Given two environmental conditions—summer and monsoon—how long will it take for a freshly painted barn to dry under each condition? Perform a psychrometric analysis assuming the following conditions:
The drying time is inversely proportional to the evaporation rate, which depends on temperature, humidity, and wind speed. Use these conditions to determine the drying times and compare them.
The drying time \( D_t \) is inversely proportional to the evaporation rate \( E_r \):
\[ D_t \propto \frac{1}{E_r} \]
The evaporation rate \( E_r \) depends on the difference between the temperature and the dew point temperature, as well as the wind speed \( v_w \). It is modeled as:
\[ E_r = k \cdot (T - T_{dp}) \cdot v_w \]
where \( T \) is the temperature, \( T_{dp} \) is the dew point temperature, and \( k \) is a proportionality constant. The dew point temperature can be approximated as:
\[ T_{dp} = T - \frac{100 - H}{5} \]
Thus, the drying time \( D_t \) is inversely proportional to the product of relative humidity \( H \) and wind speed \( v_w \):
\[ D_t \propto \frac{5}{H \cdot v_w} \]
For summer conditions, we assume:
The dew point temperature is calculated as:
\[ T_{dp} = 30 - \frac{100 - 40}{5} = 30 - 12 = 18^\circ C \]
Substituting into the drying time equation:
\[ D_t \propto \frac{5}{40 \cdot 2} = \frac{5}{80} = 0.0625 \]
For monsoon conditions, we assume:
The dew point temperature is calculated as:
\[ T_{dp} = 25 - \frac{100 - 85}{5} = 25 - 3 = 22^\circ C \]
Substituting into the drying time equation:
\[ D_t \propto \frac{5}{85 \cdot 0.5} = \frac{5}{42.5} \approx 0.1176 \]
To compare the drying times between summer and monsoon, we calculate the ratio of the drying times:
\[ \text{Drying Time Ratio} = \frac{0.1176}{0.0625} \approx 1.88 \]
Therefore, the drying time in monsoon conditions is approximately 1.88 times longer than in summer conditions.
Based on this psychrometric analysis: