Worked problem

Fan Laws: What Changes When Speed Drops?

Estimate airflow, pressure and shaft power when a fan slows from 1,200 to 900 rpm, and why the cube law does not predict electricity savings.

Mechanical, HVAC & Fluids · Last reviewed October 17, 2026

Given

A fan delivers 12,000 CFM at 1.5 in. w.g. total pressure and 6.0 bhp at 1,200 rpm. The speed is reduced to 900 rpm. Assume the same fan, the same air density, and a duct system whose resistance is a pure friction curve (pressure proportional to flow squared).

Find

The new airflow, pressure and shaft power, and whether the result predicts the change in electricity use.

Solution

The fan laws relate two operating points of one fan when the system resistance follows the same pure-friction relationship. With the speed ratio r = 900 ÷ 1,200 = 0.75:

Flow is proportional to speed: 12,000 × 0.75 = 9,000 CFM.
Pressure is proportional to speed squared: 1.5 × 0.75² = 0.84 in. w.g.
Shaft power is proportional to speed cubed: 6.0 × 0.75³ = 2.53 bhp.

Answer

9,000 CFM  |  0.84 in. w.g.  |  2.53 bhp (42% of the original power)

Why this is not a savings prediction

The cube law gives shaft power. Electricity depends on the efficiency of the motor and drive, and those change at part load. Taking an assumed motor efficiency of 91% across the line at full speed and 88% with a variable-frequency drive of 96% efficiency at the lower speed (exercise values):

	Shaft power	Electrical input
1,200 rpm, motor only	4.47 kW	4.92 kW
900 rpm, motor and drive	1.89 kW	2.23 kW
Change	−58%	−55%

The laws hold only if the system curve passes through the origin. A system with fixed pressure, such as a duct static-pressure setpoint or a filter bank held at a constant drop, needs far more power than the cube law says.
Motor and drive efficiency fall at light load, and the drive has its own losses.
Air density, belt slip and the fan operating near stall can all change the result.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Does a 25% speed reduction save 58% of the energy?

Only in the ideal case. The shaft power falls by 58%, but electricity falls by somewhat less, and a system with fixed static pressure falls by much less.

Do the fan laws work for pumps?

The same affinity laws apply to centrifugal pumps, with the same limits: the system curve must pass through the origin, so a pump working against static head does not follow the cube law.

How do I get real values?

Use the fan curve at the new speed and the system curve, and find the intersection, then use the manufacturer power data.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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