GATE 2017 CE (CE1) – Question 41
A 1 m wide rectangular channel has bed slope 0.0016 and Manning coefficient 0.04. Its normal depth is 0.5 m. At a section with gradually varied flow the measured depth is 0.6 m. Classify its profile.
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Correct answer: (C) M1
Explanation
At normal depth, $A=0.5$ m², wetted perimeter $P=2$ m, and $R=0.25$ m. Manning’s equation gives $Q=(1/0.04)(0.5)(0.25)^{2/3}\sqrt{0.0016}=0.19843$ m³/s. Critical depth is $y_c=(Q^2/(gb^2))^{1/3}=0.159$ m, below normal depth, so the slope is mild. The measured depth exceeds both $y_n$ and $y_c$, placing the profile in zone 1: M1, option C.
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