I want to experiment with geothermal cooling, and have an r-10 insulated workshop which I'd like to cool during the worst of the summer heat this year. The workshop is about 400 square feet (37 m2), and 11' (3.3 m) ceilings, with a concrete floor.
To keep costs down, I'm not interested in investing in a heat pump. I'd like to try laying long horizontal loops of pipe in the nearby ground 4–6' down (1.2–1.8 m), run water through them, and then through a radiator in the shop I can blow air through.
The ground around here is the typical 55 °F (13 °C) average temperature, and in this area is mostly heavy dense clay. The water table will be many feet below the loops in the area I plan to lay them.
While I could do this experimentally, lay an arbitrary amount of pipe, and take measurements (inflow/outflow temp difference and flow rate), I'm wondering what equations and engineering knowledge I should be looking at to give me rough back-of-the-napkin numbers on how much pipe I'm looking at to produce a certain temperature differential in the shop.