Question

A rectangular channel 2 m wide carries 2.2 cumecs water in subcritical uniform flow at a depth of 1 m. What is the height of lowest transverse hump in the bottom such that critical depth is attained at the peak?

• A. 0.31 m
• B. 0.38 m
• C. 0.44 m
• D. 0.49 m

Answer 1

The correct option is A 0.31 m

$Velocityofflow=\frac{Q}{A}=\frac{2.2}{2}=1.1m/sec$

$E=y+\frac{V^2}{2g}=1+\frac{(1.1{)}^2}{2\times 9.81}=1.0617m$

$E_{min}=\frac{3}{2}{Y}_c$

$criticaldepthofflow,y_c={\left(\frac{q^2}{g}\right)}^{1/3}$

$={\left[\frac{(2.2/2{)}^2}{9.81}\right]}^{1/3}=0.498m$

$\therefore E_{min}=\frac{3}{2}\times 0.498=0.747m$

Height of lowest transverse hump = $E-E_{min}$

= 1.0617 - 0.747 = 0.315 m