Environmental Engineering Reference
In-Depth Information
this terminology is somewhat of a misnomer since the
water in the wetland is not retained but is detained.
An alternative, and in many cases more appropriate,
model of flow through natural and constructed wetlands
assumes that the drag on the stems and leaves of emer-
gent vegetation is the predominant source of hydraulic
resistance. This model was initially proposed by Nepf
(1999), and can be expressed in the form (Kadlec and
Wallace, 2009)
Wetland Hydraulics. The Manning equation is widely
used to describe the flow of water through both natural
and FWS wetlands. However, from a fundamental view-
point, the Manning equation is usually not strictly appli-
cable to flow in wetlands. The reason for this is that the
Manning equation was developed to describe turbulent
flow in open channels where the predominant source of
hydraulic resistance is on the bottom of the channel. In
the case of natural and FWS wetlands, the flow is seldom
turbulent and the hydraulic resistance is primarily
due to drag on stems of emergent vegetation. These
inconsistencies with the Manning equation are some-
times incorporated by artificially using a roughness
coefficient that varies with the depth of flow. The form
of the Manning equation that is most frequently used is
given by
K
n
1
v
=
S
(8.9)
s
where v is the flow velocity (m/s), K 1 is a constant called
the conveyance coefficient for vegetation with a given
stem diameter (1/m·s), n s is the number of stems per unit
area (no. of stems/m 2 ), and S is the water surface slope
(dimensionless). Equation (8.9) has been validated in
the laboratory and to a limited extent in the field (Nepf,
1999). The main functional differences between Equa-
tion (8.9) and the Manning equation is that the flow
velocity is proportional to S rather than S 1 / , and for any
given S , the flow velocity is independent of the depth of
flow. In some real wetlands, there is actually a strong
inverse relationship between flow velocity and depth, an
observation that is usually attributed to microtopo-
graphic effects.
Field evidence has indicated that the flow through
natural and FWS wetlands is not generally described by
either the Manning or Nepf equation, and some inter-
mediate empirical formulation might be more appropri-
ate. The following generic formula captures the velocity
dependence on depth of flow, y , and slope of of the
water surface, S (Kadlec and Wallace, 2009),
= 1
v
n y S
2 3
/
1 2
/
(8.7)
where v is the average flow velocity (m/s), n is the
Manning roughness coefficient (dimensionless), y is the
depth of flow (m), and S is the hydraulic gradient
(dimensionless). In wetland applications where varia-
tions in n are used to compensate for the fundamental
inadequacies of the Manning equation, n can be esti-
mated in terms of the depth of flow, y (m), by the
relation
α
1 2
n
=
(8.8)
v
=
ay
b
−1
S
c
(8.10)
/
y
where a is a constant for a particular wetland, v is in m/s,
y is in meters, and S is dimensionless. recommended
values for a , b , and c are as follows:
where α is called the resistance factor , which can be
estimated using the guidance given in Table 8.3
7
1
1
1 0 10
5 0 10
.
×
×
m d
(
densely vegetated
)
a =
(8.11)
7
1
1
.
m d
(
sparsely vegetated)
TABLE 8.3.  Resistance Factor in Estimating Manning's  n
(8.12)
b = 3 .
resistance Factor, α
( s ⋅
Wetland Description
1 6
/
)
c = 1 .
(8.13)
Sparse, low standing vegetation,
y > 0.4 m (1.3 ft)
0.4
These suggested parameters (by Kadlec and Wallace,
2009) incorporate the linear slope dependence of the
Nepf (1999) model and also a depth dependence of the
flow rate. In applying Equation (8.10) to constructed
wetlands, it is usually necessary to calculate the water
depth at the inlet for a given flow rate and (controlled)
Moderately dense vegetation,
y ≥ 0.3 m (1 ft)
1.6
Very dense vegetation and litter,
y < 0.3 m (1 ft)
6.4
Source of data : reed et al., 1995.
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