Understanding and Applying the 3 Basic Fan Laws

When we are working on ventilation system redesign applications, the 3 Basic Fan Laws provide us the means by which we can correlate the relationship between fan air flow rate, static pressure, speed and horsepower.  They are useful to predict the outcomes when we want to change a known fan performance to a desired fan performance.  In this article, I’ll explain each of the fan laws, their limitations and how we would use them in a ventilation system redesign application.

3 Basic Fan Laws

Before explaining each law, I want to talk about their limitations.  These laws are only applicable when we are not changing the configuration of the fan propeller (diameter, number of blades, blade pitch angle, and hub size) and the geometry of the fan inlet or outlet.  Think of the limitations as constants in a science experiment where we would hold some variables constant and change only one variable to observe the changes in outcomes. 

Here are brief explanations of each law:

Fan Law 1 tells us that the change in air flow rate of a fan is proportional to the change in speed of the propeller.  If the propeller speed is increased by 10%, the air flow rate will also increase by 10%.

Fan Law 2 tells us that the change in total static pressure of the ventilation system will increase by the square of the change in propeller speed of the fan.If the propeller speed is increased by 10%, the total static pressure will increase 21%.

Fan Law 3 tells us that the change in horsepower required by the fan to turn the propeller will increase by the cube of the change in propeller speed of the fan.  If the propeller speed is increased by 10%, the horsepower required to turn the propeller will increase 33.1%.

Applications

We are most likely to use the 3 Basic Fan laws for a ventilation system redesign where the customer desires more air flow but doesn’t want to increase the size of the fan.  This happens often in process ventilation system redesigns where the cost of changing the ductwork limits the options for increased air flow to changing the propeller speed.  But the laws can also apply to a general ventilation redesign application.  An example of a situation we have encountered:   

• Customer desired more air flow from their belt drive exhaust fans. 
• Their exhaust fans were moving 15,000 CFM of air each with a propeller speed of 1000 RPM.
• The exhaust fan motors were rated at 1750 RPM, 5 HP but were only using peak HP of 3.75.
• The air supply to the building was through louvers with a static pressure of .15 in WG.
• The customer didn’t want to increase the negative static pressure in the building.
• They asked us:  How much air flow can each fan provide without going into the motor safety factor if they were only to change the sheave sizes in each fan?

We started with Fan Law 3 and solved for RPM₂:

RPM₂ = (HP₂/HP₁)^1/3 x RPM₁

RPM₂ = (5.0/3.75)^1/3 x 1000

RPM₂ = (5.0/3.75)^1/3 x 1000

RPM₂ = 1101    

Then we applied Fan Law 1 to determine the new air flow from each exhaust fan:

CFM₂ = CFM₁ x (RPM₂/RPM₁)

CFM₂ = 15,000 x (1101/1000)

CFM₂ = 15,000 x (1101/1000)

CFM₂ = 16,515

Fan Law 2 told us that the impact of additional air flow into the customer’s building would result in an increase in static pressure:

SP₂ = SP₁ x (RPM₂/RPM₁)²

SP₂ = .15 x (1101/1000)²

SP₂ = .18

Conclusion

Having correctly applied the 3 Basic Fan Laws, we were able to confidently tell the customer that they could expect to get a maximum of 16,515 CFM from their belt drive fans by changing only the sheave sizes.  However, we also needed to tell the customer that they would need to increase the area of their supply louvers in order keep the static pressure below their desired level.

Even though in this situation the customer decided to go a different route, our expertise in knowing how to apply the 3 Basic Fan Laws gave the customer valuable information to use in deciding how much money needed to be spent to redesign their ventilation system.

If you are in need of a ventilation system redesign, whether it as simple as changing sheaves or as complex as adding more fans, Eldridge can provide you with the options that best fit your financial situation.