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Pumping number is the ratio of impeller discharge rate (aka primary pumping capacity) to the cube of its diameter and the shaft speed:

(3.5)

It is used to calculate the flow created by the impeller, which can be used to determine a characteristic velocity in the tank. It is a function of impeller type, Reynolds number, and geometric parameters.

The units used for N and D determine the resultant units for Q. For example, if D is in feet, and N is in rpm, Q will be expressed as cubic feet per minute. Likewise, if D is in m and N is in revolutions per second, Q will be in cubic meters per second.

There are many different ways to measure impeller pumping, and they do not all give the same results. The most widely accepted methods define a discharge area around the impeller and measure flow through it, usually by use of either laser Doppler or particle image velocimeters. It is not within the scope of this book to discuss such methods. The above methods measure what is commonly called primary impeller flow or discharge. There can also be entrained flow, which can be several times as high as the primary flow. Any claimed impeller pumping capacity should state whether it is primary flow or total flow.