Question

Design a lined canal carrying a discharge of 20 cumecs. The slope is 1 in 7000. Assume suitable values for side slopes and lining.

(a) Side Slope = 1.2: 1, Depth = 4.4 m

(b) Side Slope = 1.4: 1, Depth = 4.1 m

(c) Side Slope = 1.5: 1, Depth = 3.77 m

(d) Side Slope = 1.3: 1, Depth = 4.5 m

This question was addressed to me during an internship interview.

My question is from Lining of Canal topic in chapter Lining of Irrigation Canals and its Economics of Irrigation Engineering

Answer 1

Right answer is (c) Side Slope = 1.5: 1, Depth = 3.77 m

The 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 = y^2 (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 = y^2 (0.59 + 1.5) = y^2 (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 R^2/3 x S^1/2

20 = (1/0.015) x y^2 (2.09) x (0.5y) ^2/3 x (1/7000)^1/2

y= 3.02 m

Freeboard = 0.75 m

Total depth = 3.02 + 0.75 = 3.77 m and side slope = 1.5 : 1