Fan Laws or Affinity Laws

Table of Contents

Introduction
Symbols
Fan Law 1
Fan Law 2
Fan Law 3
Derivatives of Fan 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)212)

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)312)

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)1/212)-1/2

(P1/P2) = (D1/D2)-4 (Q1/Q2)212)

(N1/N2) = (D1/D2)-1 (P1/P2)1/212)-1/2

(N1/N2) = (D1/D2)-3 (Q1/Q2)

(W1/W2) = (D1/D2)2 (P1/P2)3/212)-1/2

(W1/W2) = (D1/D2)-4 (Q1/Q2)312)