About Fan & Pump Affinity Laws Calculator
The fan and pump affinity-law calculator predicts how a centrifugal fan or pump responds when you change its rotational speed or impeller diameter. Enter the baseline flow, pressure (or head) and shaft power at the original operating point, then the original and new speed and/or diameter. The tool returns the new flow, pressure and power, along with the underlying ratios.
The affinity laws state that volumetric flow is proportional to the speed (and diameter) ratio, pressure or head is proportional to the square of that ratio, and shaft power is proportional to its cube. They are the basis for variable-speed-drive energy savings: a small reduction in speed produces a large reduction in power because of the cubic relationship.
How It Works
- Select what is changing: speed only, impeller diameter only, or both.
- Enter the baseline operating point: flow Q1, pressure or head P1, and shaft power Power1 (any consistent units).
- Enter the original and new speed N1, N2 (rpm) and/or impeller diameter D1, D2.
- The calculator forms the combined ratio r = (N2/N1)(D2/D1), then Q2 = Q1 r, P2 = P1 r^2 and Power2 = Power1 r^3.
Worked Example
A fan delivers 1000 m3/h at 500 Pa drawing 10 kW at 1000 rpm. The speed is increased to 2000 rpm (a ratio of 2). By the affinity laws the new flow is 1000 x 2 = 2000 m3/h, the new pressure is 500 x 2^2 = 2000 Pa, and the new power is 10 x 2^3 = 80 kW. Conversely, slowing the fan to 800 rpm (ratio 0.8) drops power to 10 x 0.8^3 = 5.12 kW -- a 20 percent speed cut nearly halves the power.
Formulas
- Flow (first affinity law)
Q2 / Q1 = (N2 / N1) * (D2 / D1)- Pressure / head (second affinity law)
P2 / P1 = (N2 / N1)^2 * (D2 / D1)^2- Power (third affinity law)
Power2 / Power1 = (N2 / N1)^3 * (D2 / D1)^3- Combined ratio
r = (N2/N1)(D2/D1) ; Q2 = Q1 r ; P2 = P1 r^2 ; Power2 = Power1 r^3
Standards & References
- AMCA (Air Movement and Control Association) fan laws
- Hydraulic Institute (HI) pump affinity laws
- Cameron Hydraulic Data
- ASHRAE Handbook -- HVAC Systems and Equipment
Frequently Asked Questions
Why does power change so much more than flow?
Flow is proportional to the speed ratio, but power is proportional to the cube of that ratio. Doubling speed doubles flow but multiplies power by eight. This cubic relationship is why variable-speed drives save so much energy: trimming speed slightly cuts power dramatically.
Do the affinity laws apply to both fans and pumps?
Yes. The same ratio relationships govern centrifugal fans, blowers and pumps because they share the same underlying turbomachinery physics. For fans the second law gives pressure rise; for pumps it gives head. Power follows the cube of the ratio in both cases.
When does the diameter form of the laws break down?
The diameter relationship is accurate for modest impeller trims, typically within about 10 to 15 percent of the original diameter. Large trims change the impeller-to-casing geometry and efficiency, so the simple cubic power law becomes less accurate and manufacturer data should be used.
Do the affinity laws account for the system curve?
No. The affinity laws describe the machine alone. The actual operating point is where the new fan or pump curve intersects the system resistance curve, which scales roughly with flow squared for turbulent systems. Use these laws together with a system-curve analysis for the real duty point.