Q) A Swimming pool installer in Michigan is considering installing in the future
ID: 1341397 • Letter: Q
Question
Q) A Swimming pool installer in Michigan is considering installing in the future swimming pools only with solar water heating. Typical swimming pool he installs are 20 meters long by 12 meters wide and average 2.5 meters deep. A typical Michigan summer day in this area has insolation averages about 775 w/m2 through the summer and has useful solar heating for about 9.5 hours each day. He intends to use flat modular solar water heating panels where each are 4 meters by 4 meters facing south and typically have a typical 13.5% heat loss during operation. He has determined that it is most economical for his customers if he installs three of these water heating panels per each summer pool installation. The water recirculation pump can circulate 15 liters per minute of pool water to the panels, which then flows directly back to the pool.
If one of his pool is initially filled with 15°C water, how many days will it take to heat the pool water to 30°C, Assume the pump is turned off when useful sun-heating has ended each day, and that the pool is covered with an insulting cover at sunset so that essentially no heat is lost at night.
Use the following data to answer this question:
Cp for water = 4.186 KJ/Kg-°C
The density of water is 998 kg/m3
1 m3 =1000 liters
Explanation / Answer
Volume of pool water = 20x12x2.5 = 600 Cu.m
Mass = 600 x 998 = 598800 Kg
Power of insolation = 775 w/m^2
Number of hrs availability = 9.5
Area of panel = 4x4 = 16 Sq.m, Total panel area = 16x3 = 48 sq.m
Solar energy available per day= 775 x 48 x9.5 = 353400 J
Heat loss = 13.5 %
Total heat available per day = 353400 x 0.865 = 305691 J
Mass of water being pumped per day = (15x60x9.5/1000)x 998 = 8532.9 Kg
Specific heat capacity of water Cp = 4186 J/kg-degree
Raise in temperature of pumped water = 305691/(4186x8532.9) = 0.0086 degree-c
Heat energy require to heat the pool from 15c to 30c
=598800 x 4186 x 15
Heat available per day = 305691 J
Number days required = 598800 x 4186 x 15/30569 = 1229960 days
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