GATE 2021 MN – Question 29

Surface Environment, Mine Ventilation and Underground Hazards · Mine Ventilation · 1 mark · Multiple choice

For geometrically similar fans, how does pressure scale with rotational speed n, impeller diameter D and air density $\rho$?

$nD^2\rho$
$n^2D^2\rho$
$n^2D^5\rho^2$
$n^3D^5\rho$

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Show answer and explanation

Correct answer: (B) $n^2D^2\rho$

Explanation

Fan pressure scales with density times the square of blade velocity. Blade velocity scales as nD, so $\Delta p\propto\rho(nD)^2=\rho n^2D^2$, B. The n³D⁵ dependence belongs to the power affinity law, with the appropriate density factor.

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