## What are the Affinity Laws?

*The affinity laws are a set of forumlas that predict the impact of a change in rotational speed or impeller diameter on the head and flow produced by a pump and power demanded by a pump.*

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

This law means that 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, horsepower 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

Application of the affinity laws to predict the impact of changes in speed can produce highly accurate results. However, as the diameter of an impeller changes the efficiency of the impeller also changes. Therefore, application of the affinity laws to calculate the impact on pump performance of a change in impeller diameter are helpful but not always highly accurate.

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