Question

A trapezoidal channel is to be designed to convey 50 m3 /s of water at a velocity of 2.0 m/s. The bed width to depth ratio is to be 8.0 and the side slopes are to be 1 H : 1 V. It will be lined with a material whose n = 0.02. Calculate the bed width, depth of flow and slope of the channel.

Answer 1

Answer:

Specific energy of a flowing fluid per unit weight is given by,

We know,

Q = A × V

For the Trapezoidal channel section

Let B = base width, Y = vertical depth

Side slope = 1 : m (m = horizontal and 1 = vertical)

Area of flow = A = (B + mY)Y

Here, m = 1

Given,

Depth of flow (Y) = 2 m, Discharge Q = 24 m3/s

Side slope = 1:1, Bottom width of flow (B) = 6 m

Area = (6 + 2) × 2 = 16 m2

Velocity of flow (V) = 24/16 = 1.5 m/s

Specific Energy is given by

E = 2 m + (1.5)2/(2 × 10)

E = 2 + 0.1125

E = 2.1125 m