Document dDOzVNbRmzVLQaBjG6w1r1zjG

66 CHAPTER. 3 : 949 Guide weights, namely,' 18.016/28:966 = 0.6220; hence Equation 13 can be written ' ' ' W = 0.6220 P* P - V- '......... . . ' (14) Now, even if it is assumed that both the dry air and the water vapor behave' like perfect gases, it does not follow that at saturation the partial pressure of the water vapor can be put equal to the saturation pressure of pure water at the temperature of the mixture because: (1) the coexisting liquid (or solid) phase is not pure water but contains a small amount :of dissolved air, and (2) the coexisting liquid (or: solid) phase .has to. support the ob served pressure p and not just the saturation pressure p, of pure, water. These effects are calculable but are in general smaller than the effects of mtermolecular forces which have already been ignored. Besides, the only legitimate reason for retaining Dalton's Rule is to gain simplicity; hence these effects should be disregarded also, and the humidity ratio at satura tion estimated as follows, Wt = 0.6220 ------ v - p* ; ;.r ' (15) . . ; In this chapter the ratio W/W, has been called degree of saturation,arid denoted by the greek letter, pi:. The ratio pw/p has long.been1 called relative humidity and will be denoted by the Greek letter y>. Equations 14 arid 15 can be combined to give : . y". which can be inverted to:give 1 - pJp 1 - vpjp (16) <P = 7.------ 77^- C 7 ' ' '' . ; ; 1 -- (1 - P)Pt/p - (17) Example IS. Find the relative humidity of moist 'air at 480 F,'20 per cent saturation. -' , ' Solution.' Inserting numerical data fromTable 1 into Equation 17, the answer is 0.20 ' '. v = ----------------------------- --= 0.3384' ' 1 - 0.80 X 15.294/29.921 , : . , ; Example 17. Find the degree of saturation of moist air at 70 F, 50 per cent relative humidity. . Solution. Inserting numerical data from Table 1 into Equation 16, the answer is 1 - 0.73915/29.921 0.50 0.4937 - 0.50 X ,0.73915/29.921 The foregoing examples show that there is a substantial difference be tween degree of saturation and relative humidity, particularly at higher temperatures. Of course, they both have the value zero for dry air and the value unity for saturated moist air regardless of the temperature. A Dalton Rule expression for the volume of moist air per pound of dry air obtainable directly from Equation 12 is " Thermodynamics .67 where 'j!i i'1'"' ...................... ' ft. = gas constant for dry air = 1545.31 -s- 28.966 = 53.349 (ft/F). ft. = gas constant for water "vapor = 1545.31 4- 18.016 = 85.774 (ft/F). This expression is of the form of Equation 4. According to Dalton's Rule the enthalpy of moist air is the sum of sepa rate contributions from the dry air arid the water vapor; thus, 5 .= A. + p(lF.hw) .(19) where, to be consistent, the specific enthalpies K and hw should be allowed to vary with temperature only, not with pressure or composition. This expression is of the form of Equation 5. Within the accuracy,of,Dalton's Rule the following empirical equations give suitable values of K arid h,,: ;: A. = 0.2401 - ft. = 0.4441 + 1081 (20) Equation 7 defining thermodynamic wet-bulb temperature may be written in the form, . ft -- ft';rb (W.* - lF)ft,,* = ft,* - ft' If the quantity'A' that has'been subtracted from both sides is understood to be the enthalpy at the thermodynamic wet-bulb temperature but at the humidity ratio W, then within the accuracy of Dalton's Rule ft - ft' = (0.240 + 0.444W) (1 - 1*) ft,* - ft' = (1061 + 0.4441*) (W* - W) A.* = 1* - 32 With these approximations Equation 7 becomes 0.240 + 0.444W , IF.* - W = -------------------------------- (1 -- 1 ) 1093 - 0.5561* (21) Carrier6 has.modified Equation 21 by introducing further approximations as.follows. , IF.* = 0.6220p.*/(p - p.*) IF = 0.6220p./(p - p,*) . . ;.. . 6,444 IF = 0 the first of which is part of Dalton's Rulel The result is p. = P. p - p.* : (I - W 2830 - 1.441* , (22) except that the numerical values of the constants in the denominator of the rightmost term are somewhat different than Carrier's. Equation 22 permits direct calculation of the partial pressure p,, from observed values of pressure p, temperature t, and wet-bulb temperature t*, assuming that information is available'regarding' the saturation pres sure p,.: ,The.ratio p./,pi'.is,the so-called relatiye:.humidity,,.... Example 18. Find the relative humidity of moist air at iX) F dry-bulb, and 63 F (thermodynamic-wet-bulb).' , . ...