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Fan Affinity Law — Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

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Multiply the linear flow law by the square-law pressure and you get a cube: a 5 hp fan sped from 800 to 1000 rpm needs 5 × 1.25³ ≈ 9.77 hp. That factor of nearly two for a 25% speed change is the most expensive line item in HVAC retrofit work, and it is precisely why a variable-air-volume system that spends most of the year at 60% airflow uses only about 22% of design fan energy.

Every experienced service technician has a story about a re-sheave that tripped the overloads within an hour. The rule of thumb: never raise fan speed without checking that the new power fits inside the motor's service factor. Run the numbers first — 15% more rpm is 52% more power, and there is no such thing as a small speed increase.

Fan Affinity Law — Power vs Speed
P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
Where
  • P1P_1= Fan power at speed 1
  • N1N_1= Fan speed 1
  • P2P_2= Fan power at speed 2
  • N2N_2= Fan speed 2
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Part of this formula set

The pump and fan affinity laws

7 formulasHow flow, head and power scale with impeller speed and diameter — the first, second and third power relationships behind every VFD retrofit.