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GATE 2023 CE (CE1) – Question 44

Fluid Mechanics · Continuity, momentum and energy equations · 2 marks · Multiple choice

A jet of water having a velocity of 20 m/s strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at 15 m/s. What is the percentage efficiency of the plates? (round off to one decimal place)

  1. 37.5
  2. 66.7
  3. 50.0
  4. 88.9

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Show answer and explanation

Correct answer: (A) 37.5

Explanation

For a series of flat plates on a wheel, the whole jet discharge strikes the plates, so the force is $\rho aV(V - u)$ and the work done per second is $\rho aV(V - u)u$. The kinetic energy of the jet per second is $\frac{1}{2}\rho aV^3$. The efficiency is $\eta = \frac{2u(V - u)}{V^2} = \frac{2 \times 15 \times 5}{400} = 0.375$, that is 37.5%.