Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2019
Hard
A centrifugal pump pumps water (density 1000 kg/m³) from inlet pressure 10^5 Pa to exit pressure 2×10^5 Pa. The exit is 10m above the pump. Average velocity is 10 m/s throughout (equal 10⁻³ m² inlet/outlet areas), g=10 m/s². Neglecting losses, the power (W) delivered by the pump is (rounded off to nearest integer)
2000 W(± 20 accepted)
Explanation
Ws=(Pout−Pin)/ρ+(Vout²−Vin²)/2+g·Δz=(1e5)/1000+0+10×10=100+100=200 J/kg. Mass flow=ρVA=1000×10×0.001=10 kg/s. Power=10×200=2000W.
Source: GATE CH 2019 (2019)
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