Pump Affinity Laws Are Key To Saving Money in a Hydronic System

By Chad Edmondson

What are the pump affinity laws and why are they so important? 

Pump affinity laws define the mathematical relationship that exists between pump speed, flow, total head, and power consumption. They also provide perspective on the significant operational impact that a relatively minor change in speed (RPM) or pump impeller size will have on a system.  Change either of these and the GPM capacity, head, and the brake horsepower (BHP) will either increase or decrease.  Pump affinity laws tell us how much.

Specifically the laws state that:

  1. Pump GPM capacity varies DIRECTLY as the speed (RPM) or impeller diameter ratio change.
  2. Total pump head varies directly as the SQUARE of the speed (RPM) or impeller ratio change.
  3. BHP varies directly as the CUBE of the speed (RPM) or impeller diameter ratio change.

 Considering the direct relationship between BHP and RPM, it’s clear how varying pump speed has a dramatic impact energy consumption.  In simple terms, the third affinity law tells us that if you reduce the speed of a pump by 1/3 you will reduce the horsepower (energy) usage by 1/9.  Put another way, a pump running at 33% speed will only use 12% of the horsepower.  This illustrates the potential for energy savings that comes with variable speed pump control – especially in systems with widely fluctuating demands. 

The affinity laws help us predict pump performance changes under a single set of operational conditions.  By using the calculations in Figure 1 you can plot a new pump curve based on a different RPM and compare it with the original curve to see which interacts more efficiency with your system curve.  Just remember that doing so does not reflect any changes that might occur in static head that will change the shape of the system curve.  Pump curves for various speeds must be plotted along with the specific system curve to estimate where they will operate.

 Figure 1