Stefan Wirtz Vom Fachbereich VI (Geographie/Geowissenschaften ...

Experimentelle Rinnenerosionsforschung vs. Modellkonzepte – Quantifizierung der hydraulischen und erosiven Wirksamkeit von Rinnen
variability in sediment concentration, transport and detachment rates. But the spatial and
temporal distribution of the different processes is apparently highly random.
Table 5 Equations for calculating shear stress.
Eq.
Equation
10
τ = γ
y
b
y
(
y
a
s b 2
eff
p
i
C
it
)
τ = shear stress [Pa], γ = weight density of water (force/volume) [Pa], y = flow depth assuming
laminar flow [m], b = time weighting factor in finite difference equation for continuity, s = sine
of slope angle, y b /y p = the ratio of the flow depth on a smooth surface to that in the ponds from
depressions and “dams” [m m -1 ], a = a coefficient to be estimated i eff = effective rainfall
intensity [m s -1 ]
C
it
y
p
= exp [ 0.21 ( 1)]
y
Foster (1982)
11 = a (ρ ρ) g D
12
τ
s
b
1.18
ρ S = specific weight of the sediment [kg m -3 ], ρ = specific weight of the water [kg m -3 ] D = the
particle size [m], a = an empirical factor between 0.039 and 0.09
Shields (1936), Miller et al. (1977), Parker et al. (1982), Diplas (1987), Parker (1990), Komar
(1987 a,b), Andrews (1983), Ashworth and Ferguson (1989 a,b), Komar and Carling (1991)
τ = (σ
g)
2
3
( 3
υ)
1
3
*sin
2
3
α
q
1
3
σ = fluid density [kg m -3 ], g = gravitation [9.81 m s -2 ], υ = kinematic viscosity [m 2 s -1 ]
α = slope angle, q = runoff discharge rate per unit of width [kg m -1 s -1 ]
Chisci et al. (1985)
13 = σ g R* tan(γ)
τ r
τ r = runoff shear stress [Pa], σ = fluid density [kg m -3 ], g = acceleration of gravity [9.81 m s -2 ], R
=hydraulic radius [m], γ = slope angle [°]
Torri et al. (1987)
γ
τ =
h
L
14 L
R
15
γ = unit density of water [kg m -3 ], h L = head loss due to friction [m 2 s -2 ], R = hydraulic radius
[m], L = channel length [m]
Ghebreiyessus et al. (1994)
τ
s
= ρ
w
g S R
f
f
s
tot
ρ w = water density [kg m -3 ], g = gravitation factor [9.81 m s -2 ], S = slope, R = hydraulic radius
[m], f s and f tot = Darcy-Weisbach friction factors for the bare soil and composite surface,
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