Pump Efficiency

[mas985]

Richard,

Maybe I need to clarify my methodology a bit better. My original intent was to model your pool and pump together and not to match the entire pump curve. Pump curves handle both static and dynamic head but most pools have mostly dynamic head (i.e. pool is not much lower or higher than the equipment pad). Therefore, under normal operation after priming, you will never see a condition where the head is high but the flow is near zero. So I originally modeled the pump at maximum RPM and head between 60'-80'. This should be the range that your pool operates within at that RPM. I could have done a polynomial fit but it was unlikely to offer much more accuracy.

However, going back over the formulation, I made an error calculating the constant A. At 60' of head, the pump puts out 136 GPM and not 100 GPM.

To show how well the approximation holds, I made simple spread sheet. Here are the results:

Head @ 3450 RPM	60	70	80	90
Actual GPM	136	117	97	60
Approximate GPM	137	117	102	91
Richard's GPM	132	113	90	58

Head @ 2350 RPM	28	32	37	42
Actual GPM	93	80	66	41
Approximate GPM	93	80	70	62
Richard's GPM	90	77	61	40

Head @ 1500 RPM	11	13	15	17
Actual GPM	59	51	42	26
Approximate GPM	59	51	45	40
Richard's GPM	57	49	39	25

The head ranges are scaled with RPM to stay withing the main part of each speed's head curve. So you can see that the approximate GPM is not too bad and good up to about 80 feet of head @ 3450 RPM. It is unlikely a pool would be much above that anyway. So both your's and my methods have errors but in different locations.

The other thing I would change about the formulation is to make the constant A independent of RPM which would be

GPM = A * RPM ^ 3 / Head (Pump Formula)

Where now, A = Head * GPM / RPM^3 of a particular sample point from the head curve. This makes the formula good for a range of head and all RPM values.

Also, the pool plumbing equation, Head = B * GPM ^2 comes from the Darcy-Weisbach hydraulics equation relationship between head and GPM so the accuracy is pretty good.

So with the above corrections the new formula for your pool is

GPM = (A/B)^(1/3) * RPM = .033 * RPM or a range of 114 GPM down to 13.2 GPM.

I just wanted to make sure you understood what I did.


I also want to add that using your pump formula along with the plumbing formula and solving for GPM:

GPM = 1 / 350 / (B+1/470)^(1/2) * RPM or
GPM = .033 * RPM which is the same as using my pump formula.