The affinity laws are useful local prompts for the same centrifugal pump at a changed speed or closely reviewed impeller diameter. Flow scales with ratio, head scales with ratio squared, and shaft power scales with ratio cubed. Those relationships are not a full pump-system model.
The actual operating point depends on the pump curve, system curve, static head, efficiency, NPSH margin, minimum flow, fluid properties, manufacturer limits, controls, motor/VFD data, and safe-work requirements. DOE guidance warns that static-head dominated systems can make simple savings arithmetic misleading.
Use this guide to understand the local arithmetic and the source gaps to close before changing speed, sheaves, an impeller, controls, or a VFD.
The Three Local Affinity Prompts
The first prompt is flow: Q2 = Q1 x ratio. In speed mode the ratio is N2/N1. In impeller mode the ratio is D2/D1.
The second prompt is head: H2 = H1 x ratio squared. The third prompt is shaft power: P2 = P1 x ratio cubed. These are local curve-shift prompts, not a guarantee of the actual operating point.
The actual point is where the shifted pump curve intersects the system curve. Static head, friction, controls, pump efficiency, operating region, NPSH, minimum flow, and manufacturer limits can make the field result depart from the simple arithmetic.
VFD and Static-Head Boundaries
A VFD savings review starts with the local shaft-power prompt, but it does not end there. Actual savings depend on the load profile, static head, pump and system curves, controls, motor efficiency, VFD efficiency, utility tariff, demand charges, installed cost, maintenance impacts, and metered verification.
DOE variable-speed pumping guidance warns that systems with significant static head can produce major errors if simple affinity-law energy savings are used as the whole analysis. A small speed reduction can move the pump to a low-flow or inefficient region, or fail to overcome the required static head.
Before quoting savings or payback, document the current operating point, measured electrical power, pump curve, system curve, minimum speed, NPSH/minimum-flow limits, VFD/motor data, controls, safe-work plan, and qualified review basis.
Impeller Trim Boundary
Impeller diameter prompts substitute D2/D1 for N2/N1 in the same local arithmetic, but trimmed impellers are not always geometrically similar to the original pump. The manufacturer trim curve, impeller geometry, balance, efficiency, radial load, volute match, and warranty limits control the decision.
Use the local diameter prompt only to frame questions for the pump curve and source review. Do not machine an impeller, order a trim, or assume a final operating point from the simple ratio alone.
After any approved trim, the pump record, final diameter, balance, curve basis, field measurements, and qualified review should be documented.
Reading and Shifting Pump Curves
A pump performance curve plots head against flow for a specific pump, speed, impeller, fluid basis, and test context. It may include efficiency, horsepower, and NPSHR information. The system curve shows the head required by the piping and process at each flow.
The operating point is the intersection of the pump curve and system curve. A local affinity prompt can shift a pump-curve point, but it does not calculate the full intersection, operating region, efficiency shift, NPSH margin, or minimum-flow suitability.
For important decisions, use the current manufacturer curve, selected impeller, measured field point, static head, friction losses, control logic, and qualified pump review.
Limitations and Common Mistakes
Common mistakes include applying the cube law to a positive-displacement pump, ignoring static head, ignoring minimum flow, assuming efficiency is constant, using the screen as a VFD investment model, or treating a diameter trim as manufacturer approval.
Safe work is also outside the arithmetic. Pump, motor, coupling, sheave, impeller, starter, and VFD work can involve hazardous energy, rotating equipment, stored pressure, electrical exposure, hot work, confined spaces, and process hazards. Follow current OEM instructions, employer procedures, OSHA lockout/tagout, qualified electrical work practices, NFPA 70E, and site permits.
Pump Affinity Laws Calculator
Calculate the effect of speed changes or impeller trim on pump flow, head, and power using the affinity laws. Includes energy cost savings for VFD applications.