Your pump should turn your water over at least once per day (twice is better, three times is wasting electricity). By "turn over", I mean equivalently filtering all of the water in the pool.
First, let's figure out how many gallons of water are in your pool as follows:
Diameter x Diameter x Depth X 5.9 = Number of Gallons
In your case, you didn't specify the water depth, so I will assume that the water is 4ft deep (this is the actual water depth, NOT the height of the wall). Therefore, in this example, your pool would hold approx 13,600 gallons.
Thus, you would like the filter to clean between 14,000 (one turn) and 28,000 (two turns) gallons per day.
In order to accomplish this in 8 hours (480 minutes), you would need a pump that flows 29.2 gal/min for one turn and 58.3 gal/min for two turns - or you could also run the pump at the lower rate (29.2) for 16 hours.
Next, you need to determine the flow rate for your pump (look at your spec sheet that came with the pump or look it up on the Internet).
Since you did not include the exact make and model, I will use a Hayward Model 1580X15 Power-Flo LX as an example. This pump is rated at 91 Gal/min with no height change in the water.
You did not mention anything about height changes in you plumbing, but if you are pumping water up to a solar heater on the roof or other vertical distance, then that pressure loss would also need to be considered and would reduce the flow rate of the pump.
Thus, at 91 gal/min, you could filter one turn of your water (14,000 gal) in 154 minutes or about 2.5 hours. Two turns would only take around 5 hours.
Please re-run these calculations using your exact parameters and you should be able to easily figure out how long to run your pump each day to acheive good filtration and minimize electricity costs.
Hope this helps ...
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