Question

A rectangular channel 2 m wide carries 2.2 cumecs of water in subcritical uniform flow at a depth of 1 m. The amount of lowest transverse hump (in mm, correct up to one decimal place) in the bottom such that critical depth is attained at the peak.

• A. 312

Answer 1

The correct option is A 312
Given, Q = 2.2 Cumecs, B = 2 m, Y = 1 m

$E=y+\frac{Q^2}{2g{B}^2{y}^2}$

$=1+\frac{(2.2{)}^2}{2\times 9.81\times 4\times 1}=1.062m$

$E_{min}=\frac{3}{2}{y}_c=\frac{3}{2}{\left(\frac{q^2}{g}\right)}^{1/3}$

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

$\frac{3}{2}\times 0.498m$

= 0.75 m

$(\Delta Z{)}_c=E-E_{min}$

= 1.062-0.75

= 0.312 m

= 312 mm