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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