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Mechanical Engineering2D

Pump Affinity Law Calculator

Calculate pump performance changes with speed or impeller diameter using affinity laws.

Inputs
Enter your values below
Result
New Power P2 (kW)
—
Enter values and click Calculate
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Formula
p1 × (n2 ÷ n1)³ ÷ 1000
Result unit: kW

P₂ = P₁ × (N₂/N₁)³ for variable speed. p1 in kW is converted to W by engine; /1000 returns kW. Power is proportional to speed cubed.

Introduction

Pump affinity laws predict how changing pump speed or impeller diameter affects flow rate (Q), head (H), and power (P). For variable speed drives (VSD), Q∝N, H∝N², P∝N³ — power reduction is cubic with speed.

How This Calculator Works

P₂ = P₁ × (N₂/N₁)³ for variable speed. p1 in kW is converted to W by engine; /1000 returns kW. Power is proportional to speed cubed.

Step-by-step process:

  1. Enter your input values in the calculator above
  2. The engine converts all inputs to SI base units (meters, kg, Pa)
  3. The formula is evaluated: p1 * (n2/n1)^3 / 1000
  4. Result is formatted with the appropriate unit and precision

Calculation Example

Speed increase 1450→1750 RPM (20.7%): Q=120.7, H=72.7m, P=38.7 kW (cubic relationship).

Inputs: q1=100, h1=50, p1=22, n1=1450, n2=1750
Result: 38.7 kW

Unit Conversion for Affinity Laws

**Speed units**

- 1 rpm = 1/60 rps

- 1 rps = 60 rpm

**Flow units**

- 1 m³/h = 0.2778 L/s = 4.403 US gpm

**Head units**

- 1 m = 3.28084 ft

**Power units**

- 1 kW = 1.341 hp

Affinity laws are ratio-based: Q₂/Q₁ = N₂/N₁, H₂/H₁ = (N₂/N₁)², P₂/P₁ = (N₂/N₁)³. Any consistent unit set works because only ratios are used.

Engineering Applications

  • •VFD energy savings estimation
  • •Pump speed selection
  • •Impeller trimming
  • •Retrofit evaluation

Frequently Asked Questions

What is the power savings from reducing pump speed?

Power is proportional to N³. Reducing speed 20% reduces power by ~49%. This is why VSDs are so effective for energy savings.

How accurate are affinity laws?

Within ±5% for speed changes up to 20-30%. For larger changes or diameter trimming, efficiency changes and accuracy decreases.

How do I convert pump speed units?

Pump speed is usually expressed in rpm. 1 rpm = 1/60 rps. Affinity laws are ratio-based, so any consistent speed unit works as long as both speeds use the same unit.

Related Calculators

Pump Power CalculatorPump Flow CalculatorPump Efficiency CalculatorPump Head CalculatorPump Energy Cost CalculatorPump Sizing CalculatorPump Selection CalculatorPipe Flow CalculatorFlow Rate CalculatorPressure Drop Calculator (Darcy-Weisbach)Reynolds Number Calculator

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.
Reviewed by: Industrial Engineering Team
References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook