Joe Evans, Ph.D

http://www.pumped101.com

THE AFFINITY LAWS

The Centrifugal Pump is a very capable and flexible machine. Because of this it is unnecessary to design a separate pump for each job. The performance of a centrifugal pump can be varied by changing the impeller diameter or its rotational speed. Either change produces approximately the same results. Reducing impeller diameter is probably the most common change and is usually the most economical. The speed can be altered by changing pulley diameters or by changing the speed of the driver. In some cases both speed and impeller diameter are changed to obtain the desired results.

When the driven speed or impeller diameter of a centrifugal pump changes, operation of the pump changes in accordance with three fundamental laws. These laws are known as the "Laws of Affinity". They state that:

1. Capacity varies directly as the change in speed
2. Head varies as the square of the change in speed
3. Brake horsepower varies as the cube of the change in speed

If, for example, the pump speed was doubled:

1. Capacity will double
2. Head will increase by a factor of 4 (2 to the second power)
3. Brake horsepower will increase by a factor of 8 (2 to the third power)

These principles apply regardless of the direction (up or down) of the speed or change in diameter.

Consider the following example. A pump operating at 1750 RPM, delivers 210 GPM at 75' TDH, and requires 5.2 brake horsepower. What will happen if the speed is increased to 2000 RPM?

First we find the speed ratio.

Speed Ratio = 2000/1750 = 1.14

From the laws of Affinity:

1. Capacity varies directly or:
   1.14 X 210 GPM = 240 GPM
2. Head varies as the square or:
   1.14 X 1.14 X 75 = 97.5' TDH
3. BHP varies as the cube or:
   1.14 X 1.14 X 1.14 X 5.2 = 7.72 BHP

Theoretically the efficiency is the same for both conditions. By calculating several points, a new curve can be drawn.

Whether it be a speed change or change in impeller diameter, the Laws of Affinity give results that are approximate. The discrepancy between the calculated values and the actual values obtained in tests are due to hydraulic efficiency changes that result from the modification. The Laws of Affinity give reasonably close results when the changes are not more than 50% of the original speed or 15% of the original diameter.

Here, we have described the affinity laws and applied them to a few examples. For an in-depth discussion and proof of their validity, see the “Affinity Puzzler”.

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About the Author

Joe Evans lived in beautiful Rhododendron Oregon and retired from Pump Tech Inc on 12/31/15. Since entering graduate school, a continuing interest has been one of computer control of mechanical and electronic systems. It began with the introduction of the minicomputer, in the late sixties, and continued with the advent of the PC and PLC in the eighties and nineties. He accidentally entered the pump industry in 1986 and has been trapped there since. He is passionate about the sharing of knowledge and its ability to replace memorization with understanding.