Question

A hydraulically efficient trapezoidal channel section has side slopes of 2V : 1H. The ratio of $\frac{B}{y_n}$ for the channel shown below is .

• A. 1.236

Answer 1

The correct option is A 1.236

For hydraulically efficient channel.
Half of top width = Length of any of the sloping side
$\Rightarrow \frac{B+2m{y}_n}{2}=y_n\sqrt{1+m^2}$
$m=\cot \theta =\frac{1}{2}$

$\therefore \frac{B}{2}+\frac{y_n}{2}=\sqrt{{\left(\frac{y_n}{2}\right)}^2+y_n^2}=\frac{\sqrt{5}}{2}{y}_n$
$\Rightarrow B=1.236y_n$
$\Rightarrow \frac{B}{y_n}=1.236$