Using Affinity Laws to Calculate Pump Curves at different RPMs

[BronYrAur]

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.

 

[Artisi]

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.)

 

[LittleInch]

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.

 

[Artisi]

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.)

 

[BronYrAur]

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.

 

[Artisi]

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.)

 

[LittleInch]

Even more amazingly so did I!!

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