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Pump affinity laws

What are the Affinity Laws?

The pump affinity laws are a set of formulas that help predict flow, head, power absorbed at different shaft speeds. If you know the shape of a pump performance curve at a certain speed or with a certain impeller diameter, you can use the affinity laws to predict the performance of the same pump at a different speed or with a different diameter impeller with a high degree of accuracy.

There are three affinity laws:

Law 1: Flow is Proportional to Shaft Speed or Impeller Diameter

As shaft speed or impeller diameter changes, flow changes by the same proportional amount. In other words, if shaft speed increases by 10% then flow at the same head will also increase by 10%. This law is expressed with the following formula:

Q 1/Q 2 = (N 1/N 2) or (D 1/D 2)

Where Q is equal to flow, N is equal to shaft speed, and D is equal to impeller diameter.

Law 2: Pressure is Proportional to the Square of Shaft Speed or Impeller Diameter

As shaft speed or impeller diameter changes, pressure changes in proportion to the square of the change in shaft speed or impeller diameter. In other words, if shaft speed increases by 10% then pressure at the same flow will increase by 21% (1.10 2). This law is expressed with the following formula:

H 1/H 2 = (N 1/N 2)2 or (D 1/D 2)2

Where H is equal to head, N is equal to shaft speed, and D is equal to impeller diameter.

Law 3: Power is Proportional to the Cube of Shaft Speed or Impeller Diameter

As shaft speed or impeller diameter changes, power changes in proportion to the cube of the change in shaft speed or impeller diameter. In other words, if shaft speed increases by 10% then pressure at the same flow will increase by 33.1% (1.10 3). This law is expressed with the following formula:

P 1/P 2 = (N 1/N 2)3 or (D 1/D 2)3

Where P is equal to power, N is equal to shaft speed, and D is equal to impeller diameter.

Use of the Affinity Laws

The affinity laws will produce highly accurate results when predicting the impact of changes in speed. However, as the diameter of an impeller changes the efficiency of the impeller will also change, therefore, application of the affinity laws to calculate the impact on pump performance as a result a change in impeller diameter are helpful but not always highly accurate.