Hydraulic Machines MCQ with answer and solution

Concept

For a given centrifugal pump, discharge varies directly with impeller speed (affinity law).

Formula

Q ∝ N D³; H ∝ N² D²; P ∝ N³ D⁵. For the same pump: Q ∝ N, H ∝ N², P ∝ N³

Step-by-step solution

1. Write the affinity laws for a centrifugal pump. 2. For the same pump, D is fixed, so Q ∝ N. 3. Head varies as N², so Q ∝ √H, not H. 4. So discharge is directly proportional to the revolutions per minute (N) of the impeller.

Explanation

Discharge = flow area × flow velocity, and the flow velocity grows directly with impeller speed. So when rpm doubles, discharge also doubles. Head and power change as N² and N³.

Why the other options are wrong

A: For similar pumps Q ∝ D³, not D, so it is not simple direct proportion. B: Q ∝ √H, not H. D: Inner diameter is not the controlling term in the affinity law.

Shortcut

Remember the powers 1-2-3: Q ∝ N, H ∝ N², P ∝ N³.

Common mistake

Taking Q ∝ H, or forgetting that the diameter term is D³, not D.