Peter Waddington, in his book “Koi Kichi”, says the real volume of water a fish lives in is determined by multiplying the pump's flow per hour times 24 hours per day. For instance, 3,333 gallons/hour yields a "real volume" of 80,000 gallons that the Koi actually live in, regardless of the actual size of the pond. This says that the water pump’s output is more important than the size of the pond. So people with smaller ponds will want to turn them over more often than those with larger ponds.
So let’s say you have a 5,000-gallon pond, and you want to turn it over every 1-½ hours. We simply divide the size of your pond by the number of hours you want for a complete turnover to get your flow rate. So for our example the flow needs to be 5,000 / 1.5 = 3,333 gallons per hour (GPH) or 3,333 / 60 = 55.5 gallons per minute (GPM).