Fan and Pump Affinity Laws Calculator
Flow, head and power at a new speed, showing the energy saved by slowing a fan or pump. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates flow, head or pressure, power at new speed and 1 more result from original speed, new speed and power at original speed. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Static head breaks the cube law, so savings on a pump lifting water are smaller. Below about 50% speed, motor and drive losses matter.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Indicative
Indicative. Estimation only; further engineering checks are required. Basis: Idealised affinity laws.
What this calculator checks
- The arithmetic of the simplified model for the values you entered.
What remains unverified
- Whether the simplifying assumptions listed on this page hold for your case.
- Any standard, manufacturer or site data. Treat the result as an estimate and confirm it by a further engineering check.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Fan and pump affinity laws are general similarity relationships. Application limits and performance curves are manufacturer-specific; no single standard governs this generic calculator. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Indicative |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Original speed | 1,450 rpm |
| New speed | 1,160 rpm |
| Power at original speed | 22 kW |
- Speed ratio = 1,160 / 1,450 = 0.8
- Flow = 80 %, head = 64 %
- P2 = 22 kW × 0.8³ = 11.26 kW
Assumptions
- Same fan or pump, same fluid density
- System resistance is friction-dominated with little static head
- Efficiency stays the same across the speed range
Static head breaks the cube law, so savings on a pump lifting water are smaller. Below about 50% speed, motor and drive losses matter.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Original speed | rpm | greater than 0 rpm | |
| New speed | rpm | greater than 0 rpm | |
| Power at original speed | kW | greater than 0 kW |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Flow (% of original) | (number) | Shown to 1 decimal place | |
| Head or pressure (% of original) | (number) | Shown to 1 decimal place | |
| Power at new speed | kW | Shown to 2 decimal places | |
| Power saved (%) | (number) | Shown to 1 decimal place |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with original speed
| Original speed (rpm) | Flow | Head or pressure | Power at new speed (kW) |
|---|---|---|---|
| 145 | 800 | 6,400 | 11,264 |
| 363 | 319.6 | 1,021.2 | 717.92 |
| 725 | 160 | 256 | 90.11 |
| 1,450 | 80 | 64 | 11.26 |
| 2,900 | 40 | 16 | 1.41 |
| 5,800 | 20 | 4 | 0.18 |
| 14,500 | 8 | 0.6 | 0.01 |
Other inputs are the same as in the worked example above.
Standards and further reading
- EN 12464-1 (lighting of indoor workplaces)
- CIE publications on photometry
Lamp and luminaire data come from the manufacturer; the illuminance targets that apply come from your project specification and local regulation. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter original speed, new speed and power at original speed. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Same fan or pump, same fluid density. System resistance is friction-dominated with little static head. Efficiency stays the same across the speed range.
Which calculators should I use next?
Common next steps are Motor Output Power and Efficiency Loss and Pump Shaft and Motor Power. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Fan Formulas: Air Power and Affinity Laws: Fan formulas: air power from flow and pressure, shaft power from fan efficiency, and the affinity laws for flow
- Pump Formulas: Hydraulic, Shaft and Motor Power: Pump power formulas: hydraulic power from flow and head, shaft power from pump efficiency, motor input power
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