V = average velocity
D = water depth
g = acceleration of gravity
To determine if upper or lower regime flow exists for a given set of hydraulic
conditions, a grain Froude number Fg and a variable Fg′ were defined by
Brownlie. According to Brownlie, upper regime occurs if S > 0.006 or if Fg>
1.25 Fg′ , and lower regime occurs if Fg < 0.8 Fg′ . Between these limits is the
transition zone. In the analytical method, Fg = Fg′ is used to distinguish between
upper and lower regime flow. The program will inform the user which regime is
being assumed in the calculations and if the bed forms are in the transition zone.
V
Fg=
γ -γ
g d 50 s
γ
Equation 2-47
1.74
Fg′ =
0.3333
S
where:
γs = specific weight of sediment
γ = specific weight of water
The hydraulic radius of the side slope is calculated using Manning's equation:
1.5
V ns
=
Rs
Equation 2-48
1.486 S 0.5
where:
Rs = hydraulic radius associated with the side slopes, ft
V = average velocity, fps
ns = Manning's roughness coefficient for the bank
If the roughness height ks of the bank is known, then it can be used instead of
Manning's roughness coefficient to define bank roughness. The model uses
Strickler's equation to calculate the bank roughness coefficient:
36
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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