You are asked to design a heating system for a swimming pool that is $2
\mathrm{~m}\( deep, \)25 \mathrm{~m}\( long, and \)25 \mathrm{~m}$ wide. Your
client desires that the heating system be large enough to raise the water
temperature from \(20^{\circ} \mathrm{C}\) to \(30^{\circ} \mathrm{C}\) in $3
\mathrm{~h}\(. The heater must also be able to maintain the pool at \)30^{\circ}
\mathrm{C}\( at the outdoor design conditions of \)15^{\circ} \mathrm{C}, 1
\mathrm{~atm}, 35\( percent relative humidity, \)40 \mathrm{mph}$ winds, and
effective sky temperature of \(10^{\circ} \mathrm{C}\). 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?