Question

A 4 m wide rectangular channel, having a bed slope of 0.001 carries a discharge of$16m^3/s$. Considering Manning's roughness coefficient = 0.012 and $g=10m/s^2$, the category of the channel slope is

• A. horizontal
• B. steep
• C. critical
• D. mild

Answer 1

The correct option is D mild

$Q=\frac{1}{n}A{R}^{2/3}{S}^{1/2}$

A = By

$R=\frac{By}{B+2y}$

$16=\frac{1}{0.012}\times By\times {\left(\frac{By}{B+2y}\right)}^{2/3}\times (0.001{)}^{1/2}$

$6.07=4\times \frac{y^{5/3}}{(4+2y{)}^{2/3}}$

$1.5178=\frac{y^{5/3}}{(4+2y{)}^{2/3}}$

$y=[1.5178\times (4\times 2y{)}^{2/3}{]}^{3/5}$

=3.3 m

Critical depth,
$y_c={\left(\frac{q^2}{g}\right)}^{1/3}={\left(\frac{4^2}{10}\right)}^{1/3}=1.169$

$y>y_c\Rightarrow Flowissubcritical.$

Hence channel slope is mild.