Environmental Engineering Reference
In-Depth Information
water depth at the outlet. This is a routine backwater
computation (e.g., Chin, 2013) that is done by solving
the the following continuity equation
in
ow section
1
out
ow section
2
c
d y z
dx
(
+
)
=
aWy
b
−
Q
(8.14)
ow
0.600 m
0.3 m
3
/s
S
0
= 0.1%
where
W
is the width of the wetland (L),
z
is the eleva-
tion of the bottom of the wetland
(
L),
x
is the coordinate
in the flow direction (L), and
Q
is the average flow
through the wetland (L3T−1).
3
T
−1
). The boundary condition of
Equation (8.14) is
elevation = 6.084 m
100 m
Figure 8.12.
Flow through a wetland.
a
= ×
1 10
7
m d
−
1
−
1
=
115 7
.
m s
−
1
−
1
y L
( ) =
y
o
(8.15)
b
= 3 .
where
L
is the length of the wetland (L), and
y
o
is the
depth of flow at the outlet (L). After Equations (8.14)
and (8.15) are used to calculate the depth of flow at the
inlet,
y
(0), it is necessary to ensure that the flow contain-
ment structures are of sufficient height to constrain the
flow within the wetland. This is of particular concern
during high flows.
c
= 1 .
Substituting these parameters and the other given data
into Equation (8.16) gives
3 0
.
1 0
.
0 600
2
.
+
y
(
y
+
6 184
.
)
−
0 600 6 084
100
( .
+
.
)
1
1
(
115 7 30
. )(
)
EXAMPLE 8.1
=
0 30
.
A constructed wetland containing dense vegetation is
30 m wide, 100 m long, and has a design flow of 0.30 m
3
/s.
The longitudinal slope of the wetland is 0.1%, and the
ground elevation at the exit is 6.084 m. The exit struc-
ture is a weir, which causes a depth of 0.600 m at the
outflow section under design conditions. Estimate the
water-surface elevation at the inflow section.
which yields
y
1
= 0.546 m. Hence, the stage at the inflow
section is 6.184 m + 0.546 m = 6.730 m. This result is
based on the assumption that Equation (8.10) ade-
quately describes the flow.
The flow could alternatively be described by the com-
bination of Equations (8.7) and (8.8), which combine to
yield
Solution
1
=
v
y S
7 6
/
1 2
/
(8.17)
. m /s
,
S
0
= 0.1% = 0.001,
z
2
= 6.084 m, and
y
2
= 0.600 m. These
conditions are illustrated in Figure 8.12.
The ground elevation at the inflow section,
z
1
, is
given by
z
From the given data:
W
= 30 m,
L
= 100 m,
Q
= 0 30
3
α
where
α=
s m
for very dense vegetation and
y
< 0.3 m, or
α=
6 4
.
⋅
1 6
/
.
/
1 6
s m
for moderately dense vegeta-
tion with
y
≥ 0.3 m. Since
y
2
= 0.6 m, it is appropriate
the estimate
α=
1 6
⋅
.
/
1 6
s m
. Comparing Equations (8.10)
and (8.17) shows that the previous formulation can also
be used here, provided that
1 6
⋅
=
z
+
S L
=
6 084
.
+
( .
0 001 100
)(
)
=
6 184
.
m
1
2
0
The flow depth,
y
1
, at the inflow section can be
approximated by using a finite-difference approxima-
tion to Equation (8.14), which can be put in the form
1
1
1 6
a
=
=
=
0 625
.
α
.
b
c
aW
y
+
y
(
y
+
z
)
−
(
y
+
z
)
2
1
1
1
2
2
(8.16)
=
Q
7
6
13
6
2
L
b
− = → =
1
b
where
z
1
is the bottom elevation at the inflow section.
Using the guidelines in Equations (8.11-8.13) to estimate
the parameters
a
,
b
, and
c
for dense vegetation gives
c
=
1
2
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