Question 3.2: The pressure entering and leaving an adiabatic saturator is ......
The pressure entering and leaving an adiabatic saturator is 14.696 lbf/in.², the entering temperature is 80 F, and the leaving temperature is 64 F. Compute the humidity ratio W_{1} and the relative humidity \phi_{1}.
Because the mixture leaving the device is saturated, we have p_{v2} = p_{s2}, and W_{2} can be calculated using Eq. 3-14b:
W^{*}_{s2} = 0.6219 \frac{p_{2}}{P_{v2} – p_{v2}} (3-14b)
W^{*}_{s2} = 0.6219 \frac{0.299}{14.696 – 0.299} = 0.0129 lbmv/lbma
Now using Eq. 3-21d and interpolating data from Table A-1a, we get
W_{1} = \frac{c_{pa} (t^{*}_{2} – t_{1}) + W^{*}_{s2} i^{*}_{fg2}}{i_{v1} – i^{*}_{w}} (3-21d)
= \frac{0.24(64 – 80) + (0.0129 × 1057.1)}{1096 – 32} = 0.0092 lbmv/lbm
Then solving for p_{v1} using Eq. 3-14b, we have
W_{1} = 0.6219 \frac{p_{v1}}{14.696 – p_{v1}} = 0.0092 lbmv/lbm
p_{v1} = 0.2142 psia
Finally, from Eq. 3-11
\phi = \frac{p_{v/p}}{p_{s/p}} = \frac{p_{v}}{p_{s}} (3-11)
\phi_{1} = \frac{p_{v1}}{p_{s1}} = \frac{0.2142}{0.507} = 0.423 or 42.3\%
It seems that the state of moist air could be completely determined from pressure and temperature measurements. However, the adiabatic saturator is not a practical device, because it would have to be infinitely long in the flow direction and very cumbersome.