David, thanks for the math, how did you decide on 3 degrees temperature rise?
A decent reverse flow heat exchanger the outlet temperature of the water should approach the inlet temperature of the air, but lets say you only get half way there and the air going in is 80F and the water in is 60F, the temperature rise of the water would be 10F.
Not nitpicking, but it is an interesting first year engineering question.
FYI the farm house my parents had in central Pa, had a cooling trough in the basement, water came through the wall from a spring and went out through a drain pipe on the other side of the basement.
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