What does the variable 'n' represent in the fan flow equation Q=CA(2∆P/ρ)^n?

In the fan flow equation Q = CA(2∆P/ρ)^n, the variable 'n' is known as the flow exponent. It characterizes the relationship between the airflow (Q) and the pressure differential (∆P) across a fan or a system. The flow exponent plays a crucial role in determining how changes in pressure affect the flow rate.

When 'n' is equal to 0.5, which is commonly applicable in certain scenarios, it indicates that the airflow varies with the square root of the pressure difference. This regression to an exponent less than 1 highlights the non-linear nature of airflow as pressure changes, revealing that the resistance in the system affects the flow rate in a distinct way compared to a linear relationship.

Understanding 'n' is critical in designing ventilation systems and ensuring they operate efficiently under varying conditions, as it helps in predicting how airflow will respond to changes in pressure.

The role of other variables such as flow coefficient (C), pressure differential (∆P), and air density (ρ) are important, but they serve different purposes and do not convey the same functional relationship represented by 'n' in this equation.