Fan laws
The fan laws – also known as the affinity laws – describe the relationship between the fan speed and the aerodynamic performance such as airflow, pressure and power consumption. These physical principles help you estimate what happens when you increase or decrease the speed of a fan. Very useful when designing, adjusting or optimising a ventilation system.
On this page, we explain how the fan laws work and when to apply them. You’ll also find calculation examples and tables you can use directly.
Change in frequency (= speed)
The speed of a fan can be controlled using a (frequency) inverter. Adjusting the frequency affects the airflow, pressure and absorbed power accordingly.
With the following formulas, you can calculate the new performance values.
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| Relevante formules en haar afkortingen | |
|---|---|
| Capaciteit: | Q |
| Druk: | Pa |
| Frequentie: | Hz |
| Opgenomen vermogen: | Popg. |
| Toerental: | n |
Airflow (Q) and fan speed (n) — same formula applies to both
(Hz2 / Hz1) x Q1 = Q2
(Hz2 / Hz1) x n1 = n2
Pressure (Pa) – squared relationship
(Hz2 / Hz1) ² x Pa1 = Pa2
Absorbed power (Popg.) – cubed relationship
(Hz2 / Hz1) ³ x Popg.1= Popg.2
Calculation examples:
(Hz2 / Hz1) ³ x Popg.1= Popg.2
Initial data: 15,000 m³/h at 500 Pa at 50 Hz (1,400 rpm), with absorbed power of 2.1 kW. The frequency is reduced from 50 Hz to 30 Hz.
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| Berekening aan de hand van de gegevens | |
|---|---|
| Toerental: (30/50)x1.400 | 840 opm. |
| Capaciteit: (30/50)x15.000 | 9.000 m³/ uur |
| Druk: (30/50)²x500 | 180 Pa |
| Opgenomen vermogen: (30/50)³x2.1 | 0.45 kW. |
Reverse calculation is also possible
If you want to reduce the airflow from 15,000 to 7,500 m³/h, you can calculate the required frequency using the same formula:
(Hz₂ / Hz₁) × Q₁ = Q₂
(Hz₂ / 50) × 15,000 = 7,500 → Hz₂ = (7,500 / 15,000) × 50 = 25 Hz
To reduce pressure from 500 Pa to 125 Pa:
(Hz₂ / 50)² × 500 = 125 → Hz₂ = √(125 / 500) × 50 = 25 Hz
To reduce absorbed power from 2.1 kW to 0.2625 kW:
(Hz₂ / 50)³ × 2.1 = 0.2625 → Hz₂ = ∛(0.2625 / 2.1) × 50 = 25 Hz
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Frequently asked questions about fan laws
What are the fan laws?
The fan laws describe how airflow, pressure and power change when the fan speed or size is adjusted. They are used to predict fan performance in different situations.
What are the fan laws used for?
They are used when designing or modifying ventilation systems, for example when changing fan speed or selecting a larger or smaller fan.
Which parameters are affected according to the fan laws?
Key parameters are airflow (Q), pressure (P) and power (W). These don’t change linearly, which is why the fan laws are essential for accurate calculations.
Can I use the fan laws to calculate energy consumption?
Yes. Absorbed power changes exponentially when the speed changes. This makes the fan laws very useful for energy-saving evaluations.
What is the difference between theoretical and actual performance?
The fan laws provide a theoretical estimation. Actual results may vary due to system resistance, losses or other real-world factors.
