Pump Affinity Laws: Useful Predictions and the Conditions Behind Them

What the relationships predict

The affinity laws compare the same centrifugal pump at two rotational speeds. They provide a fast projection: flow changes approximately in direct proportion to speed, developed head changes with the square of speed, and shaft power changes with the cube of speed.

That cubic power relationship explains why modest speed reduction can produce substantial energy reduction in appropriate variable-torque systems. It is a prediction of pump behavior, not a guarantee of building-system savings.

Why the system curve matters

The pump does not choose its operating point alone. The connected system imposes static head and flow-dependent resistance. A closed hydronic loop is often dominated by dynamic resistance, while an open system may include significant static lift. Control valves, coil selection, strainers, fouling, and piping configuration shape the curve the pump must meet.

If a system has substantial static head, a simple proportional flow prediction can be misleading at low speed. The pump may approach a speed at which it cannot overcome the static requirement, even though the ideal affinity calculation still produces a positive flow.

Common reasons measured results differ

A field test should expect some difference between ideal projection and measured performance. The question is whether the difference is explained and acceptable for the evaluation purpose.

• Pump efficiency changes as the operating point moves across the curve
• Variable-frequency drive and motor losses change with load
• Control valves or bypasses reposition during the test
• Parallel pumps, check valves, or minimum-flow logic alter the system boundary
• Pressure sensors are located at different elevations or across different components
• Speed feedback, flow meters, or differential-pressure sensors are inaccurate

Use the laws as a screening and diagnostic tool

Record a stable baseline operating point, change speed within an approved range, allow the system to stabilize, and collect synchronized speed, flow, differential head, valve position, and power data. Compare the measured change with the ideal relationship and the manufacturer’s current curve.

A discrepancy is not automatically a failed pump. It is a reason to examine the measurement boundary, system curve, active controls, pump condition, and the assumptions behind the prediction.