Page:Journal of the American Society of Mechanical Engineers, Volume 33.pdf/667

the constants employed, which make its inaccuracy more pronounced at lower humidities and at the higher temperature. At very high temperatures used in mechanical drying it is entirely inoperative.

59The need of an accurate rational psychrometric formula for vapor pressures using modern data is therefore apparent. The required values could be obtained indirectly from the formula already given, but computation is facilitated by another derivation giving directly the vapor pressure $e$.

60In equation [8]

$W={\frac {r'W'-C_{pa}(t-t')}{r+C_{ps}(t-t')}}$

let $t$ be the dew point corresponding to $W$, and $e$ the vapor pressure corresponding to $W$ in in. of mercury. Referring to equation [5]

$W={\frac {Se}{P-e}}$

by substitution

[15]

${\frac {S_{1}e}{P-e}}={r'\left({\frac {S'e'}{P-e'}}\right)-C_{ps}(t-t')}{r'+C_{ps}(t-t')}$

Solving for $e$

[16]

$e=P\left[{\frac {\left[{\frac {S'e'r'-(P-e')C_{pa}(t-t')}{(P-e')[r'+C_{ps}(t-t')]}}\right]}{\left\{{\frac {S_{1}(P-e')[r'+C_{ps}(t-t')]+[S'e'r'-(P-e')C_{pa}(t-t')]}{(P-e')[r'+C_{p}s(t-t')]}}\right\}}}\right]$

Assuming $S'e=S_{1}e_{1}$, this simplifies to

[17]

$e=P\left[{\frac {S'e'r'-(P-e')C_{pa}(t-t')}{S_{1}Pr'+(S_{1}C_{ps}-C_{pa})(P-e')(t-t')}}\right]$

at 100 deg.

[18]

$S_{1}C_{ps}-C_{pa}=[(0.623\times 0.46)-0.242]=0.033$

Therefore the value $-e(S_{1}C_{ps}-C_{pa})(t-t')$ is ordinarily negligible. Hence we have

[18]

$e={S'e'r'-C_{pa}(P-e')(t-t')}{Sr'+(S_{1}C_{ps}-C_{pa})(t-t')}$

61By comparison it will be found that the difference between $S'r'$ and $Sr'+(S_{1}C_{ps}-C_{pa})(t-t')$ is negligible. Hence it may be assumed