Calculator Inputs
Enter the reference pump data, choose the analysis mode, and submit to see projected performance above this form.
Formula Used
Pump affinity laws relate performance to speed and impeller diameter changes under similar conditions. They are commonly used for quick pump scaling, checks, and preliminary system planning.
Q₂ = Q₁ × (N₂ / N₁)
H₂ = H₁ × (N₂ / N₁)²
P₂ = P₁ × (N₂ / N₁)³
Q₂ = Q₁ × (D₂ / D₁)
H₂ = H₁ × (D₂ / D₁)²
P₂ = P₁ × (D₂ / D₁)³
Q₂ = Q₁ × (N₂ / N₁) × (D₂ / D₁)³
H₂ = H₁ × (N₂ / N₁)² × (D₂ / D₁)²
P₂ = P₁ × (N₂ / N₁)³ × (D₂ / D₁)⁵
These relationships assume the same fluid, comparable efficiency range, and similar operating region. Real systems also depend on pump curves, system curves, NPSH, and motor limits.
How to Use This Calculator
- Select the analysis mode that matches your scenario.
- Choose units for flow, head, power, and diameter.
- Enter baseline pump performance values from your known operating point.
- Enter the new speed or impeller diameter you want to test.
- Optionally enter annual hours and energy rate for cost impact.
- Click Calculate to show results above the form, review the graph, then export CSV or PDF.
Example Data Table
These sample cases show how the laws scale reference conditions. Values below are illustrative for quick comparison.
| Scenario | Mode | Reference Flow | Reference Head | Reference Power | Speed Ratio | Diameter Ratio | Projected Flow | Projected Head | Projected Power |
|---|---|---|---|---|---|---|---|---|---|
| Baseline | Reference | 100 m³/h | 40 m | 15 kW | 1.00 | 1.00 | 100 m³/h | 40 m | 15 kW |
| Reduced speed | Speed Change Only | 100 m³/h | 40 m | 15 kW | 0.90 | 1.00 | 90 m³/h | 32.4 m | 10.94 kW |
| Impeller trim | Impeller Trim Only | 100 m³/h | 40 m | 15 kW | 1.00 | 0.90 | 90 m³/h | 32.4 m | 10.94 kW |
| Combined increase | Combined Similarity | 100 m³/h | 40 m | 15 kW | 1.09 | 1.05 | 125.7 m³/h | 52.0 m | 24.6 kW |
FAQs
1. What do pump affinity laws predict?
They estimate how flow, head, and power change when pump speed or impeller diameter changes. They are useful for fast performance scaling before detailed curve review.
2. When are these laws most reliable?
They work best when the pump geometry stays similar, the fluid stays the same, and the operating point remains near the original efficiency region. Large changes reduce accuracy.
3. Why does power change faster than flow?
Power follows a cubic relationship. A modest increase in speed or diameter can therefore cause a much larger power rise than the corresponding flow increase.
4. Can I use this for impeller trimming?
Yes. The trim mode uses common proportional relationships for trimmed impellers. It is a planning estimate, so confirm the final point with the manufacturer curve.
5. Does this replace pump and system curves?
No. Affinity laws are screening tools. Final design should still check the actual pump curve, system curve intersection, motor loading, NPSH margin, and control strategy.
6. What if I do not know the reference power?
You can leave power blank and enter efficiency plus fluid density. The calculator then estimates input power from flow, head, and hydraulic power relations.
7. Why include annual hours and energy rate?
Those values convert power changes into yearly energy use and operating cost impact. This helps compare speed adjustments, trimming decisions, and efficiency upgrades financially.
8. Which mode should I choose?
Use speed mode for variable frequency changes, trim mode for diameter changes on the same pump, and combined similarity for broader geometric scaling studies.