Warming and Humidification of Cold, Dry Air
Outdoor air at 40°F (4.5°C) and 60% humidity is heated and humidified by saturated steam at 230°F (110°C). The airflow rate is 15,000 ft³/min (7,080 L/s), and heat is added to the air at the rate of 765,000 Btu/h (224 kW) while it absorbs 415 lb_{m}/h (0.0524 kg/s) of steam. What are the dry- and wet-bulb temperatures at the exit of this heater/humidifier if it is located at
sea level?
Given: T_{db1} = 40°F, \phi_{1} = 60\%, \dot{V}_{a} = 15,000 ft^{3}/min = 900,000 ft^{3}/h, \dot{m}_{w} = 415 lb_{w}/h, and \dot{Q}_{h} = 765,000 Btu/h.
Figure: See Figure 13.17b.
Find: T_{db2} and T_{wb2}
Lookup values: Steam enthalpy at 230°F from Table A3 by interpolation, h_{vap} = 1157 Btu/lb_{w} = h_{liq,2}.
The inlet condition moist-air enthalpy is read from the psychrometric chart (Figure 13.6) as h_{1} = 12.9 Btu/lb_{a}. Also, Specific volume v_{1} = 12.65 ft^{3}/lb_{a}.
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. |
This problem can be solved using the graphical approach with the enthalpy protractor in Figure 13.6. The enthalpy/humidity ratio needed to use the graphical construction is found from Equation 13.52:
\frac{\Delta h}{\Delta W} = \frac{\dot{Q}_{h} + \dot{m}_{w} h_{liq,2}}{\dot{m}_{w}} (13.52)
\frac{\Delta h}{\Delta W} = \frac{765,000 Btu/h + 415 lb_{w}/h \times 1,157 Btu/lb_{w}}{415 lb_{w}/h}= 3,000 Btu/lb_{a}
This value is located on the enthalpy protractor, and a line is constructed in the chart with the same slope passing through the known process start point 1. To find the termination point 2 of the process, find the exit enthalpy as follows. First, find the humidity ratio increase ΔW:
\Delta W = \frac{\dot{m}_{w}}{(\dot{V}_{a}/v_{1})} = \frac{415 lb_{w}/h}{(900,000 ft^{3}/h/12.65 ft^{3}/lb_{a})}= 0.0058 lb_{w}/lb_{a}
The end-state enthalpy is then found as follows:
h_{2} = h_{1} + \frac{\Delta h}{\Delta W} \Delta W = 12.9 + 3000 \times 0.0058 = 30.4 Btu/lb_{a}The outlet enthalpy is used to terminate the construction line at point 2, as shown in Figure 13.17. At point, we can read from the chart the following values of the outlet wet- and dry-bulb temperatures: T_{wb} = 66°F (18.9°C) and T_{db} = 86°F (30°C) .
Comments
This example demonstrates how the protractor construction can save considerable time. If the chart had not been used, then complicated, iterative solutions involving a number of equations in Section 13.4 would have been needed.