Ci = the panel Chezy roughness coefficient
Ai = the panel cross-sectional area
Pi = Wetted perimeter in wet panel i
The composite roughness coefficient, n , is calculated using the composite R
_
in the Manning equation.
k
2
1
∑A
1.486 R S
3
2
i
i=1
n=
Equation 2-25
Q
where:
S = energy slope
Q = total discharge
The alpha method ignores roughness on vertical walls, and renders roughness
contributions negligible when there are steep side slopes. When significant
roughness is contributed by vertical or steep side slopes, one of the other
compositing methods should be employed.
Equal Velocity Method
A more rational compositing method for cross-sections with rough vertical
walls or steep side slopes is the equal velocity method. It was proposed
independently by both Horton and Einstein (Chow, 1959) and assumes that the
velocity is equal in all panels. All hydraulic variables are calculated in the
normal fashion except the Manning roughness coefficient, which is calculated
using the following equation.
2/3
k -1
∑P n
1.5
i
i
n=
i= 1
Equation 2-26
2/3
k -1
∑ Pi
i= 1
where
n = the composite n-value for the total section
ni = n-value in wet panel i
k = number of panels
Since only wetted perimeter, and not hydraulic radius, appears in this
equation, it is always well behaved. EM 1110-2-1601 (USACE 1991, 1994)
discusses two other equal velocity methods. However, Horton's method was
22
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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