Question

Given impeller diameter $D$, speed of rotation $n$ and air density $\rho$, for geometrically similar fans, the fan pressure is proportional to

• A. $nD^{2}\rho$.
• B. $n^{2}D^{2}\rho$.
• C. $n^{2}D^{5}\rho^{2}$.
• D. $n^{3}D^{5}\rho$.

Hint:

Fan laws: Capacity $\propto nD^{3}$, Pressure $\propto n^{2}D^{2}$, Power $\propto n^{3}D^{5}$.

Answer 1

The Correct Option is B

Fan pressure relates to dynamic pressure generated by rotating blades.

Step 1: For dynamically similar fans, fan pressure is proportional to the square of tip velocity.
Tip velocity: $V = \pi D n$

Step 2: Pressure $\propto \rho V^{2}$.
Substitute:
$P \propto \rho (\pi D n)^{2}$
$P \propto n^{2} D^{2} \rho$.

Step 3: Therefore, among the options provided, the correct proportionality is $n^{2} D^{2} \rho$.