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GATE 2022 AG – Question 29

Soil and Water Conservation Engineering · Fluid Mechanics · 1 mark · Numerical answer

A wide rectangular earth channel carries 20 m³/s per metre width. Find critical depth in m, to two decimals. Use g=9.81 m/s².

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Correct answer: 3.42 to 3.46

Explanation

At critical flow in a rectangular channel, $Fr^2=q^2/(gy_c^3)=1$. Thus $y_c=(20^2/9.81)^{1/3}=3.44189$ m, giving **3.44 m**. Because discharge is already per unit width, no further division by channel width is needed.

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