Fan Laws or Affinity Laws
Introduction
Fan Laws, also known as Affinity Laws, govern the performance of geometrically similar Centrifugal fans. These laws apply only approximately to other, i.e. non-centrifugal, types of fans. Fan performance data are usually based on a standard air density of 0.075 lb/ft3 (1.20 kg/m3) at an elevation of zero.
Symbols
D = Fan size
N = Rotational speed
P = Pressure
Q = Volume flow rate
W = Power
ρ = Gas density
Fan Law 1
The first fan law relates the airflow rate to the fan rotational speed: Volume flow rate, Q, is directly proportional to the fan rotational speed, N.
(Q1/Q2) = (D1/D2)3 (N1/N2)
Fan Law 2
The second fan law relates the fan total pressure or fan static pressure to the fan rotational speed: Total or static pressure, P, is proportional to the square of the fan rotational speed, N.
(P1/P2) = (D1/D2)2 (N1/N2)2 (ρ1/ρ2)
Fan Law 3
The third fan law relates the total or static air power (and the impeller power), W, to the fan rotational speed: Power, W, is proportional to the cube of the fan rotational speed, N.
(W1/W2) = (D1/D2)5 (N1/N2)3 (ρ1/ρ2)
Derivatives of Fan Laws
The three main fan laws given above, when combined and rearranged, give the relationships shown below.
(Q1/Q2) = (D1/D2)2 (P1/P2)1/2 (ρ1/ρ2)-1/2
(P1/P2) = (D1/D2)-4 (Q1/Q2)2 (ρ1/ρ2)
(N1/N2) = (D1/D2)-1 (P1/P2)1/2 (ρ1/ρ2)-1/2
(N1/N2) = (D1/D2)-3 (Q1/Q2)
(W1/W2) = (D1/D2)2 (P1/P2)3/2 (ρ1/ρ2)-1/2
(W1/W2) = (D1/D2)-4 (Q1/Q2)3 (ρ1/ρ2)
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