Affinity Laws
Pump Affinity Laws Explained
Pump affinity laws are practical engineering relationships used to estimate how centrifugal pump flow, head and power change when pump speed or impeller diameter changes.
What are pump affinity laws?
Affinity laws describe the approximate relationship between pump speed, flow rate, developed head and power consumption. They are commonly used for quick estimates during pump selection, VFD evaluation, impeller trimming and troubleshooting.
Affinity laws for speed change
When only rotational speed changes and the pump geometry remains the same, the following relationships are used:
Flow changes linearly with speed, head changes with the square of speed and power changes with the cube of speed.
Why power changes so much
The cubic power relationship is the reason why VFD control can create large energy savings. A relatively small reduction in speed may create a much larger reduction in absorbed power.
Example
If pump speed is reduced from 2950 rpm to 2500 rpm, the speed ratio is 0.847. Power ratio is approximately 0.847³ = 0.607. That means about 15% lower speed can result in roughly 40% lower power demand.
Affinity laws for impeller diameter change
For impeller trimming, a similar approximate relationship is often used:
However, diameter-based affinity laws are usually less accurate than speed-based affinity laws. Trimming the impeller changes hydraulic geometry, outlet width, blade loading and efficiency.
Where affinity laws are useful
- variable frequency drive applications,
- preliminary energy-saving calculations,
- quick estimate of reduced speed operation,
- approximate impeller trimming checks,
- motor power screening,
- comparing alternative operating points.
Where affinity laws can be misleading
Affinity laws do not replace real pump curves. They assume similar hydraulic behavior, but real pumps are affected by efficiency changes, internal recirculation, NPSH behavior, minimum flow limits and mechanical constraints.
BEP and efficiency
The Best Efficiency Point moves when speed changes. Efficiency may remain similar for moderate speed changes, but it is not guaranteed. For large changes, the operating point may move away from the preferred operating region.
NPSHr and speed changes
NPSHr often increases significantly with speed. This can be critical because a pump may appear acceptable from flow, head and power perspective but fail on suction conditions.
Always check:
- NPSHa vs NPSHr,
- suction specific speed,
- minimum flow,
- runout conditions,
- vibration limits.
VFD applications
Affinity laws are especially useful for VFD-controlled pumps. Instead of throttling flow with a valve, speed control can reduce pump head and power demand. This is often more energy-efficient in variable-flow systems.
Impeller trimming limitations
Impeller trimming should always be confirmed by the pump manufacturer. Large trims can reduce efficiency, change radial loads and affect hydraulic stability. Published pump curves usually provide several impeller diameters for this reason.
Common mistakes
- Using affinity laws far away from BEP.
- Ignoring pump efficiency changes.
- Ignoring NPSHr increase at higher speed.
- Assuming impeller trimming is exact.
- Not checking motor overload margin.
- Applying water-based assumptions to viscous fluids.
- Ignoring minimum continuous stable flow.
Practical recommendation
Use affinity laws for quick estimates and early engineering decisions. For final design, always verify the result against manufacturer curves, motor sizing, NPSH margin, operating range and project requirements.