# Understanding how pump curves are generated

Industrial pump manufacturers always have available pump curves for fixed-speed pumps with full-size impellers, but what if you want to run the pump at a different RPM or use a trimmed impeller?  Well, the manufacturer should be able to provide you with a modified curve but if that is not easily obtainable just use affinity laws to modify the manufacturer’s standard curve.

Affinity laws are not courtroom jargon, just some simple formulas that can be applied to operating points on a pump curve to predict a new point when pump RPM or impeller diameter is modified.

Changing the Pump RPM: When the impeller diameter of a centrifugal pump is held constant the effect of changing the speed (RPM) is in accordance with the following formulas, where  N= RPM   Q = Capacity   H = Head, and  BHP = brake horsepower.

Q1/Q2 = N1/N2

H1/H2 = (N1/N2)2

BHP1/BHP2 = (N1/N2)3

Changing the Impeller Diameter: The effect of trimming the impeller without changing the pump speed is virtually identical to what happens when you alter only the pump speed. Therefore the formulas are also very similar, as illustrated below, where  D= impeller diameter   Q = Capacity   H = Head and  BHP = brake horsepower.

Capacity: Q1/Q2 = D1/D2

BHP: BHP1/BHP2 = (D1/D2)3

Note; Before  I show you how to use these formulas to generate a special curve there are a couple of cautionary notes.  Firstly, the accuracy of affinity laws or formulas diminishes as the percent change increases.  Generally changes of approximately 15 % or less still yield acceptable accuracy.  Secondly, when trimming an impeller you are modifying the effective length of the impeller vanes and that is what results in a modified performance.  Since the impeller vane on most pumps does not start at the center of the impeller the percent change in impeller diameter does not accurately reflect the percent change in vane length. Since impeller diameter is easier to work with than vane length, affinity laws substitute it. On high flow- low head impellers this substitution can introduce significant error and actual test tank data should be used to create modified curves instead of affinity laws.

Creating a curve for a special pump speed or impeller trim is basically the same procedure. I will therefore only demonstrate one today and that is the creation of a  pump “Head–Flow” curve.

Below is a pump curve for a 1750 rpm pump.  If we needed to create a curve for 1650 rpm we would start by calculating the shut-off point. The current shut-off point is zero flow at 125 meters as indicated by the green star. The new shut-off point at the reduced rpm would be calculated using the following two calculations

The new flow point at shut-off is calculated using the flow affinity formula  N1/N2=Q1/Q2

OR

1750/1650 = 0/Q2     therefore  Q2 is zero M3/hr

The new head point is calculated using the head affinity formula  (N1/N2)2=H1/H2

OR

(1750/1650)2 = 125/H2    therefore H2 is 111 meters

Plotting zero M3/hr at 111 meters on the curve below, we establish the calculated shut-off point for the pump at an rpm of 1650.  (indicated by the blue star below) We would next calculate the new run-out point. The current run-out point is 17.2 M3/hr at a head of 85 meters, as indicated by the red star. The run-out point at the reduced rpm would be calculated using the same two formulas as used with the shut-off point

N1/N2=Q1/Q2

OR

1750/1650 = 17.2/Q2     therefore  Q2 is 16.2 M3/Hr

The new head point is calculated using the flow affinity formula  (N1/N2)2=H1/H2

OR

(1750/1650)2 = 85/H2    therefore H2 is 75.6 meters

Plotting 16.2 M3/hr at 75.6 meters on the curve above, we establish the calculated run-out point for the pump at an rpm of 1650.  (indicated by the orange star above)

Additional points can be calculated to fill in the points between shut off and run out using the same procedure as used above, thereby filling in some points on the 1650 rpm curve as shown in the illustration below. (black stars) Finally, as shown below, connect the points, and you have a 1650 pump curve. In closing, this is how you can create a curve by yourself, however, if it is a Toyo pump curve, you may forget this blog altogether and just call 604-298-1213 and have our application team e-mail you what you need!

Cheers

RJ