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62 CHAPTER 3 v v . 1958 Guide Combining equations 37 and 38 and solving for tbe ratm (Ai -WiWr WJ, = -- + A, Wt -- Wi Gw (39) Example 8: Moist air at 20 F dry-bulb temperature and 0.80 degree of saturation is heated and humidified until it is at 120 F dry-bulb temperature and :71.5 F thermo dynamic wet-bulb'temperature. Water at. 55 F is supplied. If the air flow rate is 20,000 cfm at the initial conditions, how much heat is required? Solution a: From *, + M"t + W-ar.l) = A. Fig. 16. Solution of Example 8 on A.S.H.A.E. Pstchkometric Chart The values of these properties are: A* = 35.39; IF* = 0.01668; A* = 39.61; A,,* = 90.M70a; kWin.sg =th0e.0p8r1o4p9e;rAs.,ub=s2ti8tu.8ti4o.ns and solving for degree of saturation, M = 0.0681. The final humidity ratio is therefore 0.0681 (0.08149) = 0.005549; the final enthalpy is 28.84 + 0.0681(90.70) = 35.02 Btu per lb dry air. The rate of water addition is obtained from Equation 38. i Gw = 20 000 (0.005549 - 0.00172) = 6.32 lb per min. The heat supplied is obtained from Equation 37. Q = GUA, - A,) - GwA. = 2--0 0050- (35.02 - 6.65) - 6.32(28.08) l&.lp = 46,667 Btu per min. Solution br From the A.S:H.A.E. Chart. Locate the initial and final states on the chart and connect them with a straight line. Through the reference point on the chart, draw a line parallel to the line connecting the initial and final state points, the condition line, and read the value of the ratio (A, -- Ai)/(Wj -- W0 as 7500 from Thermodynamics 63 the protractor on the'chart (Fig. 16). From Equation 39 ':; A,-A, .' 'V. V.-fp, + A. = 7500 (jW (The rate of water supply was determined in Solution a, but will, be found from, the chart. It is .. , i.Gw = (0.0055 - 0.0017) = 6.28 lb per min Q = G.(7500 - A.) = -6.28(7500 - 23) = 46,900 Btu per min. Table 6. Pressure and Temperature for Altitudes in U. S. Standard Atmosphere Altitude Feet Z - 1,000 - 500 0 + 500 + 1,000 + 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50.000 Pressure In. of Hg P 31.02 30.47 29.921 29.38 28.86 24.89 20.58 16.88 13.75 11.10 8.88 7.04 5.54 4.36 3.436 Temp Ft +62.6 +60.8 +59.0 +57.2 +55.4 +41.2 +23:4 + 5.5 -12.3 -30.1 -47.9 -65.8 ^67.0 -67.0 -67.0 U. S. STANDARD ATMOSPHERE The definition of the U. S. Standard Atmosphere is important to the air conditioning engineer as an essential standard'of reference. The basic assumptions in defining the Standard Atmosphere are: 1. There is a linear decrease in temperature T with altitude up to the limit of the isothermal atmosphere at 35,332 ft. Thus, T = T.~ 0.003566 Z 2. The air is dry. 3. Air is a perfect gas obeying the laws of Charles and Boyle: (40) PV = RT 4. Gravity is constant at all altitudes with the standard value. 5. The temperature of the isothermal atmosphere is --66 F. Standard values at sea level, which are part of the definition of the Standard Atmosphere, are: Pressure Temperature 29.921 in. Hg 59 F