GATE 2017 ME (ME1) – Question 18

Fluid Mechanics · Dimensional analysis · 1 mark · Numerical answer

Water of density 1000 kg/m³ flows through a horizontal uniform pipe at 1 kg/s. The pressure drop is 100 kPa. Find the minimum pumping power in watts.

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Correct answer: 100 to 100

Explanation

The volume flow rate is $Q=\dot m/\rho=1/1000=0.001$ m³/s. Hydraulic power needed to overcome pressure loss is $\Delta pQ=100000(0.001)=100$ W. This is the minimum with ideal power transfer; a non-unit pump efficiency would increase the input requirement.

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