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**Cooling a pond with river water??**

Hi all, this is kind of a basic question and I am looking for a simple formula to use to illustrate how an idea is not practical. I worked almost this exact same problem years ago in a limnology class but can’t remember how I did any of it. I help manage a small pond, for this exercise let’s say it has a volume of ~7.2 million liters (roughly 6 acre feet). The maximum summer temperature of the pond is, for the sake of argument 30⁰C. Some stakeholders would like to see the temperature lowered to 25⁰C. Their idea is to construct a closed loop of piping carrying river water through the pond, at night when the river is at it's "coolest", although there's not much of of a difference, actually. The idea is that the river water is cooler and would therefore cool the pond. But the river water is at, let’s say 22⁰C. Given the relatively large volume of water in the pond, the high thermal inertia of water, and the relatively small temperature differences, I can’t see how this idea would be practical (I’ll completely agree that it is theoretically possible). If I know the difference in temperature, and the heat conductivity of likely piping materials, then it’s sort of a rate of time question, right? Is there an equation that would let the stakeholders know that if we constructed a loop of pipe holding a volume of water equivalent to the entire pond it would take X amount of time for the temperature to equilibrate? Conversely, could I then show that with a loop of pipe holding ¼ the volume of the pond water it would take 4X time, and so on? And I realize that the relationships are not linear and the heat transfer rate would change as the differential narrows etc. I’m really just looking for an simplified way to show these folks that it’s just not a practical idea for our purposes or budget. Or, conversely, if someone can show me such an equation where it might be practical I guess I’d have to go talk to my engineers. Either way, thanks, and cheers!

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