Question

A rectangular channel 6.0 m wide carries a discharge of 16.0$m^3/s$ under uniform flow condition with normal depth of 1.60 m. Manning's 'n' is 0.015.

A hump is to be provided on the channel bed. The maximum height of the hump without affecting the upstream flow conditions is

• A. 0.40 m
• B. 0.20 m
• C. 0.50 m
• D. 0.30 m

Answer 1

The correct option is A 0.40 m

When a hump is introduced on the channel bed the depth of flow at this location will reduce. If $\Delta z$ is the maximum height of hump so that the depth of flow remains same, then

$y+\frac{Q^2}{2g{A}^2}=\Delta Z+E_{min}$

$\Rightarrow 1.6+\frac{(16{)}^2}{2\times 9.81\times (9.6{)}^2}=\Delta Z+\frac{3}{2}{y}_c$

$\Rightarrow 1.74=\Delta Z+\frac{3}{2}\times {\left[\frac{(16/6{)}^2}{9.81}\right]}^{1/3}$

$\Rightarrow \Delta Z=1.74-1.35$

$\Rightarrow \Delta Z=0.39=0.4m$