ToolnozaThe three pump affinity-law ratios
For the same centrifugal pump and impeller diameter, under comparable fluid and operating conditions, let r = new rotational speed ÷ original speed. Approximate flow ratio Q₂/Q₁ = r; head ratio H₂/H₁ = r²; and power ratio P₂/P₁ = r³. These relationships describe similarity scaling, not a complete pump selection or guaranteed field result.
If only the impeller diameter changes at the same speed, different diameter-ratio approximations apply and should be checked against manufacturer curves. Do not combine diameter and speed changes as though every pump follows one exact proportional rule. This guide focuses on changing speed with the same impeller.
Worked example: a 10% speed reduction
A pump runs at 1,800 rpm, delivering 100 gpm at 120 ft of head and drawing 15 hp at the reference operating point. Reducing speed to 1,620 rpm gives r = 1,620 ÷ 1,800 = 0.90. Estimated flow is 100 × 0.90 = 90 gpm. Estimated head is 120 × 0.90² = 97.2 ft. Estimated power is 15 × 0.90³ ≈ 10.94 hp.
The power estimate drops more quickly than flow because it scales with the cube of speed. However, the system curve and efficiency can shift the actual operating point. Treat the arithmetic as a first approximation and compare it with the manufacturer’s pump curve and motor/control limits.
Why the system curve changes the delivered result
The pump curve describes head available at different flow rates for a specified speed and impeller. The system curve describes the head the piping and process require at each flow. Their intersection is the operating point. When speed changes, the pump curve shifts, and the new intersection may not match a simple flow ratio if static head, control valves, parallel pumps, or other system effects are important.
If the system has substantial static lift, the pump cannot deliver the affinity-law flow ratio down to zero speed. Minimum flow, seal cooling, motor cooling, vibration, and cavitation limits may also restrict operation. Use variable-speed control within the manufacturer’s permitted range.
Use consistent units and baseline data
Record the baseline rpm, flow, total head, and power at the same operating point. Keep units consistent between the initial and estimated values; the ratio itself is unitless. Distinguish shaft power from electrical input power. Motor and drive efficiency can change, so electrical kW will not always follow the hydraulic power cube exactly.
For water, head is often reported in feet or metres. For another fluid, density and viscosity may alter pump performance. If the fluid properties change, the same-speed similarity assumptions require additional engineering checks.
Verify NPSH, minimum flow and equipment limits
A speed change alters flow and suction conditions. Check available NPSH against the manufacturer’s required NPSH at the new duty point, using absolute pressure and the actual liquid temperature. Maintain any specified margin. Also check motor current, drive frequency, pump vibration, seal conditions, minimum continuous stable flow, and the impeller’s operating envelope.
A calculator cannot establish that the pump is safe from cavitation or that a process remains controlled. Review the pump curve and operating procedure before changing a live system.
Use the pump affinity-law calculator
- Enter the original speed, flow, head and power at a known operating point.
- Enter the proposed new speed and review the estimated flow, head and power using the speed ratios.
- Check the new point against the pump curve, system curve, motor/drive limits, NPSH requirement and minimum-flow guidance.
Use measured baseline values when available. The tool applies the affinity-law ratios; it does not model a complete hydraulic system.
Frequently asked questions
Does a 10% speed increase always increase flow by 10%? It is the same-pump ideal ratio, but the system operating point and controls can change the actual flow.
Why does power change by the cube? It follows the ideal similarity relationship for a centrifugal pump with the same impeller and comparable conditions; actual electrical input also depends on efficiencies and system behavior.
Can I use this for a positive-displacement pump? No. These affinity laws are for centrifugal-pump similarity and should not be applied blindly to positive-displacement machines.
Can I lower speed until the pump stops cavitating? Check NPSH and manufacturer curves; this calculator is not a cavitation diagnosis.
References and related tools
See the U.S. Department of Energy’s pump system resources at https://www.energy.gov/eere/amo/pump-systems and Hydraulic Institute guidance at https://www.pumps.org/. Related Toolnoza pages are linked below.