Engineering
Fan Affinity Law Calculator
Compare an original and new fan speed with explicit density ratio. Calculate scaled flow, pressure, power, percentage changes, power difference, and operating-cost change.
New-to-original speed ratio-
Affinity-law flow (m³/h)-
Affinity-law pressure (Pa)-
Affinity-law power (kW)-
Flow change-
Pressure change-
Power change (kW)-
Energy-cost change over entered hours-
Decision view
Fan affinity exponent curves
Fan affinity exponent curvesIndexed flow, pressure, and power curves diverge as the speed ratio changes, making the cubic power response visible.
Exact scenario comparisonNew fan speed (rpm) changes while all other entered assumptions remain constant.
| New fan speed (rpm) | New-to-original speed ratio | Affinity-law flow (m³/h) | Affinity-law pressure (Pa) | Affinity-law power (kW) | Flow change | Pressure change | Power change (kW) | Energy-cost change over entered hours |
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How to use Fan Affinity Law Calculator
- Enter original and new fan speeds.
- Enter the original flow, pressure, and power operating point.
- Set the density ratio and operating-cost assumptions.
- Compare the first-, second-, and third-power curves.
Calculator guide
Understanding Fan Affinity Law Calculator
Fan affinity laws scale flow linearly, pressure quadratically, and power cubically with speed. The cubic relationship means a modest speed change can have a much larger energy consequence than its flow change suggests.
Calculation method
How the calculation works
Apply first-, second-, and third-power fan affinity relationships to flow, pressure, and power with an explicit density ratio. Form the speed ratio, multiply original flow by r, pressure by r squared and density ratio, and power by r cubed and density ratio.
Detailed calculation process
Apply the correct exponent to each fan quantity
The defaults increase fan speed from 1,200 to 1,500 rpm with unchanged density.
General formula: r = N_2/N_1; Q_2 = Q_1 r; DeltaP_2 = DeltaP_1 r^2 rho_r; P_2 = P_1 r^3 rho_r; DeltaC = (P_2-P_1) h c The same speed ratio drives three different curves. Flow follows the first power, pressure the second, and power the third, so the outputs must not be scaled with one common percentage.
What each symbol means
Worked substitution with the default inputs
A 25% speed increase raises modeled flow by 25%, pressure by 56.25%, and power from 6.5 to 12.695 kW under the stated affinity assumptions.
Exponent comparison
See three outputs diverge from one speed change
Indexed curves make the cubic power penalty unmistakable.
Worked situations
Practical examples
- A speed ratio of 1.25 creates a flow index of 1.25.
- Pressure index becomes 1.5625.
- Power index becomes 1.953125.
Better inputs
Useful tips
- Check the motor and VFD against the cubic power increase.
- Use affinity laws near a valid reference operating point.
- Pair the result with a system curve.
Before relying on the result
Limitations and common mistakes
- The laws approximate geometrically similar operating conditions.
- Fan efficiency, stall, noise, duct effects, and motor limits can change.
- Density and system resistance must be treated consistently.
Reference
Key terms
- Affinity law
- Scaling relationship between fan speed and operating quantities.
- Speed ratio
- New rotational speed divided by original speed.
- System curve
- Required pressure as a function of system flow.
Important note
Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.
Frequently asked questions
Why does power change so quickly?
The ideal affinity relationship raises the speed ratio to the third power.
Does density affect flow?
In this model density ratio modifies pressure and power, not the ideal volume-flow scaling.
Can I extrapolate far from the original speed?
Large changes are less reliable because efficiency and the operating point can shift.
Why can cost change be negative?
Reducing speed can lower modeled power and therefore period energy cost.