Stable Channel Dimensions
SAM may be used to calculate stable channel dimensions that will pass a
prescribed sediment load without deposition or erosion. This analytical approach
(Copeland, 1994) determines dependent design variables of width, slope, and
depth from the independent variables of discharge, sediment inflow, and bed
material composition. It involves the solution of flow resistance and sediment
transport equations, leaving one dependent variable optional. Minimum stream
power is used as a third equation for an optional unique solution. This method is
based on a typical trapezoidal cross section and assumes steady uniform flow.
The method is especially applicable to small streams because it accounts for
transporting the bed material sediment discharge in the water above the bed, not
the banks, and because it separates total hydraulic roughness into bed and bank
components.
Basic Equations for Sand-bed Streams
If the sand-bed option is selected, SAM uses the sediment transport and resis-
tance equations developed by Brownlie (1981). There are separate resistance
equations for upper and lower regime flow. The equations are dimensionless and
can be used with any consistent set of units.
Upper regime:
0.6248
-0.2877
σ 0.0813
Rb = 0.2836 d 50 q*
S
Equation 2-45
Lower regime:
0.6539
-0.2542
σ 0.1050
Rb = 0.3742 d 50 q*
S
Equation 2-46
VD
q* =
g d 30
5
where:
Rb = hydraulic radius associated with the bed
d50 = median grain size
S = slope
σ = geometric bed material gradation coefficient
35
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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