Question

A steep wide rectangular channel takes off from a reservoir having an elevation of 101.2 m. At the entrance, the bottom elevation of the channel is 100 m. If the slope of the channel is increased by 4%, the discharge per unit length in the channel will be

• A. choked
• B. higher than 2.24 $m^2$ by 2%
• C. 2.24 $m^2/s$
• D. higher than 2.24 $m^2$ by 4%

Answer 1

The correct option is C 2.24 $m^2/s$

It is a example of supercritical canal intake, the reservoir water surface falls to the critical depth at the head of the canal and then towards the water surface follows the $S_2$ curve. The critical depth occurring at the u/s end of the channel is the control for this flow.

And critical depth only depends upon channel geometry not the slope.


$E_c=101.2-100$
$=1.2m$

$y_c=\frac{2}{3}{E}_c=0.8m$

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

$q=2.24m^2/sec$

Note: On changing the slope discharge will not, but velocity and depth vary with slope.