Environmental Engineering Reference
In-Depth Information
- the sediment transport rate along the entire canal;
- the changes in bottom level and/or bottom width.
In order to compute the sediment transport along the entire canal, it
is necessary to consider how the incoming sediment load
c
0
adapts to the
equilibrium sediment transport of the canal reaches; this is given in terms
of the sediment concentration
c
, which follows from Gallapatti's depth-
integrated model. Galappatti (1983) has developed a depth-integrated
suspended sediment transport model based on an asymptotic solution
for the two-dimensional convection equation in the vertical plane (see
Chapter 5). SETRIC uses the diffusion model developed by Galappatti.
This depth-integrated model solves the convection-diffusion equation
with the following assumptions:
- diffusion terms other than vertical are neglected;
- concentration is expressed as the depth-averaged concentration.
As mentioned the Galappatti model has two advantages over others;
firstly, no empirical relation has been used during the derivation of the
model and secondly, all possible bed boundary conditions can be used
(Wang and Ribberink, 1986). The value of
c
follows from:
c
0
)e
−
x/L
A
c
=
c
e
−
(
c
e
−
(6.5)
f
u
v
,
w
s
,
y
L
A
=
(6.6)
u
∗
where:
c
=
actual concentration (ppm)
c
e
=
equilibrium concentration (ppm)
c
0
=
initial concentration at
x
=
0 (ppm)
x
=
distance along the canal (m)
L
A
=
adaptation length (m)
For the determination of the actual sediment concentration in the
x
-direction of the canal, the values of the variables
c
0
,
L
A
,
x
and
c
e
have to be known. The first, the initial concentration
c
0
, does not depend
on the local flow condition, but instead depends on the inflowing water
and sediment and on whether a sediment trap is located at the head of the
irrigation network. At the boundaries between canal reaches, the sediment
load passing through the downstream boundary of the upstream reach will
become
c
0
for the next canal reach.
In a gradually varied flow the values of
c
e
,
y
,
v
,
u
∗
and
f
are functions
of distance
x
and time
t
. These variables may be known in advance at
any point along the canal network if the flow equations are solved first
(using the uncoupled technique). That means that
c
e
,
y
,
v
,
u
∗
and the
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