A centrifugal pump has an impeller of outer diameter of 30 cm. Water enters the impeller radially. Vane tips are radial at the outlet. The rotative speed is 1500 rpm and the manometric efficiency is 80%. What is the net head developed (in meter)? [Assuming acceleration due to gravity = g m/s²]

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

The net head developed by a centrifugal pump is related to the impeller velocity and manometric efficiency:

\( H_m = \frac{\eta_m \times u_2^2}{g} \)

Given:

\( D_2 = 0.3~m,~N = 1500~rpm,~\eta_m = 0.8,~g = 9.81~m/s^2 \)

Step 1: Calculate Impeller Tip Velocity

\( u_2 = \frac{\pi D_2 N}{60} = \frac{\pi \times 0.3 \times 1500}{60} \approx 23.56~m/s \)

Step 2: Calculate Net Head

\( H_m = \frac{0.8 \times (23.56)^2}{9.81} \approx \frac{444.5}{9.81} \approx 45.3~m \)