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GATE 2016 ME (ME3) – Question 23

Fluid Mechanics · Control-volume analysis of mass, momentum and energy · 1 mark · Numerical answer

A channel of width 450 mm branches into two sub-channels having width 300 mm and 200 mm as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is 0.9 m3/s and the velocity in the sub-channel of width 200 mm is 3 m/s, the velocity in the sub-channel of width 300 mm is _____________ m/s. Assume both inlet and outlet to be at the same elevation.

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Correct answer: 0.99 to 1.01

Explanation

The total flow is0.9m³/s. The first branch carries area0.2×1 times speed3, or0.6m³/s. The other therefore carries0.3m³/s through area0.3×1m², giving **1m/s**. Constant density allows volume-flow conservation.