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Fan Laws and Performance Formulae

Engineering Applications and Design
Industrial Electric Motors

Fan Laws and Performance Formulae

The following Formulae can be applied to any fan provided the diameter does not change. If the diameter does not change the fans must be geometrically similar. The units of density, fan rotational speed and diameter are not important as long as both are the same.

Fan Volume Flow Equation
Fan Volume Flow Equation

Fan Pressure Equation
Fan Pressure Equation

Fan Absorbed Power Equation
Fan Absorbed Power Equation

Fan Sound Power Level Equation
Fan Sound Power Level Equation

The following formulae the units shown in the nomenclature must be used to satisfy the formulae.

Density
Density

Fan Total Efficiency % Equation
Fan Total Efficiency % Equation

Fan Total Pressure Equation
Fan Total Pressure Equation

Fan Static Pressure Equation
Fan Static Pressure Equation

Fan Velocity Pressure Equation
Fan Velocity Pressure Equation

Where:

qv = volume flow of air, m3/sec
n = rotational speed of fan
d = diameter of fan
p = pressure developed by the fan
ρ = density of air, kg/m3
PR = power absorbed by the fan, kW
B = barometric pressure (millibars)
T = absolute temperature, K (K = °C + 273)
ptF = fan total pressure, Pa
psF = fan static pressure, Pa
pdF = fan dynamic/velocity pressure, Pa
pd = system dynamic/velocity pressure, Pa
V = velocity of air, m/sec
PWL = sound power level

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