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# Understanding The Key Basic Fan Laws

Fan laws: The infinity laws for fans are used in HVAC to express the relationship between variables involved in fan performance and power. They are the basic proportional relationships between:

### Fan Speed (rpm), Air Flow Volume (m3/h), Pressure (Pa) and Power (W).

They are frequently used to estimate air moving device requirements. Additionally the fan laws can be used to calculate the performance of air movers in different sizes and speeds.

### Three Basic Fan Laws: The three basic fan laws noted within this section are those that we will be concerning ourselves with most, that express the relationships as below-

• What happens to flow rate if the impeller speed changes?
• What happens to system pressure if the air volume rate changes?
• What happens to power demand if the impeller speed changes?
##### The First Law – Volume Of Air:

The volume of air moved by a fan changes in direct proportion to the change in speed of the fan impeller and can be calculated as follows-

V2 = (u2/U1) x V1

This is a useful relationship as it allows us to use changes in volume when calculating the other fan laws.

Example:

A fan produces 1000m3/h at an impeller speed of 2000rpm, what is the resulting airflow if the speed is reduced to 1000rpm?

V2 = (1000/2000) x 1000 = 500m3/h

##### The Second Law – Pressure

The pressure developed by the fan and the pressure drop in a system varies with the square of the change of speed of the impeller or volume passing through the system.

P2 = (U2/U1)2 x P1

Example:

A fan produces 200Pa at an impeller speed of 1000rpm, what is the change in pressure if the impeller speed was increased to 2000rpm?

P2 = (2000/1000)2 x 200

P2 = 800Pa

##### The Third Law – Power

The power required to move air through the fan or system varies with the cube of the change in volume and is calculated as follows:

W2 = (V2/V1)3 x W1

Interestingly the noise generated by the fan is also a power relationship and again varies with the cube of the change in air volume being handled.

##### Summary

Fan laws are essentially about impellers and what happens to their characteristics when they undergo changes in rotational speed, air density, or are scaled in size.  They also help with the understanding of ventilation systems and the relationship between air volume flow rate and system total pressure.