σ = 0.5 d 84 + d 50
Equation 2-21
d 50
d 16
TRANSITION FUNCTION:
If the slope is greater than 0.006, flow is always UPPER REGIME.
Otherwise, the transition is correlated with the grain Froude number as follows:
V
Fg=
Equation 2-22
( ss - 1) g d 50
1.74
F g' =
Equation 2-23
1/3
S
if Fg < Fg' Lower Regime Flow
if 0.8 Fg' < Fg < 1.25 Fg' Transition Flow
if Fg > Fg' Upper Regime Flow
where
Fg = grain Froude number.
ss = specific gravity of sediment particles.
V = velocity of flow.
S = bed slope.
The transition occurs over a range of hydraulic radii and not at a point. Over
this range, then, it is a double-valued function, and the transition test will give
different regimes depending on which equation is being solved for roughness at
that iteration. That is realistic since one expects the rising side of a hydrograph
to trigger the transition at a different discharge than does the falling side. This
can cause the calculations to fail to converge in the transition zone, and the
program will notify the user. If convergence fails, inspect the maximum and
minimum values printed. Usually, the depths are the same whereas the
discharges are significantly different. This signifies that the transition has been
located from both the upper regime and the lower regime curves, and the results
are the best that can be achieved.
18
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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