A centrifugal pump delivers 30 l s⁻¹ of water against static suction and delivery heads of 6 m and 10 m respectively. The length and diameter of delivery pipe are 100 m and 100 mm respectively. The outlet of delivery pipe is submerged. Friction factor for the pipe is 0.03. If the minor losses in the delivery pipe amount to 1.0 m, pressure at delivery end of the pump is
Options:
(A) 327 kPa
(B) 385 kPa
(C) 680 kPa
(D) 984 kPa
Official Answer Key:
B
Step-by-Step Solution & Explanation
Velocity in delivery pipe: v = Q/A = 0.030/[(π/4)(0.1)²] = 0.030/0.007854 = 3.820 m/s. Friction head loss, h_f = fLv²/(2gD) = 0.03×100×(3.820)²/(2×9.81×0.1) = 22.31 m. Total head at pump delivery = static suction + static delivery + h_f + minor losses = 6+10+22.31+1.0 = 39.31 m. Pressure = ρgh = 1000×9.81×39.31 = ≈385.6 kPa.
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