Question:
A centrifugal fan rotating at \(500~\mathrm{rpm}\) delivers \(70~\mathrm{m^3/s}\) of air. If the speed is reduced to \(200~\mathrm{rpm}\), the quantity of air delivered in \(\mathrm{m^3/s}\) will be
A centrifugal fan rotating at \(500~\mathrm{rpm}\) delivers \(70~\mathrm{m^3/s}\) of air. If the speed is reduced to \(200~\mathrm{rpm}\), the quantity of air delivered in \(\mathrm{m^3/s}\) will be
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Fan affinity laws:
\[
\boxed{
Q\propto N,\qquad
P\propto N^2,\qquad
\text{Power}\propto N^3.
}
\]
Updated On: Jul 14, 2026
- \(175\)
- \(55\)
- \(28\)
- \(11\)
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Apply the fan affinity law.
For a centrifugal fan,
\[
Q\propto N,
\]
where \(Q\) is the air quantity and \(N\) is the rotational speed.
Step 2: Calculate the new discharge. Given, \[ Q_1=70~\mathrm{m^3/s}, \quad N_1=500~\mathrm{rpm}, \quad N_2=200~\mathrm{rpm}. \] Hence, \[ Q_2 = Q_1\frac{N_2}{N_1} = 70\left(\frac{200}{500}\right) = 70\times0.4 = 28~\mathrm{m^3/s}. \] Thus, \[ \boxed{28~\mathrm{m^3/s}} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.
Step 2: Calculate the new discharge. Given, \[ Q_1=70~\mathrm{m^3/s}, \quad N_1=500~\mathrm{rpm}, \quad N_2=200~\mathrm{rpm}. \] Hence, \[ Q_2 = Q_1\frac{N_2}{N_1} = 70\left(\frac{200}{500}\right) = 70\times0.4 = 28~\mathrm{m^3/s}. \] Thus, \[ \boxed{28~\mathrm{m^3/s}} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.
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