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GATE 2021 AG – Question 57

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

An economical trapezoidal channel has side slope1H:1V, full depth .40 m, slope1:2500,Manning n=.01. Find discharge in m³/s, to two decimals.

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Correct answer: .18 to .22

Explanation

For an economical trapezoid,$b=2y(\sqrt{1+z^2}-z)$ and R=y/2=.20 m. With z=1,y=.4,b=.331371 m and area=y(b+zy)=.292548 m². Manning gives $Q=100(.292548)(.2)^{2/3}(.0004)^{1/2}=\mathbf{.20}$ m³/s after rounding.

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