Page:Journal of the American Society of Mechanical Engineers, Volume 33.pdf/665

$C_{pa}$ = mean specific heat of air at constant pressure between temperature $t$ and $t'$

$C_{ps}$ = specific heat of steam at constant pressure between $t$ and $t'$

$r'$= latent heat of evaporation at wet-bulb temperature $t'$

Knowing any two of the three important values of $t$, $t'$ or $W$, we may solve for the third or for any other required relation.

50Determination of Weight of Moisture in 1 Lb. of Pure Air, having a Dry-Bulb Temperature $t$ and Wet-Bulb Temperature $t'$. To determine the equation of the adiabatic line corresponding to a given saturation, or true wet-bulb temperature $t'$, and dry-bulb temperature $t$, we have from equation [6]

[7]

$[r'+C_{ps}(t-t')]W=r'W'-C_{pa}(t-t')$

[8]

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

51The diagonal adiabatic lines in the charts, Figs. 1 and 2, representing saturation or wet-bulb temperatures, are calculated from, this formula. It should be observed that they would be perfectly straight if it were not for the element $C_{ps}(t-t')$, which produces a slight curvature, becoming more pronounced at higher saturation temperatures. The dew point $t_{1}$ corresponds to $W$ on the saturation curve. The slope of these lines, neglecting $C_{ps}(t-t')$ is ${\frac {dW}{dt}}=-{\frac {C_{pa}}{r'}}$. This will always give the intercept $t$ for $W=0$.

52Wet-Bulb Depression and Cooling Effect. The wet-bulb depression or cooling effect obtained by having $t$ and $W$ known is

[9]

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

and

10

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

53Having $t$ and $W$ known, $t$ cannot be calculated except by relating $W$ to $t$ by an empirical equation. By referring to the psychrometric charts, Figs. 1 and 2, constructed chiefly for that purpose, $t$ is conveniently determined. The cooling effect $(t-t')$, to be obtained by saturating air of known temperature and moisture content, is likewise obtained from the chart.