A centrifugal pump with the impeller diameter of 125 mm delivers a power of 10 hp. If the impeller diameter is changed to 250 mm, what will be the power delivered by the pump if other parameters are kept constant?
- A40 hp
- B100 hp
- C320 hpCorrect
- D80 hp
Solution
Concept
For similar pumps, power is proportional to N3 D5.
Formula
P ∝ N3 D5, so P2/P1 = (N2/N1)3 × (D2/D1)5
Step-by-step solution
1. Speed N stays the same. Only the diameter changes. 2. So P ∝ D5. 3. D2/D1 = 250/125 = 2. 4. P2/P1 = 25 = 32. 5. P2 = 32 × 10 = 320 hp.
Explanation
By the pump affinity (similarity) laws, power varies as N3 D5. Speed is constant and the diameter is doubled. So power becomes 25 = 32 times, which is 320 hp.
Why the other options are wrong
A (40 hp) uses D2. D (80 hp) uses D3. B (100 hp) has no correct basis.
Shortcut
Double the diameter at the same speed and power becomes 32 times.
Common mistake
Using D2 or D3 instead of D5 for power.
Correct answer: C) 320 hp