GATE 2021 ME (ME1) – Question 57

Fluid Mechanics · Control-volume analysis of mass, momentum and energy · 2 marks · Numerical answer

A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant $k=1$ kN/m. The incoming jet diameter is $D=1$ cm. If the spring shows a steady deflection of 1 cm upon impingement of jet, then the velocity of the incoming jet is _____ m/s (round off to one decimal place).

Upward cylindrical water jet impinging on a horizontal plate supported by a linear spring. See the attached source image.

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Correct answer: 11.24 to 11.36

Explanation

The additional spring force is kδ=1000(0.01)=10 N. The outgoing radial flow has zero vertical momentum, so jet force is $\rho AV^2$.

With $A=\pi(0.01)^2/4$, solve $V=\sqrt{10/(1000A)}=11.2838$ m/s. **Answer: 11.3 m/s**.