Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2015
Hard
A centrifugal pump delivers 0.22 m³/s water from ground level to height H through a 0.2m-diameter vertical pipe (open reservoirs). Power input=90kW, efficiency=75%, Fanning f=0.004 (pipe length=H, other losses neglected). g=9.8 m/s², ρ=1000 kg/m³. The height H (m), rounded to 1 decimal place, is
26.1 m(± 1 accepted)
Explanation
Useful power=90×0.75=67.5kW. V=Q/A=0.22/0.0314=7.00m/s. hf=4f(H/D)(V²/2g)=0.016×(H/0.2)×2.502=0.2002H. Useful power=ρgQ(H+hf)=1000×9.8×0.22×1.2002H=2586.9H=67500 ⟹ H=26.1m.
Source: GATE CH 2015 (2015)
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