Pump Handbook
Affinity Laws
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The affinity laws express the mathematical relationship between the several variables involved in pump performance. They apply to all types of centrifugal and axial flow pumps. They are as follows: 1. With impeller diameter, D, held constant: 
2. With speed, N, held constant: 
You may occasionally need to estimate the hydraulic performance of a centrifugal pump at a speed or impeller diameter not shown on the catalog performance curves. To approximate the performance of the pump, the affinity laws should be used as follows: The pump capacity, or flow rate, "Q" varies with the ratio of RPM: 
The pump head "H" varies with the ratio of RPM2: 
The pump brake horsepower "BHP" varies with the ratio of RPM3: 
EXAMPLE: A customer has an application where he prefers to use a v-belt drive with a maximum diameter impeller, instead of operating at a standard motor speed and trimming the impeller diameter. You have a catalog curve giving the operating characteristics of the pump at 1750 RPM. You want to determine the pump curve at 1535 RPM. The calculations are as follows: 
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