 3927.1 | 8.8319 | |
800 | 1.6499 | 3662.9 | 4157.8 | 9.0576 | |
900 | 1.8041 | 3854.2 | 4395.4 | 9.2692 | |
1000 | 1.9581 | 4052.3 | 4639.7 | 9.4690 | |
1100 | 2.1121 | 4256.8 | 4890.4 | 9.6585 | |
1200 | 2.2661 | 4467.2 | 5147.1 | 9.8389 | |
1300 | 2.4201 | 4683.0 | 5409.0 | 10.0110 | |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. |
The solution is found directly from the enthalpy equation for boilers given in Table 12.2:
\dot{Q}_{in} = \dot{m}(h_{o} – h_{i})/\eta = 50 kg/s \times (2761.0 – 10.42) kJ/kg/0.9– 152,810 kW
For computer calculations, several empirical correlations exist with varying degrees of accuracy and associated complexity. One widely used correlation used to determine the water vapor saturation pressure over liquid vapor for the temperature range of 0°C–200°C (32°F–392°F) is given by (ASHRAE Fundamentals, 2013)
\ln p_{sat} = a/T + b + c \cdot T + d \cdot T^{2} + e \cdot T^{3} + f \cdot \ln T (12.12)
where
T is in absolute units (K or °R)
p_{sat} is in Pa or in psia
The numerical values of the coefcients are given in Table 12.3.
TABLE 12.2 | |||
Flow Processes in Important HVAC Equipment | |||
Equipment | Process | Heat Input/Work Input | Comments |
1 Boiler (water) and evaporators (refrigeration) | Heat input causes fluid to change from liquid to vapor. | \dot{Q} = \dot{m}(h_{2} – h_{1}) | KE and PE effects negligible. |
2 Condensers (water or refrigeration) | Heat rejection causes fluid to change from vapor to liquid. | \dot{Q} = – \dot{m}(h_{2} – h_{1}) | “ |
3 Cooling towers | Heat rejection causes water to cool down. | \dot{Q} = – \dot{m}(h_{2} – h_{1}) | “ |
4 Compressors in refrigeration | Work needed to compress vapor to a high pressure. | \dot{W} = \dot{m}(h_{2} – h_{1}) | Irreversibility due to fluid friction cannot be generally ignored; PE negligible. |
5 Turbine or reciprocating engine | Work delivered due to expansion of fluid from high pressure and temperature. | \dot{W} = \dot{m} \left\lgroup \frac{v^{2}_{1}}{2} – \frac{v^{2}_{2}}{2} + h_{1} – H_{2} \right\rgroup | “ |
PE, potential energy; KE, kinetic energy.
TABLE 12.3 | ||
Values of Coefficients Appearing in Equation 12.12 | ||
Coefficient | SI Units | IP Units |
a | −5.8002206 × 10³ | [atex]−1.0440397 × 10^{4}[/latex] |
b | 1.391499 | −1.1294650 × 10¹ |
c | −4.8640239 × 10^{−2} | −2.7022355 × 10^{−2} |
d | 4.1764768 × 10^{−5} | 1.2890360 × 10^{−5} |
e | −1.4452093 × 10^{−8} | −2.4780681 × 10^{−9} |
f | 6.545967 | 6.545967 |