Impeller speed of a centrifugal pump is increased by 30%. The power requirement of the pump increases by n times. The value of n is ________. (Rounded off to two decimal places)
Official Answer Key:
2.10 to 2.30
Step-by-Step Solution & Explanation
The affinity (similarity) laws for a centrifugal pump at a fixed impeller diameter are:
Q ∝ N (discharge)
H ∝ N² (head)
P ∝ N³ (power)
Since P = ρgQH/η and both Q and H scale with N and N² respectively, power scales with N³.
n = (N₂/N₁)³ = (1.30)³ = 2.197 ≈ 2.20
(A 30% speed rise more than doubles the power demand — the practical reason motors are easily overloaded when pumps are over-speeded.)
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