GATE 2021 ME (ME2) – Question 58

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

A high velocity water jet of cross section area = 0.01 m² and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity water jet entrains additional water from the pipe and the total water leaves the pipe with a velocity 6 m/s as shown in the figure. The flow rate of entrained water is _____ litres/s (round off to two decimal places).

High-speed inlet water jet entraining stagnant water in a pipe; combined outlet flow is uniform at 6 m/s. See the attached source image.

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Correct answer: 131.89 to 133.21

Explanation

Outlet flow is pipe area times velocity: $Q_o=\pi(0.32)^2(6)/4=0.4825486$ m³/s. Jet flow is 0.01×35=0.35 m³/s.

The difference is entrained water:0.1325486 m³/s=**132.55 L/s**. A mass balance suffices.