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GATE 2022 CH – Question 38

Fluid Mechanics and Mechanical Operations · Equations of continuity, motion and mechanical energy, Euler and Bernoulli equations · 2 marks · Multiple choice

A horizontal cylindrical water jet of diameter $D_1 = 2$ cm strikes a vertical solid plate with a hole of diameter $D_2 = 1$ cm, as shown in the figure. A part of the jet passes through the hole and the rest is deflected along the plate. The density of water is 1000 kg m$^{-3}$. If the speed of the jet is 20 m s$^{-1}$, the magnitude of the horizontal force, in N, required to hold the plate stationary is

a jet of diameter 2 cm moving at 20 m/s to the right, hitting a vertical plate that has a central hole of diameter 1 cm. The central part of the jet goes through the hole at 20 m/s and the outer part is turned through 90° along the plate.
  1. $30\pi$
  2. $10\pi$
  3. $20\pi$
  4. $5\pi$

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Show answer and explanation

Correct answer: (A) $30\pi$

Explanation

The part of the jet that passes through the hole keeps its horizontal momentum. Only the outer ring of the jet is stopped in the horizontal direction. Its area is $\frac{\pi}{4}(0.02^2 - 0.01^2) = 2.356 \times 10^{-4}$ m². The force is $\rho Av^2 = 1000 \times 2.356 \times 10^{-4} \times 400 = 94.2$ N $= 30\pi$ N.