Fan Affinity Laws

The influence of fan speed and diameter of wheel - on air flow volume, head and power consumption

Changing of Fan Speed

Changing the speed of a fan influence volume, head and power consumption:

Air Flow Volume

Air flow volume will vary directly with the speed and can be expressed as:

q₁ / q₂ = n₁ / n₂ (1)

where

q₁ = air flow at speed 1 (m³/s)

q₂ = air flow at speed 2 (m³/s)

n₁ = speed 1 of the fan (rpm)

n₂ = speed 2 of the fan (rpm)

Head Developed

Head developed will vary with square of speed and can be expressed as:

dp₁ / dp₂ = (n₁ / n₂)² (2)

where

dp = head developed (Pa)

Power Consumption

Power consumption will vary with cube of the speed and can be expressed as:

P₁ / P₂ = (n₁ / n₂)³ (3)

where

P = power consumption (W)

Note! If speed increase with 10%

• volume increase 10%
• head increase 21%
• power increase 33 %

This mean that if we want to increase the volume flow in an existing system with 10% we have to increase the power with 33%. In general the motor and the power supply must be changed.

Changing the Size of the Fan (the diameter of the wheel)

Air Flow Volume

Air flow volume will vary directly with the cube of the diameter and can be expressed as:

q₁ / q₂ = (d₁ / d₂)³ (4)

where

d = wheel diameter (m)

Head Developed

Head developed will vary with square of diameter and can be expressed as:

dp₁ / dp₂ = (d₁ / d₂)² (5)

Power Consumption

Power consumption can be expressed as:

P₁ / P₂ = (d₁ / d₂)⁵ (6)

Changing the Belt Gearing

The connection between speed of motor or belt disc and fan, and their disc diameters can be expressed as:

d_fan n_fan = d_beltdisc n_beltdisc (7)

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