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 $0.9m^3/s$ 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.

• A. 1

Answer 1

The correct option is A 1

Given data: $b_1=450mm=0.45m$
$b_2=300mm=0.30m;b_3=200mm=0.20m$
Depth: h = 1 m
$Q_1=0.9m^3/s$
$V_3=3m/s$
$V_2=?$
Apply equation of continuity, we get
$Q_1=Q_2+Q_3$
$Q_1=A_2{V}_2+A_3{V}_3$
$Q_1=b_{2}h{V}_2+b_{3}h{V}_3$
$0.9=0.30\times 1\times V_2+0.20\times 1\times 3$
$0.9=0.30V_2+0.60$

$or0.30V_2=0.9-0.6=0.30$

$or{V}_2=\frac{0.30}{0.30}=1m/s$