Fan laws were derived from a dimenionless analysis of variables involved in fan performance using the Buckingham Pi Theorem. For the user interested in learning more about this topic, see my Understanding the Fan Laws article for more information.

The calculator relates any two variables from the following list:

• Airflow
• Air velocity
• Static pressure
• Shaft speed of the fan
• Power to drive the fan
• Fan diameter

Since the fan laws are dimenionless (without units of measure), any suitable units of measure may be used. With English units of measure, the following are normally used:

• Airflow: CFM (cubic feet per minute)
• Air velocity: FPM (feet per minute)
• Static pressure: in H₂O (inches of water column)
• Shaft speed: RPM (revolutions per minute)
• Power: BHP (brake horsepower)
• Fan diameter: inches

The fan laws require 1 of the 6 variables to be held constant. When fan diameter is not selected, the app will hold fan diameter constant which is to say the fan does not change. If it is desired to change fan diameter. the app will hold shaft speed constant, unless both fan diameter and shaft speed are selected. In this case, airflow is held constant.

If airflow and air velocity are selected, the app will hold the area through which the air is flowing constant. Converting airflow to air velocity and vice versa falls outside the fans laws. It is an application of the conservation laws.

Note that the fan laws assume fan efficiency remains constant whenever fan shaft speed or fan diameter are changed. While not technically accurate, the laws do provide very good approximations when these variables are changed within a reasonable range.