Question

A 3 m wide rectangular channel carries a flow of $6m^3/s$. The depth of flow at a section P is 0.5 m. A flat-topped hump is to be placed at the downstream of the section P. Assume negligible energy loss between section P and hump, and consider g as $9.81m/s^2$. The maximum height of the hump (expressed in m) which will not change the depth of flow at section P is

• A. 0.20 m
• B. 0.40 m
• C. 0.23 m
• D. 0.30 m

Answer 1

The correct option is A 0.20 m

The maximum hump $\left(\Delta Z\right)$ that can be provided is given by
$y+\frac{Q^2}{2g{A}^2}=\Delta Z_{hump}+\frac{3}{2}{y}_c$
Here, $A=3\times 0.5=1.5m^2$
$y_c={\left(\frac{Q^2}{g{B}^2}\right)}^{1/3}={\left(\frac{6^2}{9.81\times 3^2}\right)}^{1/3}$
$=0.7415m$
$\Rightarrow 0.5+\frac{6^2}{2\times 9.81\times {1.5}^2}=\Delta Z_{hump}+\frac{3}{2}\times 0.7415$
$\Rightarrow \Delta Z_{hump}=0.20m$