You are asked to design a heating system for a swimming pool that is 2 m deep, 2
ID: 1841680 • Letter: Y
Question
You are asked to design a heating system for a swimming
pool that is 2 m deep, 25 m long, and 25 m wide. Your
client desires that the heating system be large enough to raise
the water temperature from 20°C to 30°C in 3 h. The heater
must also be able to maintain the pool at 30°C at the outdoor
design conditions of 15°C, 1 atm, 35 percent relative humidity,
40 mph winds, and effective sky temperature of 10°C.
Heat losses to the ground are expected to be small and can
be disregarded. The heater considered is a natural gas furnace
whose efficiency is 80 percent. What heater size (in Btu/h
input) would you recommend that your client buy?
Explanation / Answer
The heater size is found using the amount of heat required to power the swimming pool under relative humidity condition,
total heat transfer, dot q = convective heat transfer of water + forced heat transfer of air.
dot q = hwater * A * dT + dot m * Cp * dT ----------- eqn 1
hwater - 50 W / m2K
Cp of mixed gas - Cp of water vapor + Cp of dry air
Cp of dry air at 288 K - 1.047 kJ / kg K
Cp of water vapor at 288K - 1.864 kJ / kg K
The mass flow rate of air, dot mmixed gas = rhoair* A * V + dot mwater
The humidity ratio of the mixed air is 6 (approx) at 15 deg C and 35% RH.
dot mwater = 0.006 * dot mair = 0.006 * 1.225 * 1 * 40 * 0.44 = 0.129 kg /s
The total mass flow rate is dot mmixed gas = 1.225 * 1 * 40 * 0.44 + 6.468 = 21. 68 kg / s
Now the total heat transfer, dot q is found using the above eqn 1
dot q = hwater * A * dT + dot mmixed gas * Cp * dT
dot q = 50 * 25 * 25 * (300 - 290) + 21.68 * 3 * 3600 * (1.047+ 1.864) * (300 - 285)
dot q = 312500 + 10209849.12 = 10531349.12 W or 10.53 MW or 35.14 * 10^3 BTU / hr.
The size of the heater is 35.14*10^3 BTU/hr to heat the poole size of 652 m2.
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