Pump Affinity Laws Calculator

The affinity laws approximate performance scaling for similar conditions:

Choose the ratio:

• Speed scaling: r = N2 / N1
• Diameter scaling: r = D2 / D1

Power cross-check uses P = ρ g Q H / η with constant efficiency.

1. Select whether you are changing speed or impeller diameter.
2. Enter baseline flow, head, and shaft power from your operating point.
3. Provide efficiency to estimate power using hydraulic relations.
4. Enter the baseline and new speed, or baseline and new impeller diameter.
5. Pick output units for flow, head, and power.
6. Click Calculate Scaling to show results above the form.
7. Export results using the CSV and PDF buttons.

Example values help validate scaling and unit conversions.

These are idealized estimates; real pumps can deviate from affinity scaling.

1. Why Affinity Scaling Matters

Pump affinity laws provide a fast way to estimate how a centrifugal pump’s operating point shifts when speed or impeller diameter changes. They are widely used for preliminary sizing, retrofit checks, and variable-frequency drive studies where quick comparisons save time.

2. Baseline Data You Should Use

Start from a known operating point on the pump curve: flow (Q1), head (H1), and shaft power (P1). Field data from calibrated flow meters and pressure transmitters is ideal. If you use datasheet points, select the region near best efficiency to reduce error.

3. Core Relationships and What They Mean

For similar operating conditions, flow scales linearly, head scales with the square, and power scales with the cube of the ratio r. A modest 10% speed increase (r = 1.10) raises head by about 21% and power by about 33%, which can impact motor loading.

4. Speed Change Use Case

Speed scaling is common for VFD upgrades. If a pump delivers 120 m³/h at 30 m head at 1450 rpm, increasing to 1750 rpm gives r ≈ 1.207. The calculator estimates about 145 m³/h and about 44 m head, with power rising strongly due to the cubic relationship.

5. Diameter Change Use Case

Impeller trimming or replacement changes diameter. With diameter scaling, r = D2/D1. A change from 300 mm to 330 mm gives r = 1.10, pushing flow up 10% and head up 21%. Always verify the manufacturer’s trim limits and curve shifts.

6. Power Cross-Check with Efficiency

The calculator also computes hydraulic power using P = ρ g Q H and estimates shaft power by dividing by efficiency. This provides a practical check against the r³ estimate. In real systems, efficiency can shift with Reynolds number, viscosity, and proximity to best efficiency.

7. Limits and When Not to Trust Scaling

Affinity laws are best near the same curve family and similar fluid properties. Large speed changes, high viscosity, and cavitation risk can break assumptions. Also consider NPSH requirements, system curve intersection, and motor service factor before approving changes.

8. Practical Checklist for Engineering Decisions

Confirm your baseline point, apply scaling, then validate against constraints. Check motor current versus estimated power, verify discharge pressure ratings, and confirm NPSH margin. Use multiple scenarios to understand sensitivity and document results using the CSV or PDF export.

1) What pumps do affinity laws apply to?

They primarily apply to centrifugal pumps operating in a similar region of the performance curve, with comparable fluid properties and stable hydraulic conditions.

2) Why does power change so much with speed?

Power scales approximately with r³. Small increases in speed raise head and flow, which multiplies into hydraulic power and can quickly increase motor loading.

3) Can I use these laws for positive displacement pumps?

Not reliably. Positive displacement pumps have different behavior; flow is more directly tied to displacement and speed, while head depends on system resistance.

4) What efficiency should I enter?

Use measured or curve-based efficiency near your baseline point. If unknown, choose a conservative estimate and compare results to motor ratings and manufacturer data.

5) How accurate are the estimates?

They are best for preliminary analysis. Accuracy decreases for large scaling ratios, high viscosity, cavitation risk, or operation far from best efficiency.

6) Why do pressure units assume water?

Head conversion from pressure uses H = p/(ρg). The calculator uses ρ ≈ 1000 kg/m³, so non-water fluids require adjusting the head or using meters directly.

7) What should I verify after scaling?

Check system curve intersection, NPSH margin, motor service factor, vibration limits, and allowable casing pressure. Confirm final selection with manufacturer curves.