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The big question is how long does the water flowing in the pex tubing have to stay under ground. Constant ground temperature is about 55 degrees F around my house. I have red clay around my house. I know that the temperature as a function of time is a exponential equation.

Can somebody give me an equation temperature Vs. time spent under ground. This way I can calculate the time needed to get the right temperature water coming out of the pex tubing. Here is as many specs as I think can effect the equation:

Pex ID = 0.475"

Red clay soil

constant ground temp = 55

^{o}F

average water temp flowing into loop = 70

^{o}F