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As Jan said, the size of the pump (as well the piping details), will determine what a 'turnover' (filtering the 3 of gallons the pool holds) time is.

One turnover is usually sufficient for a home pool with few users. There are other issues that need to be considered like:

1) Weather - the hotter the weather and the stronger the sun, the more you would want to run the system. Also, if you live in a windy area and lots of stuff gets blown into the pool, you'd want to either run the system longer or think about getting a cover you could easily put on when the pool isn't in use.

2) Chlorine, or sanitizer - if you have an auto feed system, you'll want to run the pump more when the water is hot or lots of people are using the pool or when debris is constantly being introduced to the water.

3) Cloudy water - if your water is constantly cloudy, while maintaining sufficient chlorine, you'd want to up the run time. (though this is probably a result of something from #1 or 2)

As a loose rule of thumb: run the pump for 1 hour for every 10 degrees of max daytime temp per day. (this isn't the 'optimal' run time but, it's usually safe. You can always adjust the run time down by an hour/ day for a week and see how the water looks - and do further adjusting, if needed)