Correct Answer : Side Slope = 1.5: 1, Depth = 3.77 m
Explanation : Let us assume side slope as 1.5 : 1 (1.5H : 1V), the rugosity constant as 0.015.
Now let us design a triangular section.
A = y² (θ + cotθ), P = 2y(θ + cotθ), and R = A/P = y/2
Tanθ = (1/1.5) and cotθ = 1.5 and θ = 0.59
A = y² (0.59 + 1.5) = y² (2.09)
P = 2 y (0.59 + 1.5) = y (4.18)
R = 0.5y
Now Manning’s equation gives
Q = 1/n x A x Râ…” x S½
20 = (1/0.015) x y² (2.09) x (0.5y) â…” x (1/7000)½
y= 3.02 m
Freeboard = 0.75 m
Total depth = 3.02 + 0.75 = 3.77 m and side slope = 1.5 : 1
