Question

 A centrifugal pump driven by a directly coupled 3 kW motor of 1450 rpm speed, is proposed to be connected to a motor of 2900 rpm speed. The power of the motor should be

1. 6 kW
2. 12 kW
3. 18 kW
4. 24 kW

Answer 1

Correct Answer - Option 4 : 24 kW

Concept:

Velocity in pump:

\(V = \frac{{\pi \times D \times N}}{{60}} = \sqrt {2gh} \)

From above, \(h = \frac{{{\pi ^2} \times {D^2} \times {N^2}}}{{3600 \times 2g}}\)

Discharge of a pump:

Q = A × V

\(Q = \frac{{{\pi ^2} \times {D^3} \times N}}{{240}}\)

Power of a pump:

P = ρ × g × Q × h

\(P = \rho \times g \times \frac{{{\pi ^2} \times {D^3} \times N}}{{240}} \times \frac{{{\pi ^2} \times {D^2} \times {N^2}}}{{3600 \times 2g}}\)

P = K × N³

\(\frac{{{P_1}}}{{{P_2}}} = \frac{{N_1^3}}{{N_2^3}}\)

Calculation:

Given:

P₁ = 3 kW, N₁ = 1450 rpm, and N₂ = 2900 rpm.

From, \(\frac{{{P_1}}}{{{P_2}}} = \frac{{N_1^3}}{{N_2^3}}\)

\(\frac{3}{{{P_2}}} = {\left( {\frac{{1450}}{{2900}}} \right)^3}\)

P₂ = 24 kW.