Environmental Engineering Reference
In-Depth Information
Z
c
x,t
c
x,
t
Figure 5.31. Schematization of
a depth-integrated model.
X
w
here:
c
mean concentration (m
3
sediment/m
3
=
water)
E
=
entrainment rate
h
=
depth of flow (m)
u
=
mean flow velocity (m/s)
For the asymptotic solution of the convection-diffusion equation the
following two assumptions are made:
UH
Lw
s
=
δ
1
H
w
s
T
=
δ
1
This implies that the time taken for a particle to settle (
t
h
/
w
s
) is much
smaller than the time it takes to be convected along a distance
L
(
T
=
L/u
).
The general solution for the sediment concentration in non-equilibrium
conditions in terms of depth-averaged variables will be:
=
γ
21
h
w
s
∂c
∂t
+
γ
22
uh
w
s
∂c
∂x
γ
11
c
e
=
γ
11
c
+
(5.125)
T
A
∂c
L
A
∂c
∂x
c
e
=
c
+
∂t
+
(5.126)
with
w
s
u
∗
h
w
s
T
A
=
exp(
f
)
(5.127)
T
A
u
∗
h
=
exp(
f
)
(5.128)
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