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GATE 2022 ES – Question 60

Water Resources and Environmental Hydraulics · Environmental Hydraulics · 2 marks · Numerical answer

A hydraulically efficient rectangular channel has Manning n=1/80,slope .01 and discharge64 m³/s. Find depth in m, to two decimals.

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Correct answer: 1.95 to 2.05

Explanation

The most efficient rectangle has b=2y, area 2y² and hydraulic radius y/2. Manning gives $64=80(2y^2)(y/2)^{2/3}(.1)$. At y=2 m, the right side is 80×8×1×.1=64. Therefore **2.00 m**,with width4 m.

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