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Fluid Mechanics

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A channel of ...

Question

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 $0.9 m^{3} / s$ 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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Solution

The correct option is A 1

Given data: $b_{1} = 450 m m = 0.45 m$
$b_{2} = 300 m m = 0.30 m; b_{3} = 200 m m = 0.20 m$
Depth: h = 1 m
$Q_{1} = 0.9 m^{3} / s$
$V_{3} = 3 m / s$
$V_{2} = ?$
Apply equation of continuity, we get
$Q_{1} = Q_{2} + Q_{3}$
$Q_{1} = A_{2} V_{2} + A_{3} V_{3}$
$Q_{1} = b_{2} h V_{2} + b_{3} h V_{3}$
$0.9 = 0.30 \times 1 \times V_{2} + 0.20 \times 1 \times 3$
$0.9 = 0.30 V_{2} + 0.60$

$o r 0.30 V_{2} = 0.9 - 0.6 = 0.30$

$o r V_{2} = \frac{0.30}{0.30} = 1 m / s$

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