Themes > Science > Physics > Fluid Dynamics > Flying the flag for fluid dynamics > Aerodynamics > Low-speed steady aerodynamics / hydrodynamics > All you need to know about fans > The Fan Laws

Sometimes it may be necessary to determine the output of a given fan under other conditions of speed or density, or to convert the known performance of an air mover of one size to that of another geometrically similar unit of a different size. The fan laws permit this.

Geometrically similar fans can be characterized by the following four equations:

Volumetric Flowrate: G = KqND3

Mass Flow Rate: m· =Km ND3

Pressure: P = KpN2D2

Power: HP = KHPN3D5

where:

 K = constant for geometrically and dynamically similar operation G = volumetric flow rate m· = mass flow rate N = fan speed in RPM D = fan diameter HP = power output = air density

From these relationships, it is possible to calculate a fan performance at a second condition. Table 1 is a summary of the fan law equations in a form useful for fan analysis.

 Constants Variable Fan Laws Diameter (D) Density () Speed (N) G2 = G1 (N2/N1) P2 = P1 (N2/N1)2 HP2 = HP1 (N2/N1)3 Speed (N) Density () Diameter (D) G2 = G1 (D2/D1)3 P2 = P1 (D2/D1)2 HP2 = HP1 (D2/D1)5 Diameter (D) Speed (N) Volumetric Flow Rate (G) Density () P2 = P1 (2/1)2 HP2 = HP1 (2/1)5 Diameter (D) MassFlow Rate (m.) Density () G2 = G1 (2/1) P2 = P1 (2/1) N2 = N1 (2/1) HP2 = HP1 (N2/N1)2

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