Slope Conveyance Procedure

The calculation of the stage-discharge relationship should proceed as described in this section. The Water Surface
Elevation tables
represent the progression of these calculations based on the cross section shown in
Figure 7-14
. The result of this procedure is a stage-discharge curve, as shown in
Figure 7-15
. You can then use the design discharge or any other subject discharge as an argument to estimate (usually done by interpolation) an associated water surface elevation.
  1. Select a trial starting depth and apply it to a plot of the cross section.
  2. Compute the area and
    wetted perimeter weighted n-value
    (see Chapter 6) for each submerged subsection.
  3. Compute the subsection discharges with Manning’s Equation. Use the subsection values for roughness, area, wetted perimeter, and slope. (See Equation 7-1). The sum of all of the incremental discharges represents the total discharge for each assumed water surface elevation.
    Note.
     Compute the average velocity for the section by substituting the total section area and total discharge into the continuity equation.
  4. EquationObject225248
    Equation 7-4.
  5. Tabulate or plot the water surface elevation and resulting discharge (stage versus discharge).
  6. Repeat the above steps with a new channel depth, or add a depth increment to the trial depth. The choice of elevation increment is somewhat subjective. However, if the increments are less than about 0.25 ft. (0.075 m), considerable calculation is required. On the other hand, if the increments are greater than 1.5 ft. (0.5 m), the resulting stage-discharge relationship may not be detailed enough for use in design.
  7. Determine the depth for a given discharge by interpolation of the stage versus discharge table or plot.
The following x and y values apply to Figure 7‑14:
X and Y Values for Figure 7‑14
X
Y
0
79
2
75
18
72
20
65
33
65
35
70
58
75
60
79
Slope Conveyance Cross Section (click in image to see full-size image)
Figure 7-14. Slope Conveyance Cross Section
Water Surface Elevation of 66 ft.
Subsection L
Subsection C
Subsection R
Full Section
Area (ft2)
0
13.34
0
13.34
Wetted Perimeter (ft)
0
15.12
0
Hydraulic Radius (ft)
0.88
n
0.060
0.035
0.060
Q (cfs)
10.43
10.43
Velocity (fps)
0.78
0.78
Water Surface Elevation of 79 ft.
Subsection L
Subsection C
Subsection R
Full Section
Area (ft2)
92.00
226.00
153.50
471.5
Wetted Perimeter (ft)
20.75
25.67
28.01
Hydraulic Radius (ft)
4.43
8.81
5.48
n
0.060
0.035
0.060
Q (cfs)
122.98
818.33
236.34
1177.66
Velocity (fps)
1.34
3.62
1.54
2.50
Stage Discharge Curve for Slope Conveyance (click in image to see full-size image)
Figure 7-15. Stage Discharge Curve for Slope Conveyance