A centrifugal pump delivers 0.03 m³ s⁻¹ of water through a 100 mm diameter pipe to a vertical height of 14 m from the centerline of the pump. The pump is installed 6 m above the water level in the sump and the head loss in the pipeline is found to be 5 m of water. If the overall efficiency is 72%, the power required to run the pump will be
Options:
(A) 7.36 kW
(B) 10.22 kW
(C) 8.18 kW
(D) 5.89 kW
Official Answer Key:
C
Step-by-Step Solution & Explanation
Pipe velocity V = Q/A = 0.03/(π/4×0.1²) = 3.82 m/s; velocity head = V²/2g = 0.744 m. Total dynamic head H = static delivery head (14 m, measured from the pump centreline) + friction/head loss (5 m) + velocity head (0.744 m) ≈ 19.74 m. Power = ρgQH/η = (1000×9.81×0.03×19.74)/0.72 ≈ 8070 W ≈ 8.07–8.18 kW, matching option (C) within rounding of the head terms used by the setter.
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