Pump Efficiency

[mas985]

Richard,

Something does not look quite right with that equation. From the pumps perspective, GPM and Head are inversely proportionate while GPM and RPM should be proportionate. Also for the pump, GPM is the dependent variable and Head is the independent variable while for the plumbing system it is the opposite.

Here is the way I would formulate the problem using first order approximations. Note that second order effects do create some error in this methodology.

Starting with the pumping efficiency equation (note this is slightly different than the energy efficiency equation):

Eff = Head * GPM / (BHP * 3960)

and from pump affinity equations:

Effective BHP = BHP(max) * (RPM / RPM(max)) ^ 3

So solving for GPM

GPM = A * (RPM / RPM(max)) ^ 3 / Head

where A = (Eff * BHP (max) * 3960) but this can be solved for using the head curves for the pump. So for the 4x160, using 60' of head is about 100 GPM, A = 6000. A will vary some with head (second order effects) but for now we will ignore that. Also, we can test the formula for other RPMs. @ 2350 RPM and a Head of 40', GPM should be about 47. It's tough to tell from the chart but it looks about right. So this formula should work for all RPM and Head values of the pump.

Now, your pool plumbing has the relationship of:

Head = B * GPM^2

Where B can be found from the operating head and GPM. For without solar, you originally gave the head and flow rates as 45' @ 90 GPM so B = 1 / 180.

Combining the equations gives you

GPM = (A / B) ^ (1/3) * (RPM/RPM(max)) = 0.02974 * RPM

This is a single formula which characterizes both your pool and the pump together. Since the pump goes from 3450 to 400 RPM, your GPM should range from 12 up to 97 which is a great range to be able to operate over. Heck, I might go for one of these too. At the lowest rate, you could have a 24 hour turnover which is fantastic! You really never need to shut off the pump and when the solar goes on, you will just need to bump up the flow rate some. The value of B changes for solar so you can use the appropriate number. Also, if you need two turnovers a day, you can adjust the pump for 24 GPM and still run for 24 hours.

Let us know what you end up with.