-0.6
γ -γ
Y= s
γ
and
g d 503
Rg =
ν
Basic Equations for Gravel-bed Streams
If the gravel-bed option is selected, SAM uses equations more appropriate for
coarse bed streams. Sam uses the Limerinos (1970) equation to calculate grain
roughness on the bed. The Manning equation is used to calculate the roughness
on the channel side slope. Additional roughness may be added in the manner
suggested by Cowan (1956). Sediment transport is calculated using the Meyer-
Peter and Muller (1948) equation.
The Limerinos equation accounts for the grain roughness in a uniform reach
of a gravel-bed stream that is relatively free of bed forms. The Limerinos
equation may be presented in dimensionless units as:
V
R′
= 5.66 log 3.80 b
d 84
′
U*
where:
V = average velocity
′
U * = shear velocity associated with grain roughness
′
Rb = hydraulic radius associated with grain roughness
d 84 = grain size for which 84% of the bed is finer.
Manning's roughness coefficient associated with grain roughness can be
determined from the Limerinos equation:
1
′
CME Rb 6
′
nb =
R′
g 5.66 log 3.80 b
d 84
where:
′
nb = roughness coefficient associated with bed
CME = 1.486 English units
1.0 SI units
38
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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