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Find the slope of the free water surface of a rectangular stream 15 m wide and 3 m deep. The slope of the stream bed is
1 in 5000. Total discharge is 29 m3/s. Assume the slope of the energy line = 1 in 21,700 and that the depth is increasing
in the direction of the flow.
ANS 1 in 6400?
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Find the slope of the free water surface of a rectangular stream 15 m ...
Given:
Width of the rectangular stream (b) = 15 m
Depth of the rectangular stream (d) = 3 m
Slope of the stream bed (Sb) = 1 in 5000
Total discharge (Q) = 29 m3/s
Slope of the energy line (Se) = 1 in 21,700
Direction of flow: Increasing depth

To Find:
Slope of the free water surface

Solution:

Step 1: Determine the slope of the water surface (Sw)

The slope of the water surface can be determined using the energy equation:

Se = Sw + Sf + Sb

Where:
Se = Slope of the energy line
Sw = Slope of the water surface
Sf = Slope of the friction line
Sb = Slope of the stream bed

Since the depth is increasing in the direction of flow, the slope of the friction line can be assumed to be zero.

Therefore, the equation becomes:

Se = Sw + Sb

Step 2: Calculate the slope of the water surface (Sw)

Sw = Se - Sb

Given:
Se = 1 in 21,700
Sb = 1 in 5000

Sw = (1/21,700) - (1/5000)

Sw = 0.0000461 - 0.0002

Sw = -0.0001539

Step 3: Convert the slope of the water surface to a ratio

The slope can be converted to a ratio by taking the reciprocal of the absolute value of the slope.

Sw = -0.0001539

Sw = -1/6500

Therefore, the slope of the free water surface is 1 in 6500.
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Find the slope of the free water surface of a rectangular stream 15 m wide and 3 m deep. The slope of the stream bed is1 in 5000. Total discharge is 29 m3/s. Assume the slope of the energy line = 1 in 21,700 and that the depth is increasingin the direction of the flow. ANS 1 in 6400?
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