Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Apply pump affinity laws to predict flow rate, head, and shaft power changes from speed or impeller diameter modification. Apply to variable frequency drive analysis and operating condition change evaluation.
What this calculator is used for
The pump affinity laws (similarity laws) predict how a centrifugal pump's performance changes when speed or impeller diameter changes while the pump geometry stays the same.
Typical engineering use cases
Estimating energy savings from variable-frequency-drive (VFD) control
Predicting flow and head after impeller trimming
Validating pump/motor suitability after an operating-point change
Estimating shaft power demand at a new speed
Governing equation and methodology
For a speed change from n₁ to n₂, performance follows the affinity laws:
Q₂/Q₁ = n₂/n₁, H₂/H₁ = (n₂/n₁)², P₂/P₁ = (n₂/n₁)³
Flow scales with speed, head with the square, and shaft power with the cube. Reducing speed to 50% gives ~50% flow, 25% head, and ~12.5% power—far more efficient than throttling. The same form (Q∝D, H∝D², P∝D³) applies approximately for impeller diameter changes.
Engineering assumptions and limitations
Assumes efficiency stays essentially constant across the change
Large speed/diameter changes introduce error as efficiency shifts
System resistance curve (static head) effects handled separately
Cavitation (NPSH) must be rechecked with a separate calculation
Practical design notes
The affinity laws describe the pump alone; the real operating point is the intersection with the system curve. With significant static head, flow reduction does not follow the laws directly. When slowing down, ensure the reduced head still meets the required head, and check minimum continuous flow and bearing/seal effects at low flow.
Interpretation: The cube law on power is the trap — a modest 20 % speed bump needs ~73 % more motor power, so check the existing driver before reusing it. The laws assume the operating point stays on the same system curve; if friction dominates, the real point won't track the affinity prediction exactly.
Common Mistakes & Misuse
Applying the speed laws across a trim (impeller diameter) change as if identical — diameter scaling is only approximate and breaks down outside a small trim range.
Forgetting that the new operating point must still lie on the system curve; the affinity laws move the pump curve, not the duty intersection.
Extrapolating the power-cubed law to large speed turndowns where efficiency drops and the cube relation overstates the saving.
Ignoring NPSH required, which also changes with speed and can trigger cavitation at a higher speed even if head/flow look fine.
Frequently Asked Questions
What are the pump affinity laws?
Q₂/Q₁ = N₂/N₁ (flow proportional to speed), H₂/H₁ = (N₂/N₁)² (head proportional to speed squared), P₂/P₁ = (N₂/N₁)³ (power proportional to speed cubed). These apply for geometrically similar conditions.
When do affinity laws not apply?
Affinity laws are approximate. They become less accurate at very low speeds, when operating far from BEP, when system friction dominates, or when cavitation (NPSH) conditions change significantly.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.