Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: select, number
Output type: json
Sample coverage: 4
API ready: Yes

Overview

The Pump Affinity Laws Calculator estimates how a pump’s flow, head, and power change with speed or impeller diameter. Choose speed mode or diameter mode, enter the baseline and new values, and optionally provide Q₁, H₁, and P₁ to calculate the scaled operating values.

When to use

Estimate pump performance after changing motor speed or operating rpm.
Evaluate flow, head, and power changes for a different impeller diameter.
Calculate a scaling ratio when baseline flow, head, and power are not available.

How it works

1Select Speed mode to calculate ratio = n₂/n₁, or Diameter mode to calculate ratio = D₂/D₁.
2Enter the initial and new speed or impeller diameter using the available units.
3Optionally enter baseline flow Q₁, head H₁, and power P₁ with their selected units.
4The calculator applies Q₂ = Q₁·ratio, H₂ = H₁·ratio², and P₂ = P₁·ratio³, then returns the results as JSON with SI equivalents.

Use cases

Compare pump output at different variable-speed drive settings.
Estimate the effect of impeller trimming or replacing an impeller with a different diameter.
Review expected energy and hydraulic performance changes during pump selection or system adjustments.

Examples

1. Doubling pump speed

Pump engineer

Background

An engineer wants to estimate how a pump changes when its speed increases from 1,750 rpm to 3,500 rpm.

Problem

Calculate the new flow, head, and power from the known baseline operating point.

How to use

Select Speed mode and enter n₁ = 1750 rpm, n₂ = 3500 rpm, Q₁ = 10 L/s, H₁ = 20 m, and P₁ = 1000 W.

Mode: Speed; n₁: 1750 rpm; n₂: 3500 rpm; Q₁: 10 L/s; H₁: 20 m; P₁: 1000 W; Decimal places: 4

Outcome

The ratio is 2. Flow increases to 20 L/s, head increases to 80 m, and power increases to 8000 W.

2. Evaluating a larger impeller

Mechanical designer

Background

A designer is comparing a 0.20 m impeller with a 0.25 m impeller.

Problem

Estimate the changed flow and power while no baseline head is provided.

How to use

Select Diameter mode, enter D₁ = 0.20 m, D₂ = 0.25 m, Q₁ = 50 L/min, and P₁ = 2 kW.

FAQ

What are the pump affinity laws?

For the same pump, flow scales with the ratio, head scales with the ratio squared, and power scales with the ratio cubed.

What is required in Speed mode?

Enter the initial speed n₁ and new speed n₂ in rpm. Baseline flow, head, and power are optional.

What is required in Diameter mode?

Enter the initial diameter D₁ and new diameter D₂, using meters, centimeters, or millimeters.

Can I calculate only the scaling ratio?

Yes. If Q₁, H₁, and P₁ are all omitted, the calculator returns only the ratio.

Which units are supported?

Flow supports m³/s, L/s, L/min, and m³/h; head supports m and ft; power supports W, kW, and hp; diameter supports m, cm, and mm.

Mode: Diameter; D₁: 0.20 m; D₂: 0.25 m; Q₁: 50 L/min; P₁: 2 kW; Decimal places: 4

3. Returning a ratio only

Maintenance technician

Background

A technician needs the speed scaling factor before reviewing pump performance data.

Problem

Find the ratio without entering baseline flow, head, or power.

How to use

Select Speed mode and enter n₁ and n₂, leaving Q₁, H₁, and P₁ blank.

Mode: Speed; n₁ and n₂: enter the two pump speeds; Q₁: omitted; H₁: omitted; P₁: omitted

Outcome

The calculator returns the speed ratio without calculating flow, head, or power values.

Run this tool

Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Doubling pump speed

2. Evaluating a larger impeller

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

Web Image Processing Rust Samples

Absolute Value Calculator

Air Changes per Hour (ACH, n = Q/V)

Bearing Life L10 Calculator

Bolt Torque Clamp Force Calculator

3. Returning a ratio only