Fan affinity laws let engineers predict how flow, pressure, and power change when speed, impeller diameter, or air density changes, without re-testing the fan.
The Three Relationships
For a fixed fan at changing speed, flow scales linearly with speed, pressure scales with the square of speed, and power scales with the cube of speed. Halving the speed halves the flow, quarters the pressure, and cuts power to one-eighth, a dramatic and useful relationship for part-load control.
The fan laws, also called the affinity laws, describe how a given fan's performance changes when one variable is altered and everything else is geometrically similar. They are the quickest tool an engineer has to predict the effect of a speed change or a different wheel diameter without re-running a full test.
The first law ties flow to speed: halving the rotational speed halves the volume flow, while doubling speed doubles it. The second ties pressure to the square of speed, so flow at half speed comes with only a quarter of the static pressure. The third ties power to the cube of speed, which is why a small reduction in speed yields a large drop in absorbed power and why VFD control saves so much energy at part load.
The diameter laws work the same way with wheel size: flow scales with diameter, pressure with diameter squared, and power with diameter cubed, provided the fan geometry is held. In practice diameter changes also shift efficiency and noise, so the laws are a first estimate, and the final duty is confirmed on the performance curve rather than by arithmetic alone.
Density matters for altitude and temperature. Because the fan moves a mass of air against a pressure, a thinner high-altitude atmosphere reduces the achievable static pressure at the same speed and volume, and the duty must be corrected using the air density ratio so the selected unit still meets the required airflow where the plant actually sits.
The company's in-house performance laboratory lets engineers demonstrate these corrections on tested curves rather than theory alone, and with more than 30 years of manufacturing experience the technical team can advise where a speed change, not a new model, is the cheaper route to the duty a project needs.
This cubic power term is why variable-speed control saves so much energy. A fan running at 80% speed uses only about half the power of one at full speed, provided the system curve allows the lower operating point and the ductwork does not impose a higher resistance than expected.
Diameter changes follow similar but distinct rules when a different wheel is fitted: flow scales with diameter cubed, pressure with diameter squared, and power with diameter to the fifth. These are less often used than speed changes but matter when re-wheeling a casing to recover lost performance.
Air density affects mass flow and pressure. At altitude or high temperature the air is thinner, so a given volume flow carries less mass and the fan develops less pressure for the same speed and settings, which must be corrected before the fan is committed to a duty.
Practical Reference Points
The laws assume the fan operates at a similar point on its curve and that losses stay in the turbulent regime. Far from the design point the simple ratios drift, so they are a first estimate, not a substitute for a corrected curve supplied by the manufacturer for the actual duty.
For speed control, the useful message is that small speed reductions give large power savings, but also large pressure drops, so the system must still deliver the required flow at the lower pressure, and the control should not be driven so low that the space loses ventilation.
Density correction is essential for tunnels, mines, and high-altitude sites. A fan selected at sea level may fall short of pressure where the air density is 15-20% lower, unless the duty is corrected first using the actual site air density rather than a standard value.
When comparing two fans, apply the laws only to geometrically similar machines; mixing casing types, blade shapes, or inlet conditions invalidates the diameter exponents and can lead to a fan that is badly mismatched to the real system resistance.
| Item | Specification | Note |
|---|---|---|
| Speed 80% | Flow 80% | Pressure 64%, Power 51% |
| Speed 90% | Flow 90% | Pressure 81%, Power 73% |
| Speed 110% | Flow 110% | Pressure 121%, Power 133% |
| Density 0.9ρ | Pressure 90% | Altitude effect |
| Diameter ×1.1 | Flow ×1.33 | Cube relationship |
| Power vs speed | cube | Basis of VSD savings |
Selection Checklist
- Use speed changes for part-load control; expect cubic power savings.
- Keep the operating point near the design region or the laws lose accuracy.
- Apply density correction for sites above 1,000 m or above 40°C.
- Confirm the motor has margin before raising speed beyond 100%.
- For re-wheeling, use diameter exponents, not speed exponents.
- Validate any critical duty with a corrected factory curve.
About the Manufacturer
Keruite Air Conditioning Group, headquartered in Dezhou, Shandong, has more than 30 years of HVAC manufacturing experience and operates an 80,000 m² production site with its own performance testing laboratory. Products are built under ISO 9001:2015 quality management and carry CCC certification, and are supplied to customers in over 50 countries.
Our engineers respond to selection enquiries within 24 hours and can provide project-specific sizing, performance curves, and documentation to support specification and procurement.