Question 13.12: Residential Evaporative Cooler A residence in the Sonora Des......
Residential Evaporative Cooler
A residence in the Sonora Desert of Arizona is equipped with an evaporative cooler with an air-flow rate of 3000 ft³/min (1416 L/s) sized by the rule of thumb of 2 ft³/min per square foot of residence area. If the outdoor conditions in summer are 110°F (43.5°C) and 20% RH, what is the water flow rate if 80% of the available dry-bulb temperature depression is achieved?
Given: \dot{V}_{1} = 3000 cfm, T_{db1} = 110°F, and \phi_{1} = 0.2 .
Figure: See Figure 13.13.
Assumptions: The site is at sea level. (The Sonora Desert is about 300–400 m above sea level, but to avoid the complications of using the basic psychrometric equations, we will assume a sea-level elevation and use the sea-level psychrometric chart.)
Find: \dot{m}_{w}.
Lookup values: W_{1} = 0.011 lb_{w}/lb_{a}, T_{wb2} = 75.5°F (the wet-bulb temperature is the minimum temperature achievable in this process).
The exit dry-bulb temperature is rst determined given that 80% of available dry-bulb temperature depression is achieved:
0.8 = \frac{110 – T_{db2}}{110 – 75.5} or T_{db2} = 82.4°F
To find the exit humidity ratio, one moves along the 75.5°F wet-bulb line until the 82.4°F dry-bulb temperature is reached. At this point, we read the exit humidity ratio as W_{2} = 0.0176 lb_{w}/lb_{a}.
From the chart, we also read the inlet-specific volume as 14.6 ft³/lb_{a}
Then, the needed water supply rate is
\dot{m}_{w} = \dot{m}_{a} W = \frac{\dot{V} \Delta W}{v}= 3000 ft^{3}/min \times \frac{(0.0176 – 0.011) lb_{w}/lb_{a}}{14.6 ft^{3}/lb_{a}}
= 1.36 lb_{w}/min
Comments
This flow rate, which amounts to about 9.5 gal/h (0.01 L/s), is not excessive for a desert climate when compared to the savings in electric energy needed for mechanical cooling. For example, if water costs $2/1000 gal (typical of an arid western state in the United States), the water consumed costs less than 2¢/h. The electricity to operate the fan in the evaporative cooler would cost another 2–3¢/h. On the other hand, an electric cooling system would cost about four to eight times as much, depending on the weather and load as well as the electric system’s efciency.