Question

The 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)

Hint:

Recall how pump power scales with impeller speed under the pump affinity laws.

Answer 1

Correct Answer: 2.2

Step 1: Recall how pump power depends on speed.
For a centrifugal pump running at fixed efficiency, the affinity laws give discharge proportional to speed, head proportional to speed squared, and power proportional to speed cubed.
So \(P \propto N^3\).

Step 2: Write the new speed in terms of the old speed.
Speed is increased by 30%, so the new speed is \(N_2 = 1.30\,N_1\).

Step 3: Find the power ratio.
\(n = \dfrac{P_2}{P_1} = \left(\dfrac{N_2}{N_1}\right)^3 = (1.30)^3\).
\((1.30)^3 = 1.30 \times 1.30 \times 1.30 = 1.69 \times 1.30 = 2.197\).

Final Answer:
The power requirement rises by about 2.20 times the original value. \[ \boxed{n \approx 2.20} \]