Discussion
The power required by a centrifugal fan varies as
Answer: A
Correct answer: the cube of the speed
A centrifugal fan’s torque varies as the square of the speed, and power is torque times speed, so
\[ P \propto \omega^3 \]This cube law is why variable speed control of fans and pumps saves so much energy: reducing the speed by twenty per cent halves the power. It is also why a fan takes so long to run up, since the accelerating torque available shrinks steeply as the speed rises.
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