Discharge of Water through a Channel Section

Given data:
- Chezys constant = 60
- Slope of bed = 1 in 2000
- Channel section (see figure)

We can calculate the discharge of water through the channel section using the Chezy-Manning equation:

Q = (1/n) * A * R^(2/3) * S^(1/2)

Where:
- Q = discharge of water (m^3/s)
- n = Manning's roughness coefficient (dimensionless)
- A = cross-sectional area of water (m^2)
- R = hydraulic radius (m)
- S = slope of the bed (m/m)

To use the Chezy-Manning equation, we need to determine the values of A, R, and n.

Calculating Cross-sectional Area (A)

The cross-sectional area of water can be calculated by dividing the segment into rectangles and triangles and adding up their areas. In this case, the channel segment can be divided into two rectangles and one triangle.

Area of rectangle 1 = length * width = 4 * 2 = 8 m^2
Area of rectangle 2 = length * width = 4 * 4 = 16 m^2
Area of triangle = (1/2) * base * height = (1/2) * 2 * 4 = 4 m^2

Total area of water = 8 + 16 + 4 = 28 m^2

Calculating Hydraulic Radius (R)

The hydraulic radius is the ratio of the cross-sectional area of water to its wetted perimeter. In this case, the wetted perimeter consists of the bottom and two sides of the segment.

Wetted perimeter = length + width + length = 4 + 2 + 4 = 10 m

Hydraulic radius = area of water / wetted perimeter = 28 / 10 = 2.8 m

Calculating Manning's Roughness Coefficient (n)

The Manning's roughness coefficient depends on the roughness of the channel bed and the velocity of water. For this problem, we can use a roughness coefficient of 0.03 for a concrete channel.

Calculating Discharge of Water (Q)

Substituting the values of A, R, n, and S into the Chezy-Manning equation:

Q = (1/0.03) * 28 * 2.8^(2/3) * (1/2000)^(1/2) = 0.204 m^3/s

Therefore, the discharge of water through the channel section is 0.204 m^3/s.