Question

A partially open sluice gate discharges water at 6 m/s with a depth of 40 cm in a rectangular horizontal channel of width 5 m. What would be the post-jump depth of flow on the downstream of the gate by taking $g$ as $10m/s^2$?

• A. 1.85 m
• B. 1.51 m
• C. 1.95 m
• D. 0.60 m

Answer 1

The correct option is D 0.60 m


$\begin{array}{cc}q& =v_1{y}_1=6\times 0.4=2.4m^2/s\\ F_1^2& =\frac{q^2}{g{y}_1^3}=\frac{{2.4}^2}{10\times {0.4}^3}=9\\ \frac{y_2}{y_1}& =\frac{1}{2}[-1+\sqrt{1+8F_1^2}]\\ & =\frac{1}{2}[-1+\sqrt{73}]=1.51m\end{array}$

The post jump depth,
$y_2=1.51\times 0.4=0.6m$