Environmental Engineering Reference
In-Depth Information
measured, and, to some extent, by the port configura-
tion. The additional dilution that occurs in the near field
when the buoyant plume impinges on the water surface
is often not taken into account. According to lee and
Neville-Jones (1987), Equation (9.15) should be used
when
y
/
L
b
≤ 5, and Equation (9.16) used when
y
/
L
b
> 5.
It is relevant to note that neither Equation (9.15) nor
(9.16) includes the momentum length scale,
L
M
, because
in both cases, the initial discharge momentum does not
influence the plume dilution significantly. Equations
(9.15) and (9.16) include the blocking effect of the
established wastefield at the water surface and can also
be used to describe the dilution of vertical discharges
since, for buoyancy-dominated discharges, vertical and
horizontal discharges behave similarly. Rearranging
Equations (9.15) and (9.16) reveals that the ambient
current speed,
u
a
, is absent from the BDNF equation,
and the effluent buoyancy,
Q
0
g
′, is absent from the
BDFF equation. In cases where the ambient current is
equal to zero (i.e., a stagnant environment), the
minimum dilution given by Equation (9.15) is more con-
veniently described by
Solution
Calculate the basic characteristics of the effluent plume
∆ρ
ρ
1.024 0.998
0.998
−
Effective gravity
,
g
′ =
g
=
(9.81)
=
0.256
m/s
2
5 73
5
.
Port discharge
,
Q
0
=
=
1 15
.
m /s
3
π
4
(1.22)
2
2
Port area
,
A
=
=
1.169
m
p
Q
A
1.15
1.169
0
Port velocity
,
u
=
=
=
0.984
m/s
e
p
4
2
Momentum flux
,
M Q u
e
=
=
1 15
.
( .
0
984
)
=
1 13 m /s
.
0
0
4
2
Buoyancy flux
,
B Q g
0
=
′ =
1 15
.
( .
0
256
)
=
0 294
.
m /s
0
The length scales are derived from these plume charac-
teristics as follows:
Q
M
1.15
(1.13)
0
1 2
L
=
=
=
1.08
m
Q
/
1 2
/
1 3
/
B
Q
S C
=
y
5 3
/
(9.17)
BDNF
3 4
1 2
/
3 4
/
M
B
(1.13)
(0.294)
0
L
=
=
=
2.02
m
M
/
1 2
/
In stagnant (i.e., nonflowing) ocean environments, the
thickness,
h
n
, of the spreading layer and the distance,
x
n
,
of the near-field boundary from the discharge port, as
shown in Figure 9.5, are both scaled by the discharge
depth and can be approximated by (Tian, 2004a)
B
u
0.294
(0.11)
0
3
L
=
=
=
221
m
b
3
a
Based on these length scales, it is to be expected that
port geometry will only be important within 1.08 m of
the discharge port, buoyancy will be the dominant factor
in plume motion after 2.02 m, and the ambient current
will not dominate the plume motion before the plume
surfaces (
y
<<
L
b
). Using Equation (9.15) and a mid-
range value of
C
BDNF
= 0.29 to calculate the dilution
yields
h
y
x
y
n
n
=
0.11 0.16
−
and
=
2.8
(9.18)
which indicate that the wastefield thickness is 11-16%
of the discharge depth, and the boundary of the near
field, is approximately 2.8 discharge depths from the
discharge port.
5 3
/
S
(1.15)
0.11(221)
28.2
221
=
0 29
.
(9.19)
2
EXAMPLE 9.1
which gives
S
= 44. Hence, the near-field dilution at the
Central District outfall is estimated as 44.
The Central District outfall in Miami (Florida) dis-
charges treated domestic wastewater at a depth of
28.2 m from a diffuser containing five 1.22-m-diameter
ports spaced 9.8 m apart. The average effluent flow rate
is 5.73 m
3
is the 10-percentile ambient current is 11 cm/s,
and the density of the ambient seawater is 1.024 g/cm
3
.
The density of the effluent can be assumed to be 0.998
g/cm
3
. Determine the length scales of the effluent plumes
and calculate the near-field dilution. Neglect merging of
adjacent plumes.
The case of a plume discharged into a density-stratified
ocean with an ambient current is illustrated in Figure
9.7. In this case, the effluent plume entrains denser
ocean water at the lower levels of the ocean and rises
only until the density of the plume is equal to the density
of the surrounding ocean water. Since this could occur
before the plume reaches the ocean surface, there is no
guarantee that the plume will reach the ocean surface,
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