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GATE 2017 CE (CE1) – Question 58

Hydraulics · Channel hydraulics: specific energy, critical flow, uniform flow, hydraulic jump · 2 marks · Numerical answer

A sluice gate in a horizontal channel of unit width has upstream and downstream depths of 1.0 m and 0.2 m. Assume a smooth transition with no energy loss and g = 10 m/s². Find discharge in m³/s, to two decimal places.

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Correct answer: 0.80 to 0.83

Explanation

For unit width, velocities are $q/y_1$ and $q/y_2$. Bernoulli’s equation gives $y_1+q^2/(2gy_1^2)=y_2+q^2/(2gy_2^2)$. With $y_1=1$, $y_2=0.2$, rearrange to $q^2=2g(y_1-y_2)/(1/y_2^2-1/y_1^2)=16/24=2/3$. Thus discharge is $q=0.81650$ m³/s, or 0.82 m³/s.

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