Question

Design a lined canal to carry a discharge of 400 cumecs and slope is 1 in 6000. Take side slopes as 1 : 1 and rugosity constant as 0.012. Assume limiting velocity as 3 m/sec.

(a) Total Depth = 6.3 m, Bed Width = 15 m

(b) Total Depth = 6.28 m, Bed Width = 14.2 m

(c) Total Depth = 6.5 m, Bed Width = 14 m

(d) Total Depth = 6.25 m, Bed Width = 14.4 m

The question was asked by my college director while I was bunking the class.

I'm obligated to ask this question of Lining of Canal topic in section Lining of Irrigation Canals and its Economics of Irrigation Engineering

Answer 1

Right choice is (d) Total Depth = 6.25 m, Bed Width = 14.4 m

To explain I would say: V = 1/n x R^2/3 x S^1/2

3 = (1/0.012) x R^2/3 x (1/6000)^1/2

R = 4.7 m

Design a trapezoidal section canal.

A = y (B + yθ + y cotθ), P = B + 2yθ + 2y cotθ

Now Tanθ = 1/1, θ = 0.785 radians, and cotθ = 1

Now A = y (B + y x 0.785 + y x 1) = y(B + 1.785y), P = B + 2y(0.785) + 2y(1) = B + 2.57y

A = Q/V = 400/3 = 133.33 sq.m

100 = y (B +1.785y), B = 100/y – 1.785y

R = A/P = 133.33/P

4.7 = 133.33/B + 2.57Y

y= 5.5 m

B = 14.4 m

Total Depth = 5.5 + 0.75 = 6.25 m

Bed Width = 14.4 m.