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GATE 2023 ES – Question 31

Water Resources and Environmental Hydraulics · Environmental Hydraulics · 1 mark · Numerical answer

A 2 m wide rectangular channel carries10 m³/s. Find critical depth in m, to two decimals, using g=9.81 m/s².

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Correct answer: 1.35 to 1.40

Explanation

Discharge per width is $q=10/2=5$ m²/s. Critical rectangular flow has $y_c=(q^2/g)^{1/3}=(25/9.81)^{1/3}=1.36594$ m. Rounded, the answer is **1.37 m**. Width enters through unit discharge, not total discharge directly.

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