Affinity Laws, also known as the “Pump Laws”, describe the relationship between the impeller’s diameter or speed and flow, head (pressure), and power of centrifugal pumps. They are essential for predicting performance changes when system or equipment conditions are altered.

Understanding Affinity Laws is essential in pump operation and design because they allow engineers and operators to predict how changes in a pump’s impeller diameter or speed will affect its performance without physically testing every scenario.

Why Do the Affinity Laws Matter?

Predicting Performance Change: Affinity Laws provide mathematical relationships that link:

• Flow rate (Q), gallons per minute (gpm)

• Head (H), feet (ft)

• Power (P), horsepower (hp)

to changes in the pump impeller’s diameter (D) or rotational speed (N). This means one can estimate how a pump will behave without needing a full-scale trial if the pump’s:

• Impeller speed is increased or decreased

• Impeller size is modified

Optimizing Energy Efficiency: Pumps often operate under varying demands. By using the Affinity Laws, one can:

• Adjust speed or impeller size to meet system requirements.

• Avoid over-pumping, which wastes energy and can damage equipment.

• Calculate power requirements accurately to select the right motor size.

Troubleshooting and System Adjustments: When a system isn’t performing as expected, Affinity Laws help identify whether the changes in performance are due to specific factors, allowing for faster diagnosis and corrective action:

• Impeller wear or resizing

• Speed variation

• System designs changes

Scaling and Pump Selection: In design and modeling, Affinity Laws allow engineers to scale pump performance from a test model to full size and help select the right pump for different flow and head requirements.

Cost and Resource Savings: Rather than constructing multiple pumps or conducting numerous experiments, the Affinity Laws allow engineers to mathematically predict changes in pump performance. This predictive capability saves time, money, and energy during both the design and operational phases. Engineers can forecast how a system will respond to adjustments in flow, head, or power without expensive testing, making these laws especially valuable for retrofits and system upgrades.

Key Relationships

A centrifugal pump increases fluid’s velocity and converts that velocity into pressure, so its flow rate, head, and power consumption can be adjusted by changing the impeller’s diameter or rotational speed.

The Affinity Laws describe how changes in impeller speed or diameter affect the pump’s flow, head, and power. There are three main laws:

1. Flow (Q): Flow is directly proportional to the impeller diameter (D) or speed (N). For example, if the diameter or speed of the impeller doubles, the flow also doubles if all other factors remain constant. If the diameter or speed increases by 10%, then the flow rate will also increase by 10%.

2. Head (H): Changes in head (pressure) are proportional to the square of impeller diameter (D) or speed (N). For example, doubling the diameter increases the head by a factor of four if all other factors remain constant. If the diameter or speed increases by 10%, then the head will increase by 21.7% at the same flow.

3. Power (P): Power change is proportional to the cube of the impeller diameter (D) or speed (N). For example, doubling the size of the diameter of the impeller increases the pump’s power consumption eightfold if all other factors remain constant. If the diameter or speed increases by 10%, then the power will increase by 33.1%.

The Affinity Laws predict how a centrifugal pump will respond to changes in speed or impeller diameter, assuming the system remains geometrically similar, the fluid is incompressible (such as water), and the pump’s performance characteristics stay consistent during adjustments. These laws help predict changes in flow, head, and power when the impeller speed or diameter is modified.

Care must be taken when applying these formulas to changes in impeller diameter, as the impeller and volute are closely related components. Altering one can affect the pump’s design configuration. For this reason, the Affinity Laws are most reliable when the change in impeller diameter is 10% or less. If the change exceeds 10%, a new test and updated pump curve should be developed.

Additionally, the Affinity Laws do not account for changes in efficiency and may become less accurate under large speed variations or extreme operating conditions, where losses, cavitation, or turbulence may cause performance deviations.

Practical Applications

Affinity Laws are used whenever a pump’s impeller diameter or speed changes, allowing engineers to estimate new performance without physically testing the system.

Impeller Diameter Example: A centrifugal pump equipped with a 12-inch impeller delivers 150 gallons per minute (gpm) at a head of 150 feet, requiring 10 horsepower (hp). Assume the speed and system characteristics remain constant. Find the new flow rate (Q2), head (H2), and power (P2) when the impeller diameter is increased to 14 inches.

Flow (Q): Flow is directly proportional to impeller diameter, assuming the impeller speed remains constant and does not change.

Assuming the impeller speed remains constant, if the impeller diameter (D1) increases from 12 inches at flow rate of 150 gpm (Q1) to a larger 14-inch diameter (D2), what would the new flow rate (Q2) be?

When the impeller diameter increased by 16%, from 12” to 14”, the flow increased by the same percentage, from 150 gpm to 174 gpm, highlighting that flow is directly proportional to impeller diameter.

Head (H): Head (pressure) is proportional to the square of the impeller diameter (D).

Assuming the impeller speed remains constant, if the impeller diameter (D1) increases from 12 inches delivering a head of 150 feet (H1) to a larger 14-inch diameter (D2), what would the new head (H2) that the pump can deliver be?

When the impeller diameter increased by 16%, from 12” to 14”, the head increased by approximately 36%, from 150 feet to 204 feet, showing that the head is proportional to square of the impeller diameter.

Power (P): Power required is proportional to the cube of the impeller diameter (D).

Assuming the impeller speed remains constant, if the impeller diameter (D1) increases from 12 inches in a pump consuming 10 hp (PH1) to a larger 14-inch diameter (D2), what would the new power (P2) that the pump will need to run?

When the impeller diameter increased by 16%, from 12” to 14”, the power increased by approximately 59%, from 10 to 15.9 hp, showing that power is proportional to the cube of the impeller diameter.

In this example, increasing the impeller diameter from 12” to 14” changed the pump’s performance, delivering 174 gpm at 204 feet while requiring 15.9 hp.

Switching impeller diameter (D) out with speed (N), we can also predict changes to flow, head, and power similarly with the same equations.

Summary

Affinity Laws describe how a pump’s flow, head, and power change with impeller diameter or speed. Flow varies directly, head with the square, and power with the cube. They let engineers predict performance, optimize energy use, and select or scale pumps without full-scale testing. Most accurate for small changes, these laws assume geometric similarity and incompressible fluid, and don’t account for efficiency losses or extreme conditions.

Wilo is Your Solutions Provider

Wilo USA, headquartered in Cedarburg, WI, is a leading multinational pump manufacturer and a premium supplier of pumps and pumping systems for building services, water management, and industrial applications. With innovative solutions, smart products, and tailored services, Wilo is your trusted solution provider for making water move efficiently and sustainably.

By applying principles like the Affinity Laws, Wilo engineers can predict how changes in impeller size or pump speed will affect flow, head, and power, enabling optimized performance, reduced energy consumption, and precise system solutions. With Wilo, you gain not just pumps, but intelligent, eco-friendly solutions designed to meet your specific operational needs.

November 2025 | tlk

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