Rotational Speed for Centrifugal Chillers
What is the diameter of a centrifugal compressor rotor needed to isentropically compress R-22 from a saturated suction temperature of 5°C (41°F) to a condensing temperature of 50°C (122°F) and a pressure of 1.94 MPa (145 psia)? The compressor rotates at 1800 r/min (188 rad/s) at design conditions.
Given: \omega = 1800 r/min × 2\pi rad/r × 1 min/60 s = 188 s^{−1}
T_{i} = 5°C, T_{o} = 50°C, p_{o} = 1.94 MPa
Assumptions: The idealizations of the previous section apply.
Find: r_{o}
Lookup values: From Table A5: h_{i} = 406.6 kJ/kg
(saturated) and from Table A7, h_{o} = 435 kJ/kg (superheated)
TABLE A.5 (IP Units) Properties of Saturated Liquid and Saturated Vapor of R-22 |
|||||||
Temp. (°F) | Pressure (psia) | Density (lb/ft³) | Volume (ft³/lb) | Enthalpy (Btu/lb) | Entropy (Btu/lb · °F) | ||
Liquid | Vapor | Liquid | Vapor | Liquid | Vapor | ||
-250 | — | 107.37 | — | -63.169 | 76.604 | -0.21914 | 0.44952 |
-240 | — | 106.41 | — | -56.462 | 77.629 | -0.18786 | 0.42332 |
-230 | — | 105.48 | — | -51.569 | 78.669 | -0.16605 | 0.40101 |
-220 | 0.002 | 104.58 | 16805 | -47.705 | 79.724 | -0.14958 | 0.38211 |
-210 | 0.004 | 103.7 | 6982.6 | -44.426 | 80.796 | -0.13616 | 0.36538 |
-200 | 0.01 | 102.81 | 3151.5 | -41.474 | 81.882 | -0.12457 | 0.35048 |
-190 | 0.022 | 101.92 | 1527.4 | -38.706 | 82.984 | -0.11411 | 0.33715 |
-180 | 0.044 | 101.03 | 787.79 | -36.038 | 84.1 | -0.10439 | 0.32518 |
-170 | 0.084 | 100.12 | 429.22 | -33.424 | 85.23 | -0.09521 | 0.31441 |
-160 | 0.151 | 99.22 | 245.51 | -30.839 | 86.373 | -0.08644 | 0.3047 |
-150 | 0.262 | 98.3 | 146.65 | -28.269 | 87.528 | -0.078 | 0.29594 |
-140 | 0.435 | 97.38 | 91.059 | -25.708 | 88.692 | -0.06986 | 0.28801 |
-130 | 0.696 | 96.46 | 58.544 | -23.15 | 89.864 | -0.06198 | 0.28082 |
-120 | 1.08 | 95.53 | 38.833 | -20.594 | 91.04 | -0.05435 | 0.2743 |
-110 | 1.626 | 94.6 | 26.494 | -18.038 | 92.218 | -0.04694 | 0.26838 |
-100 | 2.384 | 93.66 | 18.54 | -15.481 | 93.397 | -0.03973 | 0.26298 |
-90 | 3.413 | 92.71 | 13.275 | -12.921 | 94.572 | -0.03271 | 0.25807 |
-80 | 4.778 | 91.75 | 9.7044 | -10.355 | 95.741 | -0.02587 | 0.25357 |
-70 | 6.555 | 90.79 | 7.2285 | -7.783 | 96.901 | -0.01919 | 0.24945 |
-60 | 8.83 | 89.81 | 5.4766 | -5.201 | 98.049 | -0.01266 | 0.24567 |
-50 | 11.696 | 88.83 | 4.2138 | -2.608 | 99.182 | -0.00627 | 0.2422 |
-45 | 13.383 | 88.33 | 3.716 | -1.306 | 99.742 | -0.00312 | 0.24056 |
−41.44 | 14.696 | 87.97 | 3.4048 | −0.377 | 100.138 | −0.0009 | 0.23944 |
-40 | 15.255 | 87.82 | 3.288 | 0 | 100.296 | 0 | 0.23899 |
-35 | 17.329 | 87.32 | 2.9185 | 1.31 | 100.847 | 0.00309 | 0.23748 |
-30 | 19.617 | 86.81 | 2.5984 | 2.624 | 101.391 | 0.00616 | 0.23602 |
-25 | 22.136 | 86.29 | 2.3202 | 3.944 | 101.928 | 0.0092 | 0.23462 |
-20 | 24.899 | 85.77 | 2.0774 | 5.268 | 102.461 | 0.01222 | 0.23327 |
-15 | 27.924 | 85.25 | 1.865 | 6.598 | 102.986 | 0.01521 | 0.23197 |
-10 | 31.226 | 84.72 | 1.6784 | 7.934 | 103.503 | 0.01818 | 0.23071 |
-5 | 34.821 | 84.18 | 1.5142 | 9.276 | 104.013 | 0.02113 | 0.22949 |
0 | 38.726 | 83.64 | 1.3691 | 10.624 | 104.515 | 0.02406 | 0.22832 |
5 | 42.96 | 83.09 | 1.2406 | 11.979 | 105.009 | 0.02697 | 0.22718 |
10 | 47.538 | 82.54 | 1.1265 | 13.342 | 105.493 | 0.02987 | 0.22607 |
15 | 52.48 | 81.98 | 1.025 | 14.712 | 105.968 | 0.03275 | 0.225 |
20 | 57.803 | 81.41 | 0.9343 | 16.09 | 106.434 | 0.03561 | 0.22395 |
25 | 63.526 | 80.84 | 0.8532 | 17.476 | 106.891 | 0.03846 | 0.22294 |
30 | 69.667 | 80.26 | 0.7804 | 18.871 | 107.336 | 0.04129 | 0.22195 |
35 | 76.245 | 79.67 | 0.715 | 20.275 | 107.769 | 0.04411 | 0.22098 |
40 | 83.28 | 79.07 | 0.6561 | 21.688 | 108.191 | 0.04692 | 0.22004 |
45 | 90.791 | 78.46 | 0.6029 | 23.111 | 108.6 | 0.04972 | 0.21912 |
50 | 98.799 | 77.84 | 0.5548 | 24.544 | 108.997 | 0.05251 | 0.21821 |
55 | 107.32 | 77.22 | 0.5111 | 25.988 | 109.379 | 0.05529 | 0.21732 |
60 | 116.38 | 76.58 | 0.4715 | 27.443 | 109.748 | 0.05806 | 0.21644 |
65 | 126 | 75.93 | 0.4355 | 28.909 | 110.103 | 0.06082 | 0.21557 |
70 | 136.19 | 75.27 | 0.4026 | 30.387 | 110.441 | 0.06358 | 0.21472 |
75 | 146.98 | 74.6 | 0.3726 | 31.877 | 110.761 | 0.06633 | 0.21387 |
80 | 158.4 | 73.92 | 0.3451 | 33.381 | 111.066 | 0.06907 | 0.21302 |
85 | 170.45 | 73.22 | 0.3199 | 34.898 | 111.35 | 0.07182 | 0.21218 |
90 | 183.17 | 72.51 | 0.2968 | 36.43 | 111.616 | 0.07456 | 0.21134 |
95 | 196.57 | 71.79 | 0.2756 | 37.977 | 111.859 | 0.0773 | 0.2105 |
100 | 210.69 | 71.05 | 0.256 | 39.538 | 112.081 | 0.08003 | 0.20965 |
105 | 225.53 | 70.29 | 0.2379 | 41.119 | 112.278 | 0.08277 | 0.20879 |
110 | 241.14 | 69.51 | 0.2212 | 42.717 | 112.448 | 0.08552 | 0.20793 |
115 | 257.52 | 68.71 | 0.2058 | 44.334 | 112.591 | 0.08827 | 0.20705 |
120 | 274.71 | 67.89 | 0.1914 | 45.972 | 112.704 | 0.09103 | 0.20615 |
125 | 292.73 | 67.05 | 0.1781 | 47.633 | 112.783 | 0.09379 | 0.20522 |
130 | 311.61 | 66.17 | 0.1657 | 49.319 | 112.825 | 0.09657 | 0.20427 |
135 | 331.38 | 65.27 | 0.1542 | 51.032 | 112.826 | 0.09937 | 0.20329 |
140 | 352.07 | 64.33 | 0.1434 | 52.775 | 112.784 | 0.1022 | 0.20227 |
145 | 373.71 | 63.35 | 0.1332 | 54.553 | 112.692 | 0.10504 | 0.20119 |
150 | 396.32 | 62.33 | 0.1237 | 56.37 | 112.541 | 0.10793 | 0.20006 |
160 | 444.65 | 60.12 | 0.1063 | 60.145 | 112.035 | 0.11383 | 0.19757 |
170 | 497.35 | 57.59 | 0.0907 | 64.175 | 111.165 | 0.12001 | 0.19464 |
180 | 554.82 | 54.57 | 0.0763 | 68.597 | 109.753 | 0.12668 | 0.19102 |
190 | 617.53 | 50.62 | 0.0625 | 73.742 | 107.398 | 0.13432 | 0.18613 |
200 | 686.11 | 44.44 | 0.0478 | 80.558 | 102.809 | 0.14432 | 0.17805 |
205.06 | 723.74 | 32.7 | 0.0306 | 91.052 | 91.052 | 0.15989 | 0.15989 |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. Notes: Values shown in italics are at the boiling point. Values shown in bold are at the critical point. |
TABLE A.5 (SI Units) Properties of Saturated Liquid and Saturated Vapor of R-22 |
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Temp. (°C) | Pressure (MPa) | Density (kg/m³) | Volume (m³/kg) | Enthalpy (kJ/kg) | Entropy (kJ/kg · K) | ||
Liquid | Vapor | Liquid | Vapor | Liquid | Vapor | ||
-150.00 | — | 1701.5 | — | 26.01 | 335.85 | 0.0566 | 2.5752 |
-140.00 | — | 1675.3 | — | 43.84 | 340.24 | 0.1961 | 2.4222 |
-130.00 | 0.00006 | 1649.7 | 229.29 | 57.00 | 344.75 | 0.2916 | 2.3017 |
-120.00 | 0.00023 | 1624.0 | 63.648 | 68.51 | 349.38 | 0.3694 | 2.2033 |
-110.00 | 0.00074 | 1598.0 | 21.311 | 79.47 | 354.11 | 0.4386 | 2.1220 |
-100.00 | 0.00200 | 1571.7 | 8.2980 | 90.24 | 358.93 | 0.5027 | 2.0545 |
-90.00 | 0.00480 | 1545.1 | 3.6548 | 100.95 | 363.82 | 0.5629 | 1.9982 |
-80.00 | 0.01035 | 1518.3 | 1.7816 | 111.66 | 368.75 | 0.6197 | 1.9508 |
-70.00 | 0.02044 | 1491.1 | 0.94476 | 122.36 | 373.68 | 0.6738 | 1.9109 |
-60.00 | 0.03747 | 1463.6 | 0.53734 | 133.11 | 378.58 | 0.7253 | 1.8770 |
-50.00 | 0.06449 | 1435.5 | 0.32405 | 143.91 | 383.39 | 0.7748 | 1.8480 |
-48.00 | 0.07140 | 1429.8 | 0.29469 | 146.08 | 384.35 | 0.7844 | 1.8427 |
-46.00 | 0.07890 | 1424.1 | 0.26849 | 148.25 | 385.29 | 0.7940 | 1.8376 |
-44.00 | 0.08700 | 1418.4 | 0.24507 | 150.43 | 386.23 | 0.8035 | 1.8326 |
-42.00 | 0.09575 | 1412.6 | 0.22410 | 152.61 | 387.17 | 0.8130 | 1.8277 |
−40.80 | 0.10132 | 1409.1 | 0.21256 | 153.93 | 387.72 | 0.8186 | 1.8249 |
-40.00 | 0.10518 | 1406.8 | 0.20526 | 154.80 | 388.09 | 0.8224 | 1.8230 |
-38.00 | 0.11533 | 1401.0 | 0.18832 | 156.99 | 389.01 | 0.8317 | 1.8184 |
-36.00 | 0.12623 | 1395.1 | 0.17306 | 159.19 | 389.93 | 0.8410 | 1.8140 |
-34.00 | 0.13793 | 1389.2 | 0.15927 | 161.40 | 390.84 | 0.8502 | 1.8096 |
-32.00 | 0.15045 | 1383.3 | 0.14680 | 163.61 | 391.74 | 0.8594 | 1.8054 |
-30.00 | 0.16384 | 1377.3 | 0.13551 | 165.82 | 392.63 | 0.8685 | 1.8013 |
-28.00 | 0.17815 | 1371.3 | 0.12525 | 168.04 | 393.52 | 0.8776 | 1.7973 |
-26.00 | 0.19340 | 1365.2 | 0.11593 | 170.27 | 394.39 | 0.8866 | 1.7934 |
-24.00 | 0.20965 | 1359.1 | 0.10744 | 172.51 | 395.26 | 0.8955 | 1.7896 |
-22.00 | 0.22693 | 1352.9 | 0.09970 | 174.75 | 396.12 | 0.9044 | 1.7859 |
-20.00 | 0.24529 | 1346.8 | 0.09262 | 177.00 | 396.97 | 0.9133 | 1.7822 |
-18.00 | 0.26477 | 1340.5 | 0.08615 | 179.26 | 397.81 | 0.9222 | 1.7787 |
-16.00 | 0.28542 | 1334.2 | 0.08023 | 181.53 | 398.64 | 0.9309 | 1.7752 |
-14.00 | 0.30728 | 1327.9 | 0.07479 | 183.81 | 399.46 | 0.9397 | 1.7719 |
-12.00 | 0.33040 | 1321.5 | 0.06979 | 186.09 | 400.27 | 0.9484 | 1.7686 |
-10.00 | 0.35482 | 1315.0 | 0.06520 | 188.38 | 401.07 | 0.9571 | 1.7653 |
-8.00 | 0.38059 | 1308.5 | 0.06096 | 190.69 | 401.85 | 0.9657 | 1.7621 |
-6.00 | 0.40775 | 1301.9 | 0.05706 | 193.00 | 402.63 | 0.9743 | 1.7590 |
-4.00 | 0.43636 | 1295.3 | 0.05345 | 195.32 | 403.39 | 0.9829 | 1.7560 |
-2.00 | 0.46646 | 1288.6 | 0.05012 | 197.66 | 404.14 | 0.9915 | 1.7530 |
0.00 | 0.49811 | 1281.8 | 0.04703 | 200.00 | 404.87 | 1.0000 | 1.7500 |
2.00 | 0.53134 | 1275.0 | 0.04417 | 202.35 | 405.59 | 1.0085 | 1.7471 |
4.00 | 0.56622 | 1268.1 | 0.04152 | 204.72 | 406.30 | 1.0170 | 1.7443 |
6.00 | 0.6028 | 1261.1 | 0.03906 | 207.10 | 406.99 | 1.0254 | 1.7415 |
8.00 | 0.6411 | 1254.0 | 0.03676 | 209.49 | 407.67 | 1.0338 | 1.7387 |
10.00 | 0.6812 | 1246.9 | 0.03463 | 211.89 | 408.33 | 1.0422 | 1.7360 |
12.00 | 0.7231 | 1239.7 | 0.03265 | 214.31 | 408.97 | 1.0506 | 1.7333 |
14.00 | 0.767 | 1232.4 | 0.03079 | 216.74 | 409.60 | 1.0590 | 1.7306 |
16.00 | 0.8128 | 1225.0 | 0.02906 | 219.18 | 410.21 | 1.0673 | 1.7280 |
18.00 | 0.8606 | 1217.6 | 0.02744 | 221.63 | 410.80 | 1.0756 | 1.7254 |
12.00 | 0.9104 | 1210.0 | 0.02593 | 224.10 | 411.38 | 1.0840 | 1.7228 |
22.00 | 0.9624 | 1202.4 | 0.02451 | 226.59 | 411.93 | 1.0923 | 1.7202 |
24.00 | 1.0165 | 1194.6 | 0.02319 | 229.09 | 412.46 | 1.1006 | 1.7177 |
26.00 | 1.0728 | 1186.8 | 0.02194 | 231.60 | 412.98 | 1.1088 | 1.7151 |
28.00 | 1.1314 | 1178.8 | 0.02077 | 234.14 | 413.46 | 1.1171 | 1.7126 |
30.00 | 1.1924 | 1170.7 | 0.01968 | 236.69 | 413.93 | 1.1254 | 1.7101 |
32.00 | 1.2557 | 1162.5 | 0.01864 | 239.25 | 414.37 | 1.1336 | 1.7075 |
34.00 | 1.3215 | 1154.2 | 0.01767 | 241.84 | 414.79 | 1.1419 | 1.7050 |
36.00 | 1.3898 | 1145.7 | 0.01675 | 244.44 | 415.18 | 1.1501 | 1.7024 |
38.00 | 1.4606 | 1137.1 | 0.01589 | 247.06 | 415.54 | 1.1584 | 1.6999 |
40.00 | 1.5341 | 1128.4 | 0.01507 | 249.71 | 415.87 | 1.1667 | 1.6973 |
42.00 | 1.6103 | 1119.5 | 0.01430 | 252.37 | 416.17 | 1.1749 | 1.6947 |
44.00 | 1.6892 | 1110.4 | 0.01357 | 255.06 | 416.44 | 1.1832 | 1.6921 |
46.00 | 1.7709 | 1101.2 | 0.01288 | 257.77 | 416.68 | 1.1915 | 1.6894 |
48.00 | 1.8555 | 1091.8 | 0.01223 | 260.51 | 416.87 | 1.1998 | 1.6867 |
50.00 | 1.9431 | 1082.1 | 0.01161 | 263.27 | 417.03 | 1.2081 | 1.6840 |
55.00 | 2.1753 | 1057.1 | 0.01020 | 270.31 | 417.24 | 1.2291 | 1.6768 |
60.00 | 2.4274 | 1030.5 | 0.00895 | 277.56 | 417.14 | 1.2503 | 1.6692 |
65.00 | 2.7008 | 1001.8 | 0.00784 | 285.06 | 416.65 | 1.2718 | 1.6610 |
70.00 | 2.9967 | 970.4 | 0.00684 | 292.90 | 415.69 | 1.2940 | 1.6518 |
75.00 | 3.3168 | 935.3 | 0.00594 | 301.18 | 414.09 | 1.3169 | 1.6413 |
80.00 | 3.6627 | 894.8 | 0.00511 | 310.10 | 411.60 | 1.3413 | 1.6287 |
85.00 | 4.0368 | 845.1 | 0.00433 | 320.05 | 407.72 | 1.3680 | 1.6128 |
90.00 | 4.4416 | 777.5 | 0.00355 | 331.98 | 401.33 | 1.3998 | 1.5907 |
95.00 | 4.8820 | 665.4 | 0.00264 | 348.86 | 387.46 | 1.4442 | 1.5491 |
96.14 | 4.9900 | 523.8 | 0.00191 | 366.59 | 366.59 | 1.4918 | 1.4918 |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. Notes: Values shown in italics are at the boiling point. Values shown in bold are at the critical point. |
TABLE A.7 (IP Units) Properties of Superheated Vapor of R-22 |
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Pressure | Temperature | |||||||||||
(psia) | Properties | −22°F | −4°F | 14°F | 32°F | 50°F | 68°F | 86°F | 104°F | 122°F | 140°F | 158°F |
20.31 | Volume (ftS/lb) | 2.566 | 2.687 | 2.807 | 2.926 | 3.044 | 3.16 | 3.276 | 3.392 | 3.506 | 3.621 | 3.734 |
Enthalpy (Btu/lb) | 102.4 | 105.1 | 107.8 | 110.6 | 113.3 | 116.1 | 119 | 121.9 | 124.8 | 127.8 | 130.8 | |
Entropy (Btu/lb· R) | 0.237 | 0.243 | 0.249 | 0.255 | 0.26 | 0.266 | 0.271 | 0.276 | 0.281 | 0.286 | 0.291 | |
26.11 | Volume (ftS/lb) | — | 2.066 | 2.162 | 2.256 | 2.35 | 2.442 | 2.534 | 2.624 | 2.715 | 2.805 | 2.894 |
Enthalpy (Btu/lb) | — | 104.7 | 107.5 | 110.2 | 113 | 115.9 | 118.8 | 121.7 | 124.6 | 127.6 | 130.6 | |
Entropy (Btu/lb· R) | — | 0.237 | 0.243 | 0.249 | 0.254 | 0.26 | 0.265 | 0.27 | 0.275 | 0.28 | 0.285 | |
29.01 | Volume (ftS/lb) | — | 1.849 | 1.936 | 2.022 | 2.107 | 2.191 | 2.274 | 2.356 | 2.438 | 2.519 | 2.6 |
Enthalpy (Btu/lb) | — | 104.5 | 107.3 | 110.1 | 112.9 | 115.7 | 118.6 | 121.6 | 124.5 | 127.5 | 130.6 | |
Entropy (Btu/lb· R) | — | 0.234 | 0.24 | 0.246 | 0.252 | 0.257 | 0.262 | 0.268 | 0.273 | 0.278 | 0.283 | |
36.26 | Volume (ftS/lb) | — | — | 1.529 | 1.6 | 1.669 | 1.738 | 1.805 | 1.872 | 1.939 | 2.005 | 2.07 |
Enthalpy (Btu/lb) | — | — | 106.8 | 109.6 | 112.5 | 115.4 | 118.3 | 121.3 | 124.3 | 127.3 | 130.3 | |
Entropy (Btu/lb· R) | — | — | 0.234 | 0.24 | 0.246 | 0.251 | 0.257 | 0.262 | 0.267 | 0.273 | 0.278 | |
43.51 | Volume (ftS/lb) | — | — | 1.257 | 1.318 | 1.377 | 1.436 | 1.493 | 1.55 | 1.606 | 1.662 | 1.717 |
Enthalpy (Btu/lb) | — | — | 106.3 | 109.2 | 112.1 | 115.1 | 118 | 121 | 124 | 127 | 130.1 | |
Entropy (Btu/lb· R) | — | — | 0.229 | 0.235 | 0.241 | 0.247 | 0.252 | 0.258 | 0.263 | 0.268 | 0.273 | |
50.76 | Volume (ftS/lb) | — | — | 1.063 | 1.116 | 1.169 | 1.22 | 1.27 | 1.32 | 1.368 | 1.417 | 1.465 |
Enthalpy (Btu/lb) | — | — | 105.8 | 108.8 | 111.7 | 114.7 | 117.7 | 120.7 | 123.7 | 126.8 | 129.9 | |
Entropy (Btu/lb· R) | — | — | 0.225 | 0.231 | 0.237 | 0.243 | 0.248 | 0.254 | 0.259 | 0.264 | 0.269 | |
58.02 | Volume (ftS/lb) | — | — | — | 0.965 | 1.012 | 1.058 | 1.103 | 1.147 | 1.19 | 1.233 | 1.275 |
Enthalpy (Btu/lb) | — | — | — | 108.3 | 111.3 | 114.3 | 117.4 | 120.4 | 123.5 | 126.5 | 129.7 | |
Entropy (Btu/lb· R) | — | — | — | 0.227 | 0.233 | 0.239 | 0.245 | 0.25 | 0.256 | 0.261 | 0.266 | |
65.27 | Volume (ftS/lb) | — | — | — | 0.847 | 0.89 | 0.932 | 0.972 | 1.012 | 1.051 | 1.09 | 1.128 |
Enthalpy (Btu/lb) | — | — | — | 107.9 | 110.9 | 114 | 117 | 120.1 | 123.2 | 126.3 | 129.4 | |
Entropy (Btu/lb· R) | — | — | — | 0.224 | 0.23 | 0.236 | 0.242 | 0.247 | 0.253 | 0.258 | 0.263 | |
72.52 | Volume (ftS/lb) | — | — | — | — | 0.792 | 0.83 | 0.868 | 0.904 | 0.94 | 0.975 | 1.01 |
Enthalpy (Btu/lb) | — | — | — | — | 110.5 | 113.6 | 116.7 | 119.8 | 122.9 | 126 | 129.2 | |
Entropy (Btu/lb· R) | — | — | — | — | 0.227 | 0.233 | 0.239 | 0.244 | 0.25 | 0.255 | 0.26 | |
87.02 | Volume (ftS/lb) | — | — | — | — | 0.645 | 0.678 | 0.711 | 0.743 | 0.773 | 0.804 | 0.833 |
Enthalpy (Btu/lb) | — | — | — | — | 109.7 | 112.8 | 116 | 119.2 | 122.3 | 125.5 | 128.7 | |
Entropy (Btu/lb· R) | — | — | — | — | 0.222 | 0.228 | 0.234 | 0.239 | 0.245 | 0.25 | 0.256 | |
101.53 | Volume (ftS/lb) | — | — | — | — | — | 0.569 | 0.599 | 0.627 | 0.654 | 0.681 | 0.707 |
Enthalpy (Btu/lb) | — | — | — | — | — | 112 | 115.3 | 118.5 | 121.8 | 125 | 128.2 | |
Entropy (Btu/lb· R) | — | — | — | — | — | 0.223 | 0.229 | 0.235 | 0.241 | 0.246 | 0.251 | |
116.03 | Volume (ftS/lb) | — | — | — | — | — | 0.487 | 0.514 | 0.54 | 0.564 | 0.589 | 0.612 |
Enthalpy (Btu/lb) | — | — | — | — | — | 111.2 | 114.6 | 117.9 | 121.2 | 124.5 | 127.8 | |
Entropy (Btu/lb· R) | — | — | — | — | — | 0.219 | 0.225 | 0.231 | 0.237 | 0.242 | 0.248 | |
130.54 | Volume (ftS/lb) | — | — | — | — | — | 0.423 | 0.448 | 0.472 | 0.495 | 0.517 | 0.538 |
Enthalpy (Btu/lb) | — | — | — | — | — | 110.3 | 113.8 | 117.2 | 120.6 | 123.9 | 127.3 | |
Entropy (Btu/lb· R) | — | — | — | — | — | 0.215 | 0.221 | 0.227 | 0.233 | 0.239 | 0.245 | |
145.04 | Volume (ftS/lb) | — | — | — | — | — | — | 0.395 | 0.417 | 0.438 | 0.459 | 0.479 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | 113 | 116.5 | 119.9 | 123.4 | 126.7 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | 0.218 | 0.224 | 0.23 | 0.236 | 0.241 | |
159.54 | Volume (ftS/lb) | — | — | — | — | — | — | 0.351 | 0.372 | 0.392 | 0.412 | 0.43 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | 112.2 | 115.8 | 119.3 | 122.8 | 126.2 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | 0.214 | 0.221 | 0.227 | 0.233 | 0.239 | |
174.05 | Volume (ftS/lb) | — | — | — | — | — | — | — | 0.335 | 0.354 | 0.372 | 0.39 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | 115 | 118.6 | 122.2 | 125.7 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | 0.218 | 0.224 | 0.23 | 0.236 | |
188.55 | Volume (ftS/lb) | — | — | — | — | — | — | — | 0.302 | 0.321 | 0.339 | 0.355 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | 114.2 | 118 | 121.6 | 125.1 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | 0.215 | 0.222 | 0.228 | 0.234 | |
203.06 | Volume (ftS/lb) | — | — | — | — | — | — | — | 0.275 | 0.293 | 0.31 | 0.326 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | 113.4 | 117.2 | 121 | 124.6 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | 0.212 | 0.219 | 0.225 | 0.231 | |
217.56 | Volume (ftS/lb) | — | — | — | — | — | — | — | 0.25 | 0.268 | 0.285 | 0.3 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | 112.5 | 116.5 | 120.3 | 124 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | 0.209 | 0.216 | 0.223 | 0.229 | |
253.82 | Volume (ftS/lb) | — | — | — | — | — | — | — | — | 0.218 | 0.234 | 0.248 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | — | 114.5 | 118.6 | 122.5 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | — | 0.21 | 0.217 | 0.224 | |
290.08 | Volume (ftS/lb) | — | — | — | — | — | — | — | — | — | 0.195 | 0.209 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | — | — | 116.7 | 120.9 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | — | — | 0.212 | 0.218 | |
326.34 | Volume (ftS/lb) | — | — | — | — | — | — | — | — | — | 0.163 | 0.177 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | — | — | 114.6 | 119.2 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | — | — | 0.206 | 0.214 | |
362.60 | Volume (ftS/lb) | — | — | — | — | — | — | — | — | — | — | 0.152 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | — | — | — | 117.2 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | — | — | — | 0.209 | |
398.86 | Volume (ftS/lb) | — | — | — | — | — | — | — | — | — | — | 0.13 |
Enthalpy (Btu/lb) | — | — | — | — | — | — | — | — | — | — | 115 | |
Entropy (Btu/lb· R) | — | — | — | — | — | — | — | — | — | — | 0.203 | |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. |
TABLE A.7 (SI Units) Properties of Superheated Vapor of R-22 |
||||||||||||
Pressure | Properties | Temperature | ||||||||||
(kPa) | −30°C | −20°C | −10°C | 0°C | 10°C | 20°C | 30°C | 40°C | 50°C | 60°C | 70°C | |
120 | Volume (mS/kg) | 0.188 | 0.196 | 0.205 | 0.214 | 0.222 | 0.231 | 0.239 | 0.247 | 0.255 | 0.264 | 0.272 |
Enthalpy (kJ/kg) | 393.5 | 399.7 | 405.9 | 412.3 | 418.7 | 425.2 | 431.8 | 438.5 | 445.3 | 452.2 | 459.2 | |
Entropy (kJ/kg· K) | 1.832 | 1.857 | 1.881 | 1.905 | 1.928 | 1.951 | 1.973 | 1.995 | 2.016 | 2.037 | 2.058 | |
140 | Volume (mS/kg) | 0.16 | 0.167 | 0.175 | 0.182 | 0.19 | 0.197 | 0.204 | 0.211 | 0.218 | 0.226 | 0.233 |
Enthalpy (kJ/kg) | 393 | 399.2 | 405.5 | 411.9 | 418.4 | 424.9 | 431.5 | 438.3 | 445.1 | 452 | 459 | |
Entropy (kJ/kg· K) | 1.816 | 1.841 | 1.865 | 1.889 | 1.912 | 1.935 | 1.957 | 1.979 | 2.001 | 2.022 | 2.043 | |
180 | Volume (mS/kg) | — | 0.129 | 0.135 | 0.141 | 0.146 | 0.152 | 0.158 | 0.164 | 0.169 | 0.175 | 0.18 |
Enthalpy (kJ/kg) | — | 398.3 | 404.7 | 411.1 | 417.7 | 424.3 | 431 | 437.8 | 444.6 | 451.6 | 458.6 | |
Entropy (kJ/kg· K) | — | 1.814 | 1.839 | 1.863 | 1.886 | 1.909 | 1.932 | 1.954 | 1.975 | 1.997 | 2.017 | |
200 | Volume (mS/kg) | — | 0.115 | 0.121 | 0.126 | 0.131 | 0.137 | 0.142 | 0.147 | 0.152 | 0.157 | 0.162 |
Enthalpy (kJ/kg) | — | 397.8 | 404.3 | 410.8 | 417.3 | 424 | 430.7 | 437.5 | 444.4 | 451.4 | 458.4 | |
Entropy (kJ/kg· K) | — | 1.803 | 1.828 | 1.852 | 1.875 | 1.898 | 1.921 | 1.943 | 1.965 | 1.986 | 2.007 | |
250 | Volume (mS/kg) | — | — | 0.095 | 0.1 | 0.104 | 0.108 | 0.113 | 0.117 | 0.121 | 0.125 | 0.129 |
Enthalpy (kJ/kg) | — | — | 403.2 | 409.8 | 416.5 | 423.2 | 430 | 436.8 | 443.8 | 450.8 | 457.9 | |
Entropy (kJ/kg· K) | — | — | 1.803 | 1.828 | 1.852 | 1.875 | 1.898 | 1.92 | 1.942 | 1.963 | 1.984 | |
300 | Volume (mS/kg) | — | — | 0.078 | 0.082 | 0.086 | 0.089 | 0.093 | 0.097 | 0.1 | 0.104 | 0.107 |
Enthalpy (kJ/kg) | — | — | 402.1 | 408.8 | 415.6 | 422.4 | 429.2 | 436.2 | 443.2 | 450.2 | 457.4 | |
Entropy (kJ/kg· K) | — | — | 1.783 | 1.808 | 1.832 | 1.856 | 1.879 | 1.901 | 1.923 | 1.945 | 1.966 | |
350 | Volume (mS/kg) | — | — | 0.066 | 0.07 | 0.073 | 0.076 | 0.079 | 0.082 | 0.085 | 0.088 | 0.091 |
Enthalpy (kJ/kg) | — | — | 400.9 | 407.8 | 414.6 | 421.5 | 428.5 | 435.5 | 442.5 | 449.7 | 456.9 | |
Entropy (kJ/kg· K) | — | — | 1.765 | 1.79 | 1.815 | 1.839 | 1.862 | 1.885 | 1.907 | 1.929 | 1.95 | |
400 | Volume (mS/kg) | — | — | — | 0.06 | 0.063 | 0.066 | 0.069 | 0.071 | 0.074 | 0.077 | 0.079 |
Enthalpy (kJ/kg) | — | — | — | 406.7 | 413.7 | 420.7 | 427.7 | 434.8 | 441.9 | 449.1 | 456.3 | |
Entropy (kJ/kg· K) | — | — | — | 1.774 | 1.8 | 1.824 | 1.847 | 1.87 | 1.893 | 1.914 | 1.936 | |
450 | Volume (mS/kg) | — | — | — | 0.053 | 0.055 | 0.058 | 0.061 | 0.063 | 0.066 | 0.068 | 0.07 |
Enthalpy (kJ/kg) | — | — | — | 405.7 | 412.8 | 419.9 | 427 | 434.1 | 441.3 | 448.5 | 455.8 | |
Entropy (kJ/kg· K) | — | — | — | 1.76 | 1.786 | 1.81 | 1.834 | 1.857 | 1.88 | 1.902 | 1.923 | |
500 | Volume (mS/kg) | — | — | — | — | 0.049 | 0.052 | 0.054 | 0.056 | 0.059 | 0.061 | 0.063 |
Enthalpy (kJ/kg) | — | — | — | — | 411.8 | 419 | 426.2 | 433.4 | 440.6 | 447.9 | 455.2 | |
Entropy (kJ/kg· K) | — | — | — | — | 1.773 | 1.798 | 1.822 | 1.846 | 1.868 | 1.89 | 1.912 | |
600 | Volume (mS/kg) | — | — | — | — | 0.04 | 0.042 | 0.044 | 0.046 | 0.048 | 0.05 | 0.052 |
Enthalpy (kJ/kg) | — | — | — | — | 409.8 | 417.2 | 424.6 | 431.9 | 439.3 | 446.7 | 454.1 | |
Entropy (kJ/kg· K) | — | — | — | — | 1.75 | 1.776 | 1.801 | 1.825 | 1.848 | 1.87 | 1.892 | |
700 | Volume (mS/kg) | — | — | — | — | — | 0.035 | 0.037 | 0.039 | 0.041 | 0.042 | 0.044 |
Enthalpy (kJ/kg) | — | — | — | — | — | 415.4 | 422.9 | 430.5 | 438 | 445.5 | 453 | |
Entropy (kJ/kg· K) | — | — | — | — | — | 1.757 | 1.782 | 1.806 | 1.83 | 1.853 | 1.875 | |
800 | Volume (mS/kg) | — | — | — | — | — | 0.03 | 0.032 | 0.034 | 0.035 | 0.037 | 0.038 |
Enthalpy (kJ/kg) | — | — | — | — | — | 413.4 | 421.2 | 428.9 | 436.6 | 444.2 | 451.9 | |
Entropy (kJ/kg· K) | — | — | — | — | — | 1.739 | 1.765 | 1.79 | 1.814 | 1.837 | 1.86 | |
900 | Volume (mS/kg) | — | — | — | — | — | 0.026 | 0.028 | 0.029 | 0.031 | 0.032 | 0.034 |
Enthalpy (kJ/kg) | — | — | — | — | — | 411.4 | 419.5 | 427.4 | 435.2 | 443 | 450.7 | |
Entropy (kJ/kg· K) | — | — | — | — | — | 1.722 | 1.749 | 1.775 | 1.799 | 1.823 | 1.846 | |
1000 | Volume (mS/kg) | — | — | — | — | — | — | 0.025 | 0.026 | 0.027 | 0.029 | 0.03 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | 417.6 | 425.7 | 433.7 | 441.7 | 449.6 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | 1.734 | 1.761 | 1.786 | 1.81 | 1.833 | |
1100 | Volume (mS/kg) | — | — | — | — | — | — | 0.022 | 0.023 | 0.024 | 0.026 | 0.027 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | 415.7 | 424 | 432.2 | 440.3 | 448.3 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | 1.72 | 1.748 | 1.773 | 1.798 | 1.822 | |
1200 | Volume (mS/kg) | — | — | — | — | — | — | — | 0.021 | 0.022 | 0.023 | 0.024 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | 422.3 | 430.7 | 439 | 447.1 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | 1.735 | 1.761 | 1.787 | 1.811 | |
1300 | Volume (mS/kg) | — | — | — | — | — | — | — | 0.019 | 0.02 | 0.021 | 0.022 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | 420.5 | 429.1 | 437.5 | 445.8 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | 1.723 | 1.75 | 1.776 | 1.8 | |
1400 | Volume (mS/kg) | — | — | — | — | — | — | — | 0.017 | 0.018 | 0.019 | 0.02 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | 418.6 | 427.5 | 436.1 | 444.6 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | 1.711 | 1.739 | 1.765 | 1.79 | |
1500 | Volume (mS/kg) | — | — | — | — | — | — | — | 0.016 | 0.017 | 0.018 | 0.019 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | 416.5 | 425.7 | 434.6 | 443.2 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | 1.699 | 1.728 | 1.755 | 1.781 | |
1750 | Volume (mS/kg) | — | — | — | — | — | — | — | — | 0.014 | 0.015 | 0.015 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | — | 421.1 | 430.6 | 439.7 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | — | — | 1.731 | 1.758 | |
2000 | Volume (mS/kg) | — | — | — | — | — | — | — | — | — | 0.012 | 0.013 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | — | — | 426.3 | 436 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | — | — | 1.708 | 1.737 | |
2250 | Volume (mS/kg) | — | — | — | — | — | — | — | — | — | 0.01 | 0.011 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | — | — | 421.3 | 431.9 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | — | — | 1.685 | 1.716 | |
2500 | Volume (mS/kg) | — | — | — | — | — | — | — | — | — | — | 0.009 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | — | — | — | 427.4 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | — | — | — | 1.696 | |
2750 | Volume (mS/kg) | — | — | — | — | — | — | — | — | — | — | 0.008 |
Enthalpy (kJ/kg) | — | — | — | — | — | — | — | — | — | — | 422.2 | |
Entropy (kJ/kg· K) | — | — | — | — | — | — | — | — | — | — | 1.674 | |
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. |
Equation 17.8 is used to find the tangential velocity. From the known angular velocity, the rotor diameter can be found. The tangential velocity is
v_{to} = \sqrt{h_{o} – h_{i}} (17.8)
v_{to} = [(435.0 – 406.6) kJ/kg \times 1000 J/kJ]^{1/2} = 168.5 m/sThe rotor outer radius is then
r_{o} = \frac{v_{to}}{\omega} = \frac{168.5 m/s}{188 s^{-1}} = 0.90 m (3.0 ft)Comments
This result is refrigerant specific, but for the common CFCs, there is not much difference. For example, for R-12, the rotor radius for the aforementioned example would be 0.76 m. However, for ammonia operating between the same two conditions, the enthalpy change would have been 52 kJ/kg and the rotor radius about 1.20 m. This is a relatively large rotor size to be economically manufactured.
Of course, the rotor size can be reduced if the rotor is spun faster. Centrifugal forces increase with the square of angular velocity and linearly with the rotor radius.
The mass flow rate of refrigerant through centrifugal compressors is set by the depth of the impeller, i.e., the dimension into the plane of Figure 17.7.