Marine Outfalls 32.4 Hydraulic Analysis and Design 725
Part C | 32.4
computed iteratively using the implicit Colebrook–
White formula given in (32.6), or approximated using
the explicit Swamee–Jain equation given in (32.7). The
Swamee–Jain approximation is accurate to within a few
percent of the value computed using the Colebrook–
White equation over the typical ranges of roughness
values and fully turbulent Reynolds numbers
1
p
f c
D D2 log
k S
3:7D c
C
2:51
Re c f
1=2
c
!
(32.6)
f c
0:25
h
log
kS
3:7Dc
C
5:74
Re 0:9
c
Ái 2
(32.7)
where: k S is the Nikuradse equivalent sand grain roughness of the conduit wall [m], Re c is the conduit
Reynolds number [] D
VcDc
, is the effluent kinematic viscosity [m
2
=s].
The kinematic viscosity of water for various temperatures and salinities can be obtained using the relationships provided in Sharqawy et al. [32.25]. Wall
roughness values for common pipe materials can be
found in any hydraulics data handbook, while roughness values for segmentally lined tunnels are presented
in Pitt and Ackers [32.26]. It is customary to make an
allowance for increased wall roughness over the conduit
design life to account for aging and degradation.
Local head losses arise from flow through bends,
tee or wye junctions, flow or pressure control devices
(e.g., valves), and expansions or contractions in crosssectional flow area. Local head losses will also occur
at conduit entrances, at submerged discharges, and any
location in the system where flow separation occurs. As
shown in the second term of (32.5), local head loss is
expressed as a multiple of the velocity head at the particular component of interest. The local loss coefficient,
K L , depends on the component geometry and is determined experimentally. Loss coefficients for common
system components can be found in any hydraulics data
handbook. Several references such as Miller [32.27]
and Idelchik [32.28] are devoted entirely to local head
loss coefficients and include many components present
in marine outfall systems.
As local head loss coefficients are always based on
some reference velocity, it is important to ensure consistency between a given K L and the velocity, V L , in the
associated velocity head term (V
2
L =2g). For components
with constant cross-sectional area such as certain bends,
K L is normally based on the average velocity through
the bend. However, there is no standard reference velocity for components like nozzles or sudden expansions
or contractions which have multiple cross-sectional areas; some sources may use the upstream velocity for
reference, while others may use the downstream velocity. Using an incorrect reference velocity could result in
significantly higher or lower head losses.
For complex hydraulic systems, it is important to
note that the total local head loss may not simply be the
sum of individual local loss components as (32.5) suggests. Rather, head loss coefficients are typically subject
to certain limitations. For example, the coefficient for
a single tee-junction can only be applied to a series of
tee junctions (such as in a dividing manifold) if the separation distance between successive junctions is, say,
5 to 10 times the manifold diameter. Correctly applying local head loss coefficients will help to minimize
under- or over-prediction of total local head loss. For
cases in which the loss coefficient limitations are not
clearly defined or the system configuration cannot easily be broken down into standard components (such
as through a rosette-style outfall structure), physical
and numerical modeling can be used to confirm head
losses.
32.4.2 Diffusers – Hydraulic Design
Outfall systems usually consist of a manifold (also referred to as a diffuser) whereby a common pipe or tunnel supplies flow to multiple risers, ports, or branches.
Although a manifold is an example of parallel flow in
which the head loss between the outfall shaft and each
exit port is the same, it is critical to note that the flow
rate out of each port will not necessarily be the same.
The variation in flow rate can be attributed to (i) decreasing flow and total head along the length of the
manifold, (ii) changing depth along the manifold, and
(iii) head loss coefficients for tee junctions which are
a function of (a) the ratio of conduit diameter to branch
diameter, and (b) the ratio of local flow through the conduit to flow through the branch. Head loss curves for
a range of tee-junction configurations can be found in
Miller [32.27].
Given that effluent dilution is directly related to port
exit velocity, the overall design objective should be to
achieve equal exit velocities (or as close to equal as possible) at each port to ensure consistent dilution levels
over the length of the manifold. Traditional analytical methods of solving for the hydraulic performance
of manifolds involve making an initial guess about the
flow conditions at the most downstream port, then using
an iterative approach to progressively work upstream,
port by port, until a final solution is reached. An alternative approach using simultaneous equations is presented
in this section. The resulting set of equations can be
quickly solved using a spreadsheet application with
built-in equation solver. The spreadsheet can be set up
to optimize port velocities by varying known quantities such as the port and manifold diameters and/or port
Part C | 32.4
computed iteratively using the implicit Colebrook–
White formula given in (32.6), or approximated using
the explicit Swamee–Jain equation given in (32.7). The
Swamee–Jain approximation is accurate to within a few
percent of the value computed using the Colebrook–
White equation over the typical ranges of roughness
values and fully turbulent Reynolds numbers
1
p
f c
D D2 log
k S
3:7D c
C
2:51
Re c f
1=2
c
!
(32.6)
f c
0:25
h
log
kS
3:7Dc
C
5:74
Re 0:9
c
Ái 2
(32.7)
where: k S is the Nikuradse equivalent sand grain roughness of the conduit wall [m], Re c is the conduit
Reynolds number [] D
VcDc
, is the effluent kinematic viscosity [m
2
=s].
The kinematic viscosity of water for various temperatures and salinities can be obtained using the relationships provided in Sharqawy et al. [32.25]. Wall
roughness values for common pipe materials can be
found in any hydraulics data handbook, while roughness values for segmentally lined tunnels are presented
in Pitt and Ackers [32.26]. It is customary to make an
allowance for increased wall roughness over the conduit
design life to account for aging and degradation.
Local head losses arise from flow through bends,
tee or wye junctions, flow or pressure control devices
(e.g., valves), and expansions or contractions in crosssectional flow area. Local head losses will also occur
at conduit entrances, at submerged discharges, and any
location in the system where flow separation occurs. As
shown in the second term of (32.5), local head loss is
expressed as a multiple of the velocity head at the particular component of interest. The local loss coefficient,
K L , depends on the component geometry and is determined experimentally. Loss coefficients for common
system components can be found in any hydraulics data
handbook. Several references such as Miller [32.27]
and Idelchik [32.28] are devoted entirely to local head
loss coefficients and include many components present
in marine outfall systems.
As local head loss coefficients are always based on
some reference velocity, it is important to ensure consistency between a given K L and the velocity, V L , in the
associated velocity head term (V
2
L =2g). For components
with constant cross-sectional area such as certain bends,
K L is normally based on the average velocity through
the bend. However, there is no standard reference velocity for components like nozzles or sudden expansions
or contractions which have multiple cross-sectional areas; some sources may use the upstream velocity for
reference, while others may use the downstream velocity. Using an incorrect reference velocity could result in
significantly higher or lower head losses.
For complex hydraulic systems, it is important to
note that the total local head loss may not simply be the
sum of individual local loss components as (32.5) suggests. Rather, head loss coefficients are typically subject
to certain limitations. For example, the coefficient for
a single tee-junction can only be applied to a series of
tee junctions (such as in a dividing manifold) if the separation distance between successive junctions is, say,
5 to 10 times the manifold diameter. Correctly applying local head loss coefficients will help to minimize
under- or over-prediction of total local head loss. For
cases in which the loss coefficient limitations are not
clearly defined or the system configuration cannot easily be broken down into standard components (such
as through a rosette-style outfall structure), physical
and numerical modeling can be used to confirm head
losses.
32.4.2 Diffusers – Hydraulic Design
Outfall systems usually consist of a manifold (also referred to as a diffuser) whereby a common pipe or tunnel supplies flow to multiple risers, ports, or branches.
Although a manifold is an example of parallel flow in
which the head loss between the outfall shaft and each
exit port is the same, it is critical to note that the flow
rate out of each port will not necessarily be the same.
The variation in flow rate can be attributed to (i) decreasing flow and total head along the length of the
manifold, (ii) changing depth along the manifold, and
(iii) head loss coefficients for tee junctions which are
a function of (a) the ratio of conduit diameter to branch
diameter, and (b) the ratio of local flow through the conduit to flow through the branch. Head loss curves for
a range of tee-junction configurations can be found in
Miller [32.27].
Given that effluent dilution is directly related to port
exit velocity, the overall design objective should be to
achieve equal exit velocities (or as close to equal as possible) at each port to ensure consistent dilution levels
over the length of the manifold. Traditional analytical methods of solving for the hydraulic performance
of manifolds involve making an initial guess about the
flow conditions at the most downstream port, then using
an iterative approach to progressively work upstream,
port by port, until a final solution is reached. An alternative approach using simultaneous equations is presented
in this section. The resulting set of equations can be
quickly solved using a spreadsheet application with
built-in equation solver. The spreadsheet can be set up
to optimize port velocities by varying known quantities such as the port and manifold diameters and/or port