Question

A very wide rectangular channel carries a discharge of 8 $m^3/s$ per m width. The channel has a bed slope of 0.004 and manning's roughness coefficient, n=0.015. At a certain section of the channel, the flow depth is 1 m.

What Gradually Varied Flow profile exists at this section?

• A. $S_2$
• B. $S_3$
• C. $M_3$
• D. $M_2$

Answer 1

The correct option is B $S_3$

Critical depth,

$y_c={\left(\frac{q^2}{g}\right)}^{1/3}={\left(\frac{8^2}{9.81}\right)}^{1/3}=1.868m$

From Manning's equation, we have

$q=\frac{1}{n}(y_n{)}^{5/3}{S}^{1/2}$

$\Rightarrow 8=\frac{1}{0.015}\times \left(y_n{)}^{5/3}\right(0.004{)}^{1/2}$

$\Rightarrow y_n=1.468m$

Given that

$y=1m$

$\therefore y_c>y_n>y$

$\therefore \text{The gradually varied profile will be}{S}_3$.