I think that your real goal is to minimize operating cost.
If you have a varying load, whether random or otherwise, you need to make a Flowrate vs Percent_of_Operation_Time chart.
As an initian approximation, Look at a BEP around
the Sum of all values of (Flowrate x Percent_Op_Time)
That's your expected average flowrate.
For good general pump operating characteristics, some
Additional constraints are
minimum flowrate >= 50% BEP and
Maximum flowrate <= 115% of BEP.
If you can't meet the addtional constraints, you may want to think of multiple pumps in parallel, or
perhaps a VFD, but be very carefull when looking at VFDs by calculating exact power consumption operating costs, including the efficiencies of the VFD and motor at partial loads and that the head at low flows and low VFD rpms is sufficient for your system curve.
That's only an approximation of average flowrate. The actual cost of operation could still vary considerably, if the flowrate range is wide, due to the variable head of the pump curve over a wide range of flows and the varying efficiency at each flowrate. Using the average alone, while still having substantial operating times away from the average florate, will not give you the lowest operating cost, so you'll still have to calculate the operating cost for each flowrate multiplied by the percent time operating at that flowrate. Then minimize that value by choosing a pump curve from several possible pumps that all give the highest operating efficiencies in the most utilized flowrate ranges.
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