Document MoE63Ej1M9J5xgE8knzVBq8xL

34 CHAPTER 3 1960 Guide For water, a.W, + t, - a.W, + L, or, with (?* -- L, -- Lt, Gi{Wt - W\) = C. (42) The condition line for this process has a slope which can be determined from a combination of Equations 41 and42. Thus, hf -- hi tqt + Ljkmt -- LJlat Wt - W\ " U - Lt . Solution a: From the data of Table 2. As previously stated, the final temperature of the mixture will be the thermodynamic wet-bulb temperature at the initial state. This must first be determined by the method of Example 8, and is 55.51 F. At this temperature the humidity ratio at saturation and enthalpy at saturation are 0.01350 and 30.45, respectively. The humidity ratio at the initial state is 0-60(0.01882) * 0.01129; the initial enthalpy U 0.60(20-59) + 13.018 * 30.372, neglecting h. The weight of water added is therefore 0.01350 -- 0.01129 0.00221 lb per lb of dry air; the enthalpy change is 30.45 -- 30372 =* 0.078 Btu per In of dry air. .. Solution b: From the ASHBAE Chart. Since the initial and final states have the same thermodynamic wet-bulb tempera ture, the results may be read directly from the chart. Addition of Heat and Water Vapor to an Air Stream in Steady How Fig. 16 is a schematic representation of a system operating at constant pressure. An energy balance for the system gives where Ggh{ + >9t + " Cfe*> + Uh~, (41) Gg ~ rate of flow of dry air, pounds per minute. G, -- rate of evaporation of the water, pounds per minute, h. enthalpy of the liquid water entering, Btu per pound. L " flow rate of liquid water. q -- rate of beat addition, Btu per minute. . A mass balancegives: For air. Flow rate -=<?* -- inflow rate outflow rate t-t . 1-2 hwi fig. T6.... Illustration of Addition of Heot and Water Vapor to an Air Stream in Steady Flow If the water enters and leaves at the mmo temperature, Ai hmi, and Equation 43 becomes h% -- ht Wt - Wt -<7, + i- (44) If Lt -- 0, that is, if all of the water entering is earned away as water vapor, this also leads to Equation 44. Example 8: Moist sir at 20 F dry-bulb temperature and 0.80 degree of saturation is heated and humidified until it is at 120 F ary-bulb temperature and 71A F thermodynamic wet-bulb temperature. Water is supplied at 55 F at a rate of 10 lb per min, and the excess water leaves at 65 F. The air flow rate is 20,000 cfm measured at the initial conditions. Find the re quired rate of beat addition and the rate of water evaporation. Solution a: Using the data of Table 2. The initial humidity ratio is Wt 0.80 (0.002152) -* 0.001722; the initial enthalpy is hi = 4-804 + 0.80 (2.302) * 6.646, neglecting ; the initial specific volume is Vi * 12.084 -f- 0.80 (0.042) > 12.12, neglecting v. The degree of saturation at the final state p* is computed from Equation 8, which may be written in the form hat + * + hwtWt* + -- Arj'ff'rt} ** A,** The properties are: ** 35.39, 0.01668, hat* " 39.61, 90.70, Ifn - 0.08149, hat 28.84. The term is obtained in two steps: (1) solve for t*t assuming A* * 0, (2) compute At from at thus determined and see if the correction is warranted. The first step yields p* 0.0681. Then, ^t(l - nOB 0.0681(0,9319)0.1050 " 1 +1.6078 " 1 + 1.6078(0-08149X0.0681) 0.0066 Btu per lb. This correction amounts to 0.01 in the second decimal place (which is not appreciable for most purposes), whereby &* + a* 28.85. A second value of Mt now is computed, but the correction is so small that there is no'tnunerical influence. Hence,.** *= 0.0681 remains valid. The final humidity ratio is IF* 0.0681 (0.08149) -- 0.005549. The final enthalpy is A* - 28.84 + 0.01 + Q.06S1 (90.70) - 35.03 Btu/lb dry air. The air rate is Ge -- 20,000 + 12.12 -- 1650 lb dry air per min. The rate of water evaporation is found from Equation 42. <? - Gt(Wx - Wt) - 1650(0.005549 - 0.001722) -- 6.32 lb per coin The rate of water discharge is Li * Lt -- <?w = 3.68 lb per min The liquid water enthalpies are taken from Table 2 as Am s 23.12, hat *" 33.11 Btu per lb. This use of Table 2 assumes that the water enters and leaves the apparatus in contact with air at a pressure of 1 atmosphere. The rate of beat supply is obtained from Equation 41 in the form i? " Gi(At -- Ai) + Lthwt -- Lthmt - 1650(35.03 - 6.646) + 3.68(33.11) - 10(23.12) - 46,730 Btu/min Thermodynamics 35 Table 7.... Pressure and Temperature for Altitudes in U. S. ' Standard Atmosphere Altitude Feet Z Putnam la. of Hg f Imp F t Fig. T7 .... Solution of Examp/e $ on ASHRAE Prychrometrie Chart Solution 5: From the ASHRAE Chart. Locate the initial and final states on the chart and connect them with a straight line, which is the condition line of the process (Fig. 17). On the chart protractor draw a line parallel to the condition line, and read the ratio (A* -- Ai)/(Wt -- IPj) -- 7500. Equation 43 then becomes ht--- hi ?KM '7* Llhml -- Ljhat W,-W,~ 7SW (Lt - Lt) The water evaporation rate, Lt -- Lt Gw , is computed, as before, from Equation 42 and the humidity ratios are read from the chart. This yields Ga "* 6.27 Ib/tnin. With Lt , Lt , hat , hat all established, the magnitude of Q iscomputed from the above equation in the form i?i TM 750O(Li -- Lt) -- Lihai + Lthat - 7500(6.27) - 10(23.1) + 3.68(33.1) *= 46,900 Btu/min The difference between this result and the previous one is due to the limitation in number of significant figures that can be obtained in graphical readings. U. -S. STANDARD ATMOSPHERE ' The definition of the U. S. Standard Atmosphere is Im portant to the air-conditioning engineer as an essential stand ard of reference. The basic assumptions in defining the Stand ard Atmosphere are: 1. There is a linear decrease in temperature T with altitude up to the lower limit of the isothermal atmosphere at 35,332 ft. Thus, T - T. - 0.003566 Z (45) 2. The air is dry. 3. Air is a perfect gas obeying the laws of Charles and Boyle: 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, winch are part of the definition of the Standard Atmosphere, are: Pressure Temperature Absolute Temperature. Gravity Density 29.921 in. Eg 59 F 518.67 F abs 32.1740 ft per (sec) (sec) 0.076505 lb per cu ft -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 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 +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 Values of pressure and temperature are listed in Table 7 for altitudes in the standard atmosphere from --1000 to 50,000 ft above 'sea level. For further explanation. References 12 and 13 should be consulted. Air-conditioning engineers frequently use a standard air density, at 1 atmosphere pressure, of 0.075 Ib/cu ft. From Ta ble 2, this is represented by dry air at 69.4 F. Noting further that the density being employed here is in lb mixture per cu ft, the density of 0.075 also corresponds to variously humid air at higher temperatures than 69.4 F; at 70 F this density is achieved with a humidity ratio of 0.001125, for example. The relationship here is expressed in terms of specific volume per lb dry air given on the ASHRAE Pstchbometric Chart, as (cu ft mixture per lb mixture) -- (cu ft mixture per lb dry air) *- (lb mixture per lb dry air). LETTER SYMBOLS USED IN CHAPTER 3 A = degree of saturation (decimal). 4 * relative humidity (decimal). ton * work done by the system on the surroundings between states 1 and 2, Btu. a ratio of apparent molecular weight of dry air (28.966) to the molecular weight of water (18.016) =- 1.6079. A = coefficient from Table 6 for use in Equation 34 (ob tained from Table 6). B -- coefficient to be used in Equation 35 (obtained from Table 6). C s coefficient for use in Equation 36 (obtained from Table 6). c,, specific beat at constant pressure, Btu per pound- Bp -- fluid potential energy, Btu per pound of dry air. Eg = fluid kinetic energy, Btu per pound of dry air. / Fc " compressibility factor. . /. -- factor accounting for effect of mixing air and water, dimensionless. G - mass flow rate, pounds per hour. Gg * flow rate of dry air, pounds per minute. Gm K rate of evaporation of water, pounds per minute. H = enthalpy of the system, Btu. B = enthalpy of the flowing medium, Btu per pound of dry air. A = enthalpy of moist air, Btu per pound of dry air. A' = enthalpy of fluid, Btu per pound.