Water Surface Slopes in a Rectangular Channel

Given data:
- Width of rectangular channel (b) = 6 m
- Discharge (Q) = 36.16 m3/sec
- Bed slope (S) = 0.0061
- Mining coefficient (n) = 0.0015

To calculate the water surface slopes at sections of depth 2.5 m and 1.8 m, we need to use Manning's equation which relates the discharge, channel geometry, and roughness coefficient to the water surface slope.

Manning's equation is given as:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where,
Q = discharge
n = Manning's roughness coefficient
A = cross-sectional area of flow
R = hydraulic radius
S = bed slope

Cross-sectional area of flow can be calculated as:
A = b * y
where,
y = depth of flow

Hydraulic radius can be calculated as:
R = A / P
where,
P = wetted perimeter
P = b + 2*y

Now, we can substitute the values in Manning's equation to find the water surface slope at different depths.

Water surface slope at depth 2.5 m:
- Cross-sectional area of flow = 6 * 2.5 = 15 m2
- Wetted perimeter = 6 + 2*2.5 = 11 m
- Hydraulic radius = 15 / 11 = 1.36 m
- Using Manning's equation, we get:
36.16 = (1/0.0015) * 15 * 1.36^(2/3) * S^(1/2)
S = 0.0008
- Therefore, the water surface slope at a depth of 2.5 m is 0.0008.

Water surface slope at depth 1.8 m:
- Cross-sectional area of flow = 6 * 1.8 = 10.8 m2
- Wetted perimeter = 6 + 2*1.8 = 9.6 m
- Hydraulic radius = 10.8 / 9.6 = 1.125 m
- Using Manning's equation, we get:
36.16 = (1/0.0015) * 10.8 * 1.125^(2/3) * S^(1/2)
S = 0.0012
- Therefore, the water surface slope at a depth of 1.8 m is 0.0012.

Explanation:
The water surface slope is an important parameter in open channel flow as it determines the energy gradient and the flow velocity. In this problem, we have used Manning's equation to calculate the water surface slope at different depths in a rectangular channel. The equation takes into account the channel geometry, roughness coefficient, discharge, and bed slope to find the water surface slope. We have also used the concept of hydraulic radius and wetted perimeter to calculate the cross-sectional area of flow. The calculated water surface slopes at different depths can be used to design and analyze open channel flow systems.