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GATE 2024 AG – Question 55

Soil and Water Conservation Engineering · Fluid Mechanics · 2 marks · Numerical answer

A rectangular channel carries2 m³/s at 1 m/s. Depth is half the width. Manning n=.02. Find bed slope in percent, to two decimals.

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Correct answer: 0.09 to 0.11

Explanation

Flow area is $A=Q/v=2$ m². With b=2y,$2y^2=2$,so y=1 m and b=2 m. Wetted perimeter is 4 m, giving hydraulic radius.5 m. Manning velocity gives $S=[vn/R^{2/3}]^2=[.02/.5^{2/3}]^2=.00100794$. Multiply by 100 to obtain **0.10%**.

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