For a given centrifugal pump (where N is speed, Q is discharge, H is head and P is power)

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  1. H α 1/N2
  2. H α N5
  3. Q α N2
  4. Q α N

Answer (Detailed Solution Below)

Option 4 : Q α N
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Concept:

Affinity Laws:

A set of formulas that is used to predict the operation of a centrifugal pump at any operating point based on the original pump characteristics is known as the affinity laws.

These formulae can also be used to compare pumps of similar shapes.

Affinity laws for Speed change:

\(\frac {Q_1}{Q_2} = \frac {N_1}{N_2}\)

\(\frac {H_1}{H_2} = ({\frac {N_1}{N_2}})^2\)

\(\frac {P_1}{P_2} = ({\frac {N_1}{N_2}})^3\)

Affinity laws for Diameter change:

\(\frac {Q_1}{Q_2} = \frac {D_1}{D_2}\)

\(\frac {H_1}{H_2} = ({\frac {D_1}{D_2}})^2\)

\(\frac {P_1}{P_2} = ({\frac {D_1}{D_2}})^3\)

From the above laws, it is clear that The discharge varies directly as the speed

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