Chapter 6, Problem 6.78P

An expression for the actual water vapor partial pressure in terms of wet-bulb and dry-bulb temperatures, referred to as the Carrier equation, is given as
$p_v=p_{gw}-\frac{\left(p-p_{gw}\right)\left(T_{\text{db}}-T_{\text{wb}}\right)}{1810-T_{\text{wb}}}$
where $p_v,p_{gw},$ and p are the actual partial pressure, the saturation pressure at the wet-bulb temperature, and the total pressure (all in bars), while $T_{\text{db}}$ and $T_{\text{wb}}$ are the dry- and wet-bulb temperatures in kelvins. Consider air at 1 atm and $37.8°\text{C}$ flowing over a wet-bulb thermometer that indicates $21.1°\text{C}\text{.}$

1. Using Carrier's equation, calculate the partial pressure of the water vapor in the free stream. What is the relative humidity?
2. Refer to a psychrometric chart and obtain the relative humidity directly for the conditions indicated. Compare the result with part (a).
3. Use Equation 6.65 to determine the relative humidity. Compare the result to parts (a) and (b).