Page:Journal of the American Society of Mechanical Engineers, Volume 33.pdf/660

DERIVATION OF A RATIONAL PSYCHROMETRIC FORMULA

41⁠As already pointed out, it is possible to derive a rational psychrometric formula based on the fundamental principles, A, B and C.

42⁠In considering the interchanges of heat occurring in psychrometric phenomena, it is essential to consider primarily the relative weights of dry air and of water vapor rather than the usual density temperature relationship; that is, it is necessary to express moisture content as weight of water vapor per pound of pure air, rather than as weight of water vapor per cubic foot of space. Moreover, this relationship is much more adaptable to all of the usual calculations in air conditioning and in meteorology. The author, accordingly, has constructed all his formulae and psychrometric charts upon this basis. In the deduction of the formulae and in the construction of the accompanying charts, the following fundamental data were employed:

a	Standard barometric pressure = 29.92 in. mercury = 14.6963 lb. per sq. in. = 2116.3 lb. per sq. ft.
b	Absolute temperature = $t$ + 459.62 deg. fahr.
c	B.t.u. = heat required to raise 1 lb. of water from 32° to 212°/180°
d	Mechanical equivalent of heat = 777.52 ft-lb.
e	Specific volume of air = weight of 1 cu. ft. of pure air at 32 deg. fahr. and 29.92 in. barometric pressure = 0.080728 lb. per cu. ft. Therefore ${\frac {p_{v}}{T}}=53.35$
f	Instantaneous specific heat of air[1] $C_{pa}=0.24112+0.000009t$ deg. fahr.
g	Vapor pressure, Holborn and Henning’s modification of the Theisen formula $(t+495.6)\log {}{\frac {p}{14.70}}=5.409(t-212)-3.71x10^{-10}[(689-t)^{4}-(477)^{4}]$, as calculated in tables of Marks and Davis (1909)
h	Specific volume of steam as calculated in steam tables of Marks and Davis[2] (1909)

1. Harvey N. Davis, Trans.Am.Soc.M.E., vol. 30, p. 750, 1908.
2. W. F. G. Swann, Phil. Trans. Royal Soc., series A, vol. 210, pp. 199-238, 1909.