What are the affinity laws?

The affinity laws (also called fan laws or pump laws) are a set of three relationships that describe how flow, head/pressure, and power change with rotational speed or impeller diameter for centrifugal pumps, fans, and turbines. Flow varies linearly, head varies as the square, and power varies as the cube of the speed ratio.

When do affinity laws apply?

Affinity laws apply to centrifugal pumps, fans, and blowers operating on a fixed system curve. They assume geometrically similar conditions and incompressible flow. They work best for speed changes up to about ±30% from the design point.

What are the limitations of affinity laws?

Affinity laws are approximations. They do not account for efficiency changes at off-design conditions, system curve shifts, cavitation, or compressibility effects. For large speed or diameter changes (>30%), actual performance may deviate significantly from predictions.

How does VFD speed control save energy?

Because power varies as the cube of speed, even a small speed reduction yields large energy savings. Reducing speed by 20% reduces power consumption by approximately 49% (0.8³ = 0.512). This is why Variable Frequency Drives (VFDs) are highly cost-effective for flow control compared to throttling valves.

What is the relationship between flow and pressure?

Per the affinity laws, if speed changes by a ratio r, flow changes by r and pressure/head changes by r². So if you double the speed, flow doubles but pressure quadruples. If you halve the speed, flow halves but pressure drops to one quarter.

Free Engineering Tool

Affinity Laws Calculator

Calculate new flow, head/pressure, and power when pump or fan speed (or impeller diameter) changes. Based on the centrifugal pump affinity laws.

Pumps & Fans Speed & Diameter VFD Savings

Results

New Flow Q₂

—

New Head / Pressure H₂

—

New Power P₂

—

Speed Ratio (n₂/n₁)

—

Flow Ratio (Q₂/Q₁)

—

Head Ratio (H₂/H₁)

—

Power Ratio (P₂/P₁)

—

The Three Affinity Laws

The affinity laws relate flow rate, head (pressure), and power to changes in rotational speed or impeller diameter for centrifugal pumps, fans, and blowers:

Where the ratio can be either n₂/n₁ (speed change) or D₂/D₁ (diameter change).

Speed Change vs. Diameter Change

The same mathematical relationships apply for both speed changes and impeller diameter changes:

Parameter	Speed Change	Diameter Change
Flow Q	Q₂ = Q₁ × (n₂/n₁)	Q₂ = Q₁ × (D₂/D₁)
Head H	H₂ = H₁ × (n₂/n₁)²	H₂ = H₁ × (D₂/D₁)²
Power P	P₂ = P₁ × (n₂/n₁)³	P₂ = P₁ × (D₂/D₁)³

VFD Energy Savings

Key Insight: Power varies as the cube of speed. A 20% speed reduction saves approximately 49% of power (0.8³ = 0.512). This is why Variable Frequency Drives (VFDs) are one of the most cost-effective energy saving measures for pumps and fans.

Speed Reduction	Flow Reduction	Head Reduction	Power Savings
10%	10%	19%	27%
20%	20%	36%	49%
30%	30%	51%	66%
40%	40%	64%	78%
50%	50%	75%	88%

Practical Example

Example — Centrifugal Pump Speed Increase

Given: n₁ = 1450 RPM, n₂ = 1750 RPM, Q₁ = 100 m³/h, H₁ = 25 m, P₁ = 7.5 kW

Speed ratio r = 1750 / 1450 = 1.2069

Q₂ = 100 × 1.2069 = 120.7 m³/h

H₂ = 25 × 1.2069² = 36.4 m

P₂ = 7.5 × 1.2069³ = 13.2 kW

⚠️ Limitations: Affinity laws assume constant efficiency, geometrically similar conditions, and incompressible flow. For speed changes beyond ±30%, actual performance may deviate significantly. Impeller trimming laws are less accurate than speed change laws — always verify with manufacturer curves.

Affinity Laws Calculator | Pump & Fan Speed Change

Published by admin on February 15, 2026 February 15, 2026