Question:
A centrifugal fan rotating at \(600\) rpm delivers \(70\ \mathrm{cu.m/s}\) of air. If the speed is reduced to \(300\) rpm, the quantity of air delivered in \(\mathrm{cu.m/s}\) will be
A centrifugal fan rotating at \(600\) rpm delivers \(70\ \mathrm{cu.m/s}\) of air. If the speed is reduced to \(300\) rpm, the quantity of air delivered in \(\mathrm{cu.m/s}\) will be
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Fan affinity law:
\[
\boxed{Q\propto N.}
\]
If the speed is halved, the air quantity is also halved.
Updated On: Jul 14, 2026
- \(140\)
- \(35\)
- \(70\)
- \(17.5\)
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Verified By Collegedunia
The Correct Option is B
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, \[ Q_1=70\ \mathrm{m^3/s},\qquad N_1=600\ \mathrm{rpm},\qquad N_2=300\ \mathrm{rpm}. \] Using \[ Q_2=Q_1\left(\frac{N_2}{N_1}\right), \] \[ Q_2 = 70\left(\frac{300}{600}\right) = 70\times\frac12 = 35\ \mathrm{m^3/s}. \] Hence, \[ \boxed{35\ \mathrm{m^3/s}} \] is the correct answer. Therefore, \[ \boxed{(B)} \] is the correct answer.
Step 2: Calculate the new discharge. Given, \[ Q_1=70\ \mathrm{m^3/s},\qquad N_1=600\ \mathrm{rpm},\qquad N_2=300\ \mathrm{rpm}. \] Using \[ Q_2=Q_1\left(\frac{N_2}{N_1}\right), \] \[ Q_2 = 70\left(\frac{300}{600}\right) = 70\times\frac12 = 35\ \mathrm{m^3/s}. \] Hence, \[ \boxed{35\ \mathrm{m^3/s}} \] is the correct answer. Therefore, \[ \boxed{(B)} \] is the correct answer.
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