Q.41 What is the relation between the delivery head of the centrifugal pump and the shaft speed (N)?
- AThe delivery head is inversely proportional to N².
- BThe delivery head is inversely proportional to N.
- CThe delivery head is directly proportional to N².Correct
- DThe delivery head is directly proportional to N.
Solution
Concept
For a centrifugal pump of the same size, head varies as the square of speed (affinity laws).
Formula
H ∝ N2 D2; for same D: H2/H1 = (N2/N1)2
Step-by-step solution
1. Head coefficient gH/(N2 D2) is constant for similar pumps. 2. So H ∝ N2 D2. 3. For the same pump, D is constant. 4. So H ∝ N2, which means head is directly proportional to N².
Explanation
The impeller gives energy to water through blade velocity u = πDN/60. Head depends on u2/g, so head grows with the square of speed. If speed doubles, head becomes four times.
Why the other options are wrong
A: Head increases with speed, it does not decrease. B: Head is not inversely related to speed. D: The relation is with N², not N (N is for discharge).
Shortcut
Affinity laws: Q ∝ N, H ∝ N², P ∝ N³.
Common mistake
Mixing up the laws and taking H ∝ N (that is for discharge Q).
Correct answer: C) The delivery head is directly proportional to N².