A open channel of most economical section having form of half hexagonal shape with horizontal bottom is required to give maximum discharge of 20.2 m³/s of water. The slope of channel bottom is 1 in 2500, C=60, determine the dimensions of the cross section.

Solution :

Given :

1. Max discharge, $\quad Q=20.2 \mathrm{~m}^3/ \mathrm{~s} $

2. Bed slope, $\quad i=\frac{1}{2500}$

3. Chezy's constant, $\quad C=60 $

As the channel is the form of a half hexagon as mentioned in question.

That means the angle between the sloping side with horizontal will be $60^{\circ}$.

$$ \begin{aligned} \therefore …