 # The Affinity Laws

As part of our ongoing quest for knowledge and perfection, we at Hagler are starting a group of instructional posts pertaining to pumps and their properties.  Of course, without basic fundamental knowledge of pumps, sizing and selectioin can be utterly confusing.  Let’s put some of that confusion to rest.

## Centrifugal Pump Affinity Laws

Centrifugal pumps are very agile machines that are more capable than even I originally thought.  Changing certain characteristics can drastically affect the overall output/performance of the pump.  Consider the following:  If I change the output RPMs of the pump, then I have now changed the capacity, head and brake horse power required.  Of course the same can be said about changing the diameter of the impeller.

It’s important to note that the Affinity Laws are not exact because fluid properties vary.  If we remain within 50% of our original speed or 15% of our original impeller diameter, then we can conclude that the results will be reasonably close.  Therefore, these calculations are a very good approximation that can help determine the proper RPMs, Impeller Diameter and BHP for the given application.

## Laws

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.

Let’s look at some calculations to decipher the Affinity Laws.

## Calculations and Examples

First let’s establish our properties:  150 GPM @ 75’TDH with 7.2 BHP.

The first calculation is simple.  Determine the speed ratio.  If the change in speed is known, just divide the new speed (RPM2) by the original (RPM1).  Let’s use the following as an example.  I currently have 1750 RPMs all the way to the wet end but want to know what would happen if I used a 3500 RPM motor.

Speed Ratio: 3500/1750 = 2

Remember the first law.  Capacity is a direct relationship.

2 X 150 GPM = 300 GPM

2 X 2 X 75 TDH = 300 TDH

Brake Horse Power cubes the speed ratio

2 X 2 X 2 X 7.2 BHP = 57.6 BHP

It’s important to note that these values will be less accurate considering the speed ratio changed by 100% of the original speed.  So let’s use the same properties and assume a VFD (Variable Frequency Drive) is being used to change the RPMs from 1750 to 1000.

Speed Ratio: 1000/1750 = .5714

First Law: .5714 X 150 GPM = 85.71 GPM

Second Law: .5714 X .5714 X 75 TDH = 24.49 TDH

Third Law: .5714 X .5714 X .5714 X 7.2 BHP = 1.34 BHP

## Conclusion

As you can see, the Affinity Laws have an incredible impact on the application and can reduce a lot of headaches if they are recalled constantly.  Theoretically, efficiency values remain the same no matter the condition.  This is important to remember when determining proper sizing and/or speed.  I sincerely hope this helps in your sizing dilemmas as it has helped me. About Blake Austin