A centrifugal pump, driven by a directly coupled 2 kW motor of speed 1400 rpm, is proposed to be connected to a motor of speed 2800 rpm. The power of the motor should be:
- A16 kWCorrect
- B8 kW
- C24 kW
- D4 kW
Solution
Concept
For the same pump (same impeller diameter), power varies as the cube of speed.
Formula
P ∝ N3 (same D), so P2 = P1 × (N2/N1)3
Step-by-step solution
1. Same pump, so diameter D is the same. 2. Affinity law: P ∝ N3. 3. Speed ratio N2/N1 = 2800/1400 = 2. 4. P2 = 2 × (2)3 = 2 × 8 = 16 kW.
Explanation
For the same pump, discharge varies as N, head as N2 and power as N3. Doubling the speed makes the power 23 = 8 times. So the new motor must give 2 × 8 = 16 kW.
Why the other options are wrong
B (8 kW) uses P ∝ N2. D (4 kW) uses P ∝ N. C (24 kW) does not follow any affinity law.
Shortcut
Double the speed means 8 times the power.
Common mistake
Using P ∝ N2 (the head relation) instead of P ∝ N3.
Correct answer: A) 16 kW