Marine Outfalls 32.4 Hydraulic Analysis and Design 723
Part C | 32.4
is the length of the diffuser [m], n is the cost per outlet
port [$], and n ports is the number of outlet ports.
The basic premise used in Wilkinson [32.23] is that
the profile of the water depths as a function of distance
offshore (i. e., the length of the marine outfall, L p ) can
be expressed as the power curve, L p D rz
s , where r and
s are constants that express the least-squares, best-fit
shape of the across shelf bathymetry that may be obtained from navigational charts and z is the water depth.
Expressions for the length of the diffuser and the
number of outlet ports can be obtained from Table 32.2
and the total cost can then be rewritten as
T c D l.rz
s
/Cm
 SQ
2f ent U
z
1
Ã
Cn
 SQ
3:14f
2
ent U
z
2
Ã
;
(32.2)
where S is the dilution required to comply with licence
conditions or environmental guidelines.
To minimize the total cost, the above expression
is differentiated with respect to the water depth (z),
equated to zero and solved. The result gives the depth
at which the minimum cost for the marine outfall is
achieved. Substituting this value for depth into the
equations in Table 32.2, gives the length of the diffuser
and the number of outlet ports that comprise the marine
outfall.
Actual costs do not need to be known. If the relative costs among l, m, and n are known, then the total
cost of the marine outfall can be expressed in terms of
a normalized cost, T c =l. Again, it is stressed that this
analysis is preliminary and is only intended as a starting point for outfall design.
32.4 Hydraulic Analysis and Design
It is often necessary to define the physical extent of
a brine or wastewater outfall system for project planning and design purposes. While the ambient sea in
the vicinity of an outfall structure typically defines the
downstream boundary of an outfall system, defining the
upstream boundary may not necessarily be as straightforward. For the purposes of this chapter, the upstream
boundary is assumed to be a free surface which exists
somewhere upstream of the outfall conduit entrance.
Typical locations for this boundary could be the effluent
level in outfall shafts, deaeration chambers, sedimentation basins, or pumping wet wells. For configurations
without any free surfaces between the treatment process and outfall conduit, the upstream boundary may
be taken at some hydraulically arbitrary point. Regardless of its physical location, this boundary represents
a key design interface that must be properly integrated
with the treatment plant as a whole. Determining the
piezometric head at the upstream boundary of an outfall
system is therefore a critical hydraulic design objective.
32.4.1 Governing Hydraulics
Consider the gravity-driven outfall system shown in
Fig. 32.5 which includes an upstream shaft to capture plant effluents, as well as rosette style outfall
structures installed on the seabed. (A rosette structure
typically has multiple nozzles that are arranged around
its perimeter.) The piezometric head at the outfall shaft,
defined by point 0 on the fluid surface, can be obtained
by applying the energy equation between this point and
point 1 which is located precisely at the tip of the nozzle. It does not matter which outfall structure or nozzle
is used to define point 1 because this multiple riser configuration is an example of parallel flow. For parallel
flow, the total head loss must be equal through each parallel flow path.
The energy equation applied between (0) and (1)
is written in terms of total head (i. e., energy per unit
weight of effluent),
V
2
0
2g
C
p 0
e g
C z 0 D
V
2
1
2g
C
p 1
e g
C z 1 C
X
H L.0!1/ ;
(32.3)
where V is the velocity [m=s], p is the pressure [Pa], z
is the elevation above an arbitrary datum [m], z SL is the
elevation of sea level above datum [m],
P H L.0!1/
is the total head loss between locations (0) and (1) [m],
e is the density of effluent [kg=m
3 ], a is the density of
ambient seawater [kg=m
3 ].
Working with gauge pressures and assuming negligible effluent velocity in the outfall shaft, the first two
terms on the left-hand side of (32.3) are reduced to
zero. Using the assumption that the pressure at (32.1)
is hydrostatic based on the density of seawater, or p 1 D
.z SL z 1 / / a g, this relationship is substituted into (32.3)
to yield an expression for effluent level in the outfall
shaft, z 0 .
z 0 D
 V
2
1
2g
Ã
C
Ä a
e
.z SL z 1 / C z 1
C
X
H L.0!1/
(32.4)
Equation (32.4) demonstrates that the effluent level in
the outfall shaft is a combination of (i) the head required
to drive effluent out of the nozzle at the specified velocity, V 1 , (ii) elevation to the center of the exit port (z 1 /
Part C | 32.4
is the length of the diffuser [m], n is the cost per outlet
port [$], and n ports is the number of outlet ports.
The basic premise used in Wilkinson [32.23] is that
the profile of the water depths as a function of distance
offshore (i. e., the length of the marine outfall, L p ) can
be expressed as the power curve, L p D rz
s , where r and
s are constants that express the least-squares, best-fit
shape of the across shelf bathymetry that may be obtained from navigational charts and z is the water depth.
Expressions for the length of the diffuser and the
number of outlet ports can be obtained from Table 32.2
and the total cost can then be rewritten as
T c D l.rz
s
/Cm
 SQ
2f ent U
z
1
Ã
Cn
 SQ
3:14f
2
ent U
z
2
Ã
;
(32.2)
where S is the dilution required to comply with licence
conditions or environmental guidelines.
To minimize the total cost, the above expression
is differentiated with respect to the water depth (z),
equated to zero and solved. The result gives the depth
at which the minimum cost for the marine outfall is
achieved. Substituting this value for depth into the
equations in Table 32.2, gives the length of the diffuser
and the number of outlet ports that comprise the marine
outfall.
Actual costs do not need to be known. If the relative costs among l, m, and n are known, then the total
cost of the marine outfall can be expressed in terms of
a normalized cost, T c =l. Again, it is stressed that this
analysis is preliminary and is only intended as a starting point for outfall design.
32.4 Hydraulic Analysis and Design
It is often necessary to define the physical extent of
a brine or wastewater outfall system for project planning and design purposes. While the ambient sea in
the vicinity of an outfall structure typically defines the
downstream boundary of an outfall system, defining the
upstream boundary may not necessarily be as straightforward. For the purposes of this chapter, the upstream
boundary is assumed to be a free surface which exists
somewhere upstream of the outfall conduit entrance.
Typical locations for this boundary could be the effluent
level in outfall shafts, deaeration chambers, sedimentation basins, or pumping wet wells. For configurations
without any free surfaces between the treatment process and outfall conduit, the upstream boundary may
be taken at some hydraulically arbitrary point. Regardless of its physical location, this boundary represents
a key design interface that must be properly integrated
with the treatment plant as a whole. Determining the
piezometric head at the upstream boundary of an outfall
system is therefore a critical hydraulic design objective.
32.4.1 Governing Hydraulics
Consider the gravity-driven outfall system shown in
Fig. 32.5 which includes an upstream shaft to capture plant effluents, as well as rosette style outfall
structures installed on the seabed. (A rosette structure
typically has multiple nozzles that are arranged around
its perimeter.) The piezometric head at the outfall shaft,
defined by point 0 on the fluid surface, can be obtained
by applying the energy equation between this point and
point 1 which is located precisely at the tip of the nozzle. It does not matter which outfall structure or nozzle
is used to define point 1 because this multiple riser configuration is an example of parallel flow. For parallel
flow, the total head loss must be equal through each parallel flow path.
The energy equation applied between (0) and (1)
is written in terms of total head (i. e., energy per unit
weight of effluent),
V
2
0
2g
C
p 0
e g
C z 0 D
V
2
1
2g
C
p 1
e g
C z 1 C
X
H L.0!1/ ;
(32.3)
where V is the velocity [m=s], p is the pressure [Pa], z
is the elevation above an arbitrary datum [m], z SL is the
elevation of sea level above datum [m],
P H L.0!1/
is the total head loss between locations (0) and (1) [m],
e is the density of effluent [kg=m
3 ], a is the density of
ambient seawater [kg=m
3 ].
Working with gauge pressures and assuming negligible effluent velocity in the outfall shaft, the first two
terms on the left-hand side of (32.3) are reduced to
zero. Using the assumption that the pressure at (32.1)
is hydrostatic based on the density of seawater, or p 1 D
.z SL z 1 / / a g, this relationship is substituted into (32.3)
to yield an expression for effluent level in the outfall
shaft, z 0 .
z 0 D
 V
2
1
2g
Ã
C
Ä a
e
.z SL z 1 / C z 1
C
X
H L.0!1/
(32.4)
Equation (32.4) demonstrates that the effluent level in
the outfall shaft is a combination of (i) the head required
to drive effluent out of the nozzle at the specified velocity, V 1 , (ii) elevation to the center of the exit port (z 1 /