Fan laws, often referred to as fan affinity laws, are a set of mathematical relationships that describe the behaviour of fans in response to changes in speed, size, and other parameters. These laws allow engineers to predict how a fan will behave under varying operating conditions. The primary fan laws are as follows:

 

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1. Flow Law The flow law states that the airflow produced by a fan is directly proportional to its speed (revolutions per minute, rpm). This means that if the speed of the fan is increased, the airflow will increase proportionally.

 

Formula:

 

 

 

 

Where:

 

● Q1 and Q2 are the airflow rates at fan speeds N1 and N2 respectively.

 

This relationship helps in determining the changes in airflow when a fan speed is adjusted, which is particularly useful in applications where the airflow needs to be controlled dynamically.

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2. Pressure Law The pressure law dictates that the static pressure developed by the fan is proportional to the square of its speed. Therefore, if the speed of the fan is doubled, the pressure will increase by a factor of four.

 

Formula:

 

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Where:

 

● P1 and P2 are the pressures at speeds N1 and N2 respectively.

 

This law is particularly important when considering fan systems for high-resistance environments like military vehicles or aircraft, where higher pressure is required to overcome the resistance of ducts or filters.

 

 

3. Power Law The power law shows that the power required by the fan is proportional to the cube of its speed. This means that a small increase in fan speed will result in a large increase in the power consumption.

 

Formula:

 

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Where:

 

● W1 and W2 are the power values at speeds N1 and N2 respectively.

 

This law is critical when designing fan systems where energy efficiency is a major concern, particularly in defense systems where power consumption directly impacts operational costs and performance.

 

These fan laws are fundamental when designing fan systems to meet specific flow, pressure, and power requirements. They allow engineers to anticipate the system's response to changes in parameters such as fan speed or size and optimize the system accordingly.