′
Rb = bed hydraulic radius associated with grain roughness ( ft or m)
g = acceleration of gravity (ft/s or m/s)
d 84 = grain size for which 84" of the bed is finer (ft or m)
Additional bed roughness may be added to the grain bed roughness using the
Cowan (1956) method. Roughness may be added to account for factors such as
surface irregularities, variability in channel shape, obstructions, vegetation and
meandering. Meandering is accounted for with a meandering coefficient, m. In a
straight channel the meandering coefficient is 1.0. Appropriate values for the
meandering coefficient and additions to the grain roughness n-value can be found
in Cowan (1956) and Chow (1959). Using the Cowan equation the total bed
roughness coefficient is:
nb = m (nb′ + nb )
′
′
where:
nb = total bed roughness coefficient
m = Cowan meander coefficient
nb′ = bed roughness other than grain roughness.
′
Using the Manning equation the hydraulic radius associated with the bed is
calculated
3
Vn
2
Rb =
b
12
S CME
where:
S = channel slope.
The hydraulic radius associated with the bank or side slope is
3
Vn
2
Rs =
s
2
1
S CME
where:
ns = the roughness coefficient associated with the side slope.
Values for m, nb′ , and ns must be selected by the user and provided as program
′
input.
39
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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