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Using Affinity Laws to Calculate Pump Curves at different RPMs

Using Affinity Laws to Calculate Pump Curves at different RPMs

Using Affinity Laws to Calculate Pump Curves at different RPMs

(OP)
I'm probably missing something obvious here, but why is there such a difference between actual and "calculated" pump curves? By that I mean that I made a random pump selection and had the software generate curves for 1750 RPM and 1225 RPM. I then wrote down several data points from the 1750 RPM curve. I had to "eyeball" them, so they are not exact, but they are close enough for my question. I took those data points to a polynomial regression calculator. A quadratic wasn't close enough. A cubic was probably good enough, but I went ahead and used a 4th degree polynomial.

I obtained an equation and graphed it. It very closely matched the manufacturer's pump curve for 1750 RPM (which is where I obtained the data). So now here is my issue. I applied the pump laws relating head and RPM and generated a curve for 1225 RPM. It is quite different from the manufacturer's curve. They start out similar but they become increasingly different as the flow increases.

What am I missing here? What is causing the difference? Attached are graphs from the pump selection software and the ones I generated.

Thanks for your feedback.

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

Not sure what you are missing but a quick look at your 1225 rpm curve compared to the 1750 rpm curve, it is obvious that your 1225 rpm curve is wrong.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

I can see your error.

What you seem to have done is reduce the head at the same flow point by 1250^2 / 1750^2, i.e. about 0.51.

However this is incorrect as the same point on the curve for the lower speed pump is actually the 1750 flow x (1250/1750), i.e. about 0.71.

If you replot your curve using the head figures, but for the 1250 case actually plot flow as the 1750 flow x 0.71, I think you'll find a much better fit.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

New Q = Q X 1225/1750
New H = H X (1225/1750)^2
New P = P X (1225/1750)^3

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

(OP)
Got it, thanks.

I had my equation of y=ax^4+bx^3+cx^2+dx+e, where y is head and x is flow.

I curve fit that from the 1750 rpm data. I then multiplied by (1225/1750)^2 to get my new head formula at the reduced rpm.

The mistake I made was plotting this against my original GPMs. Those original GPMs DO REMAIN AS MY X-VALUES IN THE EQUATION, however, you must plot those y-value results against the reduced flow x-valves of (1225/1750).

When I did this, my calculated 1225 rpm curve very closely matched the manufacturer's data.

Thanks for your help.

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

Amazing, the manufacturer got it right.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

RE: Using Affinity Laws to Calculate Pump Curves at different RPMs

Even more amazingly so did I!!

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

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