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.

[chem geek]

Hi Mark,

GPM and Head go in opposite directions which is why there is the minus sign in my formula, but they cannot be inversely proportional since the pump curves show a positive non-zero head with a GPM of 0. This is where the pump is spinning just to generate equivalent pressure against the head -- or another way of looking at it is that as much water is pumped towards the head as is leaked backwards so that the net GPM is 0. Your formulas don't work for that, unless I'm misinterpreting them. The formula I gave almost exactly matches all the pump curves (within 1 or sometimes 2 feet of head) for both the full IntelliFlow and the IntelliFlow 4x160 (except the latter appears to have a mistake labeling the 750 RPM which appears to really be 950 RPM).

Anyway, I'm going to call my pool contractor to see if they can do the work to replace my pump and I'll very likely go with the full IntelliFlow. I'll keep y'all posted as to my results after it gets installed.

Thanks,
Richard

[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.

[chem geek]

NOTE TO MODERATORS:

Could you please move the posts from #14 (somewhat arbirtrary, but I think that's a decent break) on to this thread I started in The China Shop? We are getting more technical than we should be for the general forum, but I do want to continue the discussion in a "safe" place that won't scare off newbies. Any net results, simple rules, or other useful information will continue to be posted in this thread, but the mathematics of fluid dynamics and statics and pump efficiencies will be kept out of this thread and placed in The China Shop.

Thanks,
Richard