Question

A partially open sluice gate discharges water into a rectangular channel. The tailwater depth in the channel is 3 m and Froude number is $\frac{1}{2\sqrt{2}}$. If a free hydraulic jump is to be formed at downstream of the sluice gate after the vena contra of the jet coming out from the sluice gate, the sluice gate opening should be (coefficient of contraction $C_c=0.9$)

• A. 0.4 m
• B. 0.9 m
• C. 0.3 m
• D. 0.69 m

Answer 1

The correct option is D 0.69 m

For hydraulic jump,

$\frac{y_1}{y_2}=\frac{1}{2}[-1+\sqrt{1+8F_2^2}]$

Given, $y_2=3m;$

$F_2=\frac{1}{2\sqrt{2}}$

$\therefore y_1=\frac{3}{2}[-1+\sqrt{1+8\times \frac{1}{4\times 2}}]$

$\Rightarrow y_1=0.62m$

Sluice gate opening

$=\frac{Y_1}{C_c}=\frac{0.62}{0.9}=0.69m$