Environmental Engineering Reference
In-Depth Information
required discharge rate under the available head differ-
ence. The port area,
A
p
, is given by
5 3
/
SQ
u L
y
L
0
2
=
C
BDNF
a
b
b
5 3
/
(2.87)
(0.11)(551)
S
30
551
π
π
=
0.29
A
=
D
2
=
4
(0.777)
2
=
0.474
m
2
p
p
2
4
the effluent velocity,
u
e
, is given by
which yields
S
= 26. This dilution exceeds the target
minimum dilution of
S
= 20.
Since the diffuser depth,
y
, is 30 m, the minimum port
spacing,
s
p
, for the plumes not to merge can be estimated
as (see Table 9.5)
Q
A
2.87
0.474
0
u
=
=
=
6.05
m/s
e
p
and the port Froude number,
F
p
, is given by Equation
(9.52) as
s
=
0 5
.
y
=
0 5 0
. (
3
)
=
15
m
p
Using this port spacing, the required diffuser length,
L
,
is given by
u
g D
6.05
(0.256)(0.777)
e
F
=
=
=
13.6
p
′
p
L N
=
(
−
1
)
s
=
(
2 1
−
)
15
=
15
m
p
p
Since
F
p
>> 1, saltwater intrusion into the diffuser is not
expected to be a problem. Also, since the minimum port
diameter recommended for discharging secondary-
treated effluent is 65 mm, clogging of the port is not
expected to be a problem.
In summary, the diffuser should be 15 m long, less
than 3.48 m in diameter, and have two ports spaced
15 m apart. The first port along the diffuser should have
a diameter of 0.777 m.
For a critical velocity,
V
c
, of 60 cm/s, the maximum
allowable diameter,
D
d
, of the diffuser is given by
π
4
Q
V
5.73
0.60
2
D
=
=
d
c
which yields
D
d
= 3 48
.
m
9.2.2 Far-Field Mixing
Therefore, any diffuser with diameter less than or equal
to 3.48 m will be sufficient to maintain a self-cleansing
velocity in the diffuser.
At the most upstream port in the diffuser, the head
difference, Δ
h
, across the port is given by
Far-field mixing occurs after initial plume dilution (near-
field mixing). Far-field mixing is dominated by spatial
and temporal variations in ocean currents, and far-field
models are generally applicable when the momentum
and buoyancy fluxes of the effluent plume are over-
whelmed by ocean currents. The transition from near
field to far field is illustrated in Figure 9.12, where the
concentrated boil is caused by the surfacing plume, and
advection of the plume downstream is indicative of far-
field transport.
The dispersion coefficient in the ocean increases with
the size of the contaminant plume, a phenomenon that
is observed in practically all tracer experiments in the
ocean, and is attributed to the fact that as a tracer cloud
grows the cloud experiences a wider range of velocities,
which leads to increased growth rates and larger diffu-
sion coefficients. In a landmark set of experiments,
Okubo (1971) analyzed the results of several field-scale
dye experiments and derived an empirical expression
for the oceanic diffusion coefficients as a function of the
size of the tracer cloud. Within observed tracer clouds,
the area enclosed by each concentration contour was
used to define a circle of radius
r
e
enclosing the same
area as the irregular concentration contour, and then
∆
h
=
32 m 3 m 2 m
−
0
=
Using ports with rounded entrances cast directly into
the wall of the diffuser, Equation (9.50) gives the coef-
ficient of discharge,
C
D
, as
2
2
V
g h
=
0.60
2 9.81 2
=
d
C
=
0.975 1
−
0.975 1
−
0.966
D
2
∆
×
×
The port discharge is then given by Equation (9.49) as
Q C A
=
2
g h
∆
0
D p
π
D
p
2
2.87
=
0.966
(2)(9.81)(2)
4
which yields
D
p
= 0.777 m. Therefore, a port diameter
of 0.777 m is required to discharge the effluent at the
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