Fan and pump speed affinity

Scale a known operating point for a speed change at unchanged impeller geometry and fluid density.

How this calculation works

Enter a known operating point with its original speed, volume flow, pressure rise and shaft power, followed by the proposed speed. The ratio of new speed to original speed scales flow directly, pressure rise by its square and shaft power by its cube. These results describe corresponding operating points under the affinity assumptions: the impeller geometry and fluid density remain unchanged, and efficiency is treated as constant. Shaft power must be used consistently rather than substituting motor electrical input without considering losses. The scaled point is not automatically the point where an actual system will operate. Static head, changing resistance and control behavior can alter that intersection. The calculation also does not verify permitted speed, motor loading, NPSH or other equipment operating limits.

Inputs and units

Original speed (r/min)
New speed (r/min)
Original volume flow (L/s)
Original pressure rise (kPa)
Original shaft power (kW)

Method and formula

r = N2/N1; Q2 = Q1r; Δp2 = Δp1r²; Pshaft,2 = Pshaft,1r³.

Worked example

Example inputs

Original speed: 1500 r/min
New speed: 1200 r/min
Original volume flow: 100 L/s
Original pressure rise: 20 kPa
Original shaft power: 5 kW

Calculation steps

Speed ratio = 1200 / 1500 = 0.8 fraction.
Scaled flow = 100 × 0.8 = 80 L/s; scaled pressure rise = 20 × 0.8² = 12.8 kPa.
Scaled shaft power = 5 × 0.8³ = 2.56 kW.

Example results

Scaled volume flow: 80 L/s
Scaled pressure rise: 12.8 kPa
Scaled shaft power: 2.56 kW
Speed ratio: 0.8 fraction

Assumptions

Same impeller, density and geometrically similar operating point; efficiency unchanged.

Limitations

Not a new operating-point solver for a system with static head, changing resistance or controls.
Does not verify motor loading, pump NPSH, surge or permitted speed.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

DOE Fundamentals: Fluid Flow: Continuity and Bernoulli energy balance; centrifugal pumps, equations 3-19 through 3-25; series and parallel piping
DOE: Improving Fan System Performance: Printed page 3: fan speed affinity laws