Algorithms for Pit Pressure Changes and Head Losses in Stormwater Drainage Systems
Geoffrey O'Loughlin* and Bob Stack**
Anstad Pty Ltd, 72 Laycock Road, Penshurst, NSW, 2222, Australia, Anstad@tpgi.com.au
Watercom Pty Ltd, 105 Queen Victoria St., Bexley, NSW, 2207, rstack@watercom.com.au
*
**
Abstract
Theories and experimental work on changes to energy and hydraulic grade lines at pits or
manholes are outlined. Four algorithms describing these changes are compared against
selected experimental results. The comparisons are inconclusive, with no method being
obviously superior. However, this information should provide the basis for further
development of an empirical algorithm, which needs to cover the misalignment of pipes.
Case studies are presented to provide a perspective on (a) the types of pit geometries
occurring in separate stormwater drainage systems, and (b) the overall importance of pit
pressure changes in the analysis and design of separate stormwater drainage systems. An
extended reference list and bibliography are provided.
1. Introduction
Head losses at pits or manholes, represented by changes in energy and hydraulic grade lines,
are required to adequately describe flow behaviour in stormwater drains and sanitary sewers.
Flow through these facilities can be extremely complex. Despite the application of theories
and many experimental studies, existing analytical and design procedures are incomplete.
This paper considers the problem of losses and pressure changes from the viewpoint of a
software developer seeking an algorithm to calculate pressure changes in separate stormwater
drainage systems subject to unsteady full and part-full pipe flow conditions.
2. The Phenomenon
In sanitary sewer systems, manholes provide access for inspection and maintenance, and a
junction point where pipe branches can connect, or where pipes can change size or direction.
In combined and separate stormwater drains, they are also entry points for surface runoff.
Manholes and pits are nearly always larger than pipes, and the expansion of pipe flows
entering the junction, the mixing of pipe and surface inflows and the effects of downstream
water levels create complex flow conditions, with energy losses and increases in water levels,
sometimes causing overflows.
Complexity comes from the almost infinite variety of conditions that can occur. Some relate
to the system geometry. For a pit with a single outlet, this can involve:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
various numbers of pipes entering the pit (0 to 3 or more),
the presence of a surface inlet or grate flow,
the angles of the inlet pipes relative to the outlet pipe in the horizontal plane,
the various heights of the invert pipes and drops in the pit,
the pipe diameters,
whether pipe inflows are opposed, so that jets will interfere with each other,
whether jets from inlet pipe are directed into the outlet pipe, or against a pit wall,
1
(h) the size and shape of the pit, and
(i) whether benching or deflectors are placed in the pit.
Also important are flow characteristics, including:
(j)
(k)
(l)
(m)
the flowrates in the inlet pipes and from the surface inlet,
whether the pipes are running full or part-full, supercritical or subcritical,
the effect of tailwater level and the water level in the pit,
in the case of junctions with two or more upstream pipes, time-dependent flow ratios, as
contributing hydrographs in upstream pipes pass through a pit.
The problem is likely to be approached differently when dealing with (a) sanitary and
combined sewer systems, and with (b) separate stormwater systems. The former usually
involves circular manholes, energy grade lines (EGLs), and energy or head loss coefficients,
while the latter relates to with rectangular pits, hydraulic grade lines (HGLs) and pressure
change coefficients (Figure 1). This paper focuses upon separate systems and mostly
employs the terminology associated with these.
Figure 1 Drainage Systems with Grade Lines and Changes Shown
The energy loss and pressure changes mentioned above are expressed in the usual form of
head losses, as coefficients multiplied by the velocity head in the downstream pipe:
Energy or head loss (m), h L = k L
Vo2
V2
and pressure change (m), h P = k P o , … (1 & 2)
2g
2g
with Vo being the outlet pipe velocity (m/s) and g being acceleration due to gravity (m/s2).
Hare (1983) has noted that the actual water surface in a pit can be higher than the HGL level
when there is a change of direction, due to conversion of kinetic energy. He proposed a third
relationship with a coefficient kW,
V2
Water Level, WL = k W o
… (3)
2g
In determining changes and coefficients, EGLs and HGLs in pipes are projected upstream or
downstream to the centre of the pit. From Bernoulli’s Equation, for a system with one inlet
pipe and one outlet pipe, the coefficients are related by:
2
Vu2
, with Vu being the velocity in the upstream pipe (m/s)
… (4)
Vo2
kP factors can be negative where the pit outlet pipe is larger than the inlet pipes, and the outlet
pipe velocity head is less than that of the inlet pipes.
Large differences in the pressure change coefficient can occur from the particular alignments
of pipes as they enter or leave pits. Hare (1983) showed that losses depend on how a jet of
flow emerging from an inlet pipe is directed to the outlet pipe. If it is directed straight at the
pipe, as in Figure 2(a), head losses will be low; if it impinges onto a wall, as in Figure 2(b),
losses will be much higher, as indicated by the data in Table 1, drawn from experiments with
single-inlet pipe systems.
k P = (1 + k L ) −
Figure 2 Alternative Alignments of Pipes meeting at a Pit
Table 1 Pit Pressure Change and Water Level Coefficients for Different Pipe
Alignments with a Change of Direction of 45 o
Ratio of inlet and outlet
diameters,
Du/Do
0.7
0.8
0.9
1.0
kP Coefficients for a
Branch Point on the
Downstream Face of a
Square Pit
-0.90
0.0
0.45
0.60
Coefficients for a Branch Point
on the Upstream Face of a
Square Pit
kP
kW
2.05
2.90
2.10
2.60
2.15
2.50
2.20
2.30
3. Theory
Mass conservation at a junction is simply:
Sum of Inflows - Sum of Outflows = Change in Storage
… (5)
which can be ignored unless the volume of a pit is large, or storage is considered to include
the surface area above a pit.
Energy conservation can be described in various ways. Yen (2001) presents this as:
 Vi2
n
pi
∑ Q . 2g + γ
i =1
i


V2
dY n
+ z i  − Q j h j = s
+ ∑ Q i k L,i i
2g
dt i =1

… (6)
where Qi are the flows in pipes entering and leaving a pit (m3/s), being positive for inflows
and negative for outflows, Vi are the corresponding flow velocities (m/s), pi are the
piezometric heads above pipe inverts at levels zi (m), γ is the specific weight of water (N/m3),
3
Qj represents flows introduced or extracted at the pit, such as surface grate inflows, and jj is
the corresponding energy transfer (m), s is the storage in the pit (m3), Y is the depth of water
in the pit, and kL,i are the exit or entrance loss coefficients for the various pipes.
A variation on this is the power loss approach proposed by Chang et al. (1994) using the
semi-empirical formulation:
m Qj
Vj2
Qj
Vo2 n Qi
Vi2 m
∆E = α1
+ ∑ α 2,i
+ ∑ α 3. j
(z j + D j − d mH ) + ∑ α 4, j
2g
2g i =1 Q o
2g i =1
Qo
j=1 Q o
… (7)
where ∆E is the composite energy loss (m),
α1 is a contraction loss coefficient,
α2,i is an expansion loss coefficient for each submerged inflow pipe i,
α3,j is a plunging loss coefficient for each plunging inflow pipe j,
α4,j is an expansion loss coefficient for each plunging inflow pipe j,
dmH is the water depth in the manhole relative to the common datum (m),
Dj is the diameter of the jth plunging inlet pipe (m), and
n and m are the numbers of inflow pipes that are submerged and are plunging.
Momentum conservation can also be applied in various forms. One equation that considers
impulse and force acting in the direction of a single outlet pipe is:
m
∑ P A cosθ
i =1
i
i
i
m


− Po A o − R = ρ. Q o Vo − ∑ Q i Vi cosθ i 
i =1


… (8)
where Pi and Ai are the pressure (N/m2) and cross-sectional area (m2) in m inlet pipes, θi is
the angular difference between the directions of Pipe i and the outlet pipe, Po and Ao are the
outlet pipe pressure and cross-sectional area, R is the reaction force in the direction of the
outlet pipe (N), ρ is the density of water (kg/m3), Qo and Qi are the outlet and inlet pipe
flowrates (m3/s) and Vo and Vi are the corresponding velocities (m/s).
This equation should adequately describe the situation at a closed junction, where pipes meet
without a chamber in which expansion can occur.
One analytical approach has been to separate energy losses into two additive components - an
exit loss as a pipe flow jet enters a pit and an entrance loss as flow enters the outlet pipe.
Other theories applied to the flow situation in pits include submerged jet theory (Bo
Pedersen and Mark, 1990, Mudgal and Pani, 1993) and various computational fluid
dynamics techniques, such as a stochastic turbulence-closure model (Stein et al., 1999).
While these relationships appear to be straightforward, the complications noted in Section 2
mean that simple theoretical concepts cannot be applied to all situations. The projected
straight grade lines mask quite complex turbulence, exit and entrance losses, jet behaviour,
swirl and air entrainment effects.
4. Laboratory Modelling of Pit Energy Losses and Pressure Changes
There has been little direct field testing of pit pressure changes. It appears that the many
calibrations of monitored systems, such as the large sewer described by Jacobsen and
Harremoes (1984), have not provided any published conclusions about manhole head losses.
4
Almost all information comes from laboratory tests on scale models that are typically onetenth of prototype size. The seminal study was that of Sangster et al (1958) at the University
of Missouri. This was followed by studies in the UK (Ackers, 1959, Archer et al., 178,
Howarth and Saul, 1984), Canada (Townsend and Prins, 1878, Marsalek, 1981, 1984, 1985,
1988, Dick and Marsalek, 1985) Australia (Hare, 1981, Black and Piggott, 1983, DeGroot
and Boyd, 1983, Johnston and Volker, 1990, Hare et al., 1990, Hare and O’Loughlin, 1991),
Sweden (Lindvall, 1984, 1987) and Denmark (Bo Pedersen and Mark, 1990). There have
also been studies in Greece (Christodoulou, 1987, 1991), Japan (Kusuda and Arao, 1987,
Kusuda et al., 1993, Sakakibari, 1996, Arao and Kusuda, 1999), India (Mudgal and Pani,
1993), Germany (Merlein and Valentin, 1999) and Italy (Calomino et al, 1999).
A significant addition to this list is the extensive modelling by Chang et al. (1994) for the US
Federal Highway Administration (FHWA), from which the algorithm described by GKY
Associates Inc (1999) and Stein et al. (1999) has been developed.
While most laboratory studies have measured losses under steady flow conditions, Howarth
(1984), Howarth and Saul (1984), Hare et al. (1990) and Merlein and Valentin (1999)
describe experiments using systems of valves and sensors to create unsteady flow conditions
and to measure time-varying head losses. Howarth and Saul (1984) concluded that loss
coefficients were similar for unsteady and steady flow conditions in the absence of swirl in a
manhole, but that steady state results overestimate loss coefficients when swirl occurred.
Hare (Personal communication, 2002) points out that at any instant of time in a complex flow
event, unsteady pressure change coefficients are similar to the experimentally-derived steadystate values, but that they will change significantly during the event.
5. Design Aids
Experimenters have attempted to obtain generalised relationships from their experimental
data, using methods such as dimensional analysis, semi-empirical formulations and
regression analysis. Some have developed design aids such as the "Missouri Charts" of
Sangster et al. (1958), a set of nine charts describing the situations described in Table 2.
These charts are complex and their diverse formats, based on different sets of parameters,
make computer implementation difficult.
Other studies noted previously have provided useful design information, particularly those by
Hare (1983), Marsalek (1985) and Chang et al. (1994). The derived equations or graphs are
in different forms and are difficult to implement within computer programs. The
relationships developed by Chang et al. (1994) have been incorporated into the HYDRA
program, which is part of the HYDRAIN suite (GKY & Associates Inc., 1999). An energybased formulation was employed, rather than the power loss formulation presented in an
appendix to the FHWA Hydraulic Engineering Circular 22 (US FHWA, 1996).
Equations, algorithms and software implementations have been developed to define pressure
change and loss coefficients. Some examples are discussed in the following sections.
6. Computer Modelling of Piped Urban Drainage Systems
Computer modelling of drainage systems is used to design and check new systems, and to
analyse established drainage systems to develop remedies to problems or inadequacies.
5
Many models have been developed and modelling can be undertaken using software
involving full hydrodynamic calculations, such as SWMM, Hydroworks and MOUSE, or
simpler models. The effects of pit junctions are incorporated in various ways. For example,
in SWMM head losses are modelled as exit and entrance losses in some computations, but are
ignored or included as equivalent pipe lengths in others. MOUSE currently allows users a
choice of nine loss coefficient types based on geometry.
Table 2 “Missouri Chart” Formulations
No.
Configuration
Chart 1
Chart 2
Nomenclature
Rectangular grated inlet pit
at top of a line, no pipe inlets
Rectangular pit, no grate
flow, one inlet, straightthrough flow
Same pit as for Chart 3, with
grate flow
Rectangular pit with two
inlets, one straight-through,
the other at 90o to the outlet
pipe, plus grate flow
Rectangular pit with two
directly-opposed inlets at
90o to outlet, and grate flow
Rectangular pit with two
inlet pipes at 90o to outlet,
not opposed, and grate flow
Square manhole with two
inlet pipes, one straightthrough and the other at 90o
Same as for Chart 8
Chart 3
Chart 4
Chart 5
Chart 6
Chart 7
Chart 8
Chart 9
Chart 10
Square or round manhole
with the same configuration
as for Chart 8
Type of Relationship (using Sangster et al. Terminology)
KG coefficient vs submergence ratio d/DO - two curves for surface
grate inflow direction
KU coefficient vs DU/DO with three curves for different manhole
lengths and another for a rounded outlet pipe entrance
KU coefficient vs DU/DO with six curves for different QG/QO ratios
and another chart for adjustment to allow for water depth in pit, d
Ku and KL coefficient vs DU/DO with seven curves for different
QU/QO ratios, with adjustment charts for different QG/QO and
DU/DO ratios
K coefficients estimated from factors H and L taken from charts
based on ratios of diameters and flows, depending on which is the
higher-velocity flow
KN and KF (nearest and furthest from outlet) coefficients obtained
in two charts, for ratios of flows and two ratios of diameters
KL, the lateral pipe coefficient, is found from two charts based on
diameter and flow ratios and submergence depth; there is an
adjustment factor for manhole shape (square to round)
KU coefficient for the same situation as in Chart 2, as a function of
flow and diameter ratios - the form of the two charts is different
than Chart 8, and a correction for deflectors is provided
KU and KL coefficients based on DU/DO and QU/QO ratios over a
greater range that Charts 8 and 9, with ten curves. Charts 8 and 9
are preferred where both alternatives can be used
The authors have reviewed available information to develop a reliable procedure for
calculating pit pressure change coefficients in DRAINS (O’Loughlin and Stack, 2001), a
quasi-unsteady simulation model that calculates HGL positions in drainage systems at time
steps during storm events. These calculations should occur without the user having to specify
detailed pit characteristics, or having to interact with the program when entering data.
DRAINS currently allows users to specify constant kP coefficients or to define these using a
form of the relationship suggested by Mills (Mills and O’Loughlin, 1998):
Qg
Q
… (9)
k P = 0.5 + 2 m + 4
Qo
Qo
where Qm refers to the total flows from misaligned inlet pipes, which are out of alignment
with the outlet pipe by more than Do/4, horizontally or vertically, Qg refers to surface inlet or
grate flows plus any pipe flows that enter the pit above the water level, and Qo is the outlet
flowrate (all in m3/s). Modifications are made by adding factors for deflectors or benching
(-0.5), opposed pipes (1.0) and for increases in pipe diameters (-0.5). This method is
6
intended to provide a rough estimate in situations where drops (vertical misalignments of
inlet and outlet pipes) occur. It only applies to pipes flowing full.
The use of constant kL or kP coefficients applying to peak flow conditions is valid when using
the Rational Method and only considering peak flowrates. In unsteady flow models,
coefficients should change to reflect the changing flow conditions occurring at each time step
during an analysis of a storm event.
7. Comparison of Algorithms
To explore suitable methods of determining pit pressure change coefficients, four methods
were examined. Each of these can be applied at each time step in an analysis, with a current
coefficient being calculated from the instantaneous flow conditions.
The first method was Mills’ Equation (9). The second was an equation developed by Hare
(Hare et al., 1990) from the momentum equation (8). For n inlet pipes this is:
D
k P = 2.3 − 2.0. o
 Qo



2
2
 Q  2
Q
Q 
 1  cos θ 1 +  2  cos θ 2 + ... +  n
 D1 
 D2 
 Dn
2


 cos θ n 



… (10)
where D represents pipe diameters (m), Q flowrates for full-pipe flow (m3/s), θ the angular
differences between directions of inlet pipes and the outlet pipe, with subscript o referring to
the outlet pipe and subscripts 1, 2, .. n referring to inlet pipes. Theoretically, the first number
on the left hand side of the equation should be 2.0. The change to 2.3 is an empirical
adjustment suggested by Hare and O’Loughlin (1991) to fit experimental data better.
The third relationship was a regression equation developed by Parsell (1992) from the Hare
(1983) data and verified against the Sangster et al. (1958) data. The pressure change
coefficient is found from:
kP = 2.3479 - 0.3794 P1 - 1.2894 P2 - 0.1146 P3 - 0.9703 P4 - 0.1657 P5
+ 0.0519 P12 -0.3755 P22 + 0.3032 P32 +0.8078 P42 + 0.0108 P52
… (11)
where P1, P2, …, P5 are factors related to lost forces, conserved forces, head requirements,
grate inflow ratio and submergence ratio. A similar relationship is provided for kw
coefficients.
These relationships depend on a measure of the misalignment of the inlet and outlet pipes,
defined in terms of the intersection of their horizontal and vertical projections on the
downstream pit wall and in the output pipe.
The fourth relation tested was the algorithm developed for the FHWA, which has the form:
kL = (C1.C2.C3+ C4).ω
… (12)
where C1 is a coefficient related to the relative sizes of the pipes and manhole,
C2 is a coefficient related to water depth in a manhole,
C3 is a coefficient related to lateral flow, lateral angle and plunging flow,
C4 is a coefficient related to relative pipe diameters, and
ω is a correction factor for benching (with a value of 1.0 for no benching).
7
The relationships for the C factors are provided by GKY & Associates Inc. 1999) and Stein et
al. (1999). C3 is the most complicated, being derived as the sum of five terms.
These four methods are not strictly comparable because different levels of coverage are
intended. The Mills equation is approximate, and generally conservative. The Hare equation
assumes that pipes are directed to the centre of the pit and it does not allow for pipe drops and
misalignments. The Parsell algorithm can allow for misaligned pipes and drops. All three
apply only to full-pipe flows. The FHWA algorithm is the most comprehensive, covering
part- and full-pipe flow, drops and other situations.
In Table 3, results from the four algorithms, calculated by a spreadsheet macro, are compared
with the Sangster et al. (1958) and Hare (1983) charts for cases with no pipe inlet and with
one inlet. Cases of two or more inlet pipes are not considered, and it is assumed that all pipes
are aligned to minimise energy losses. The FHWA Equations have been implemented from
the descriptions in the HYDRA manual and the associated papers. The kL coefficients
calculated by this method were converted to kP coefficients by Equation 4. For submergence
ratios less than 1.0, part-full pipe velocities were used, corresponding to the higher of the
normal and critical depths in the inlet and outlet pipes.
Although only a few of the possible geometric configurations are covered, the values in Table
3 reveal some of the complexity of kP coefficients and the large variations that can occur.
Even the determination of the Chart estimates is complicated, with some estimates requiring
several operations. It is evident that no method matches the Chart values accurately for all
cases. Mills’ method specifies a minimum kP coefficient of 0.5 and is generally conservative.
The Hare procedure gives values that match the general form of the Chart values.
Coefficients from the Parsell method appear to match the Chart values most closely. The
FHWA algorithm does not appear to perform better than the Hare or Parsell methods.
Assessment is therefore difficult, with methods matching experimental data well in some
cases but not in others. While the FHWA method appears, on the basis of its rigorous
derivation, to be the best candidate for an algorithm, it will need qualifications and extensions
to cover all situations, particularly those involving misalignments of pipes, which it does not
include. It is likely that the Mills and Parsell methods, which allow for misalignments, will
perform better when tested in cases where these occur.
8. Implications for Analysis of Separate Stormwater Drainage Systems
To investigate how pit pressure change coefficients affect actual analyses, three established
drainage systems and two newly-designed systems in the Sydney Area have been examined
to classify pits into categories, as shown in Table 4. The categories allow for changes of
direction and pipe size (from a set of standard pipe diameters), and for numbers of inlet pipes.
The existing systems have some cases of outlet pipe diameters being less than those of inlet
pipes at pits. These are due to (a) pipe enlargement works that have been implemented only
partially, and (b) surcharge pits, associated with “converters”, short lengths of pipe that carry
flows under cross-streets and discharge into street gutters. Both designs include interallotment drainage pipes as well as pipes in streets. The “PL” design is a conventional one,
while the “SP” design involves a number of pits with reductions in pipe sizes to divert runoff
to stormwater treatment devices. The changes of direction greater than 90o at some pits
reflect the curved streets in the “SP” subdivision layout.
8
Table 3 Comparison of Fitted Data and Estimated Pit Pressure Change Coefficients
Case
Pit at top of a line, no inlet pipes
(Missouri Chart 2)
- submergence ratio = 0.5
- submergence ratio = 1.5
- submergence ratio = 3
- submergence ratio = 6
One inlet pipe, straight-through flow,
no grate flow (Missouri Chart 3)
- Du/Do = 0.833, submergence ratio = 0.5
- Du/Do = 0.833, submergence ratio = 1.5
- Du/Do = 0.833, submergence ratio = 3.0
- Du/Do = 1.0, submergence ratio = 0.5
- Du/Do = 1.0, submergence ratio = 1.5
- Du/Do = 1.0, submergence ratio = 3.0
- Du/Do = 1.2, submergence ratio = 0.5
- Du/Do = 1.2, submergence ratio = 1.5
- Du/Do = 1.2, submergence ratio = 3.0
One inlet pipe, straight-through flow,
33% grate flow (Missouri Chart 4)
- Du/Do = 0.833, submergence ratio = 0.5
- Du/Do = 0.833, submergence ratio = 1.5
- Du/Do = 0.833, submergence ratio = 3.0
- Du/Do = 1.0, submergence ratio = 0.5
- Du/Do = 1.0, submergence ratio = 1.5
- Du/Do = 1.0, submergence ratio = 3.0
- Du/Do = 1.2, submergence ratio = 0.5
- Du/Do = 1.2, submergence ratio = 1.5
- Du/Do = 1.2, submergence ratio = 3.0
One inlet pipe, 90o change of direction,
no grate flow, pit width = 2 x outlet
diameter (Missouri Chart 8)
- Du/Do = 0.833, submergence ratio = 1.5
- Du/Do = 0.833, submergence ratio = 3
- Du/Do = 1, submergence ratio = 1.5
- Du/Do = 1, submergence ratio = 3
- Du/Do =1.2, submergence ratio = 1.5
- Du/Do = 1.2, submergence ratio = 3
One Inlet Pipe, no grate flow,
submergence ratio = 3.0 (Hare, 1983),
changing direction at downstream wall
- Du/Do = 0.833, angular change=0o
- Du/Do = 0.833, angular change=22.5o
- Du/Do = 0.833, angular change=45o
- Du/Do = 1.0, angular change=0o
- Du/Do = 1.0, angular change=22.5o
- Du/Do = 1.0, angular change=45o
kP Coefficients
Hare
Parsell
Charts
Mills
FHWA
6.6 or 9.51
3.1 or 3.81
1.95
4.5
4.5
4.5
2.3
2.3
2.3
2.15
1.97
1.77
0.19
1.34
2.69
2.40
-0.85
-0.85
0.12
0.12
0.72
0.72
0.0
0.0
0.5
0.5
0.5
0.5
-0.58
-0.58
0.3
0.3
0.91
0.91
-0.40
-0.58
0.46
0.28
1.21
1.04
0.58
-0.91
-0.76
0.53
0.17
0.32
0.50
0.69
0.84
1.35
0.95
1.9
1.3
2.3
1.5
1.83
1.83
1.83
1.83
1.83
1.83
1.02
1.02
1.41
1.41
1.68
1.68
0.91
0.73
1.27
1.10
1.60
1.42
0.71
0.77
1.44
0.69
1.25
1.92
0.68
1.48
2.15
1.68
1.68
1.62
1.62
1.55
1.55
0. 0
0.0
0.5
0.5
0.5
0.5
2.30
2.30
2.30
2.30
2.30
2.30
1.87
1.70
1.98
1.81
2.07
1.90
-0.91
-0.76
0.32
0.17
0.69
0.84
-0.70
-0.40
0.15
0.20
0.30
0.60
0.0
0.0
0.0
0.5
0.5
0.5
-0.58
-0.36
0.34
0.30
0.65
0.88
-0.58
-0.55
-0.09
0.28
0.29
0.61
-0.76
-0.76
-0.76
0.32
0.32
0.32
Notes:
The flowrates used in these comparisons are typical values, producing full-pipe velocities of 1 to 2 m/s.
Generally, relative flows are more important than absolute values and kP coefficients did not change much with
flowrates..
1
Values depend on the direction of the approach flow to the surface inlet relative to the outlet pipe direction.
Experimental evidence for Chart 2 is inconclusive, and curves tend to overestimate kP coefficients. It can be
argued that comparison with kW coefficients is more valid that with kP coefficients.
9
Table 4 Distribution of Size and Angle Changes and Pit Configurations for Five Systems
Pipe Arrangement,
Direction and Pipe Size
Change
Total number of pits
Pits at the Start of a Line
Straight-through flow pipes:
- more than one size down
- one size increment down
- same pipe size
- one size up
- two sizes up
- three or more sizes up
5o to 30o change of direction:
- one size down
- same pipe size
- one size up
- two sizes up
- three or more sizes up
30o to 60o change of direction:
- more than one size down
- one size down
- same size
- one size up
- two sizes up
- three or more sizes up
60o to 85o change of direction:
- one size down
- same pipe size
- one size up
- two sizes up
- three or more sizes up
90o change of direction:
- more than one size down
- one size down
- same pipe size
- one size up
- two sizes up
- three or more sizes up
> 90o change of direction:
- more than one size down
- same pipe size
- one size up
Surcharge pit (for converter)
Alternative Categories:
Pits with no inlet pipe
Pits with one inlet pipe
Pits with two inlet pipes
Pits with three inlet pipes
Pits with four inlet pipes
Catchment
“WS”
“CR”
“HC”
“PL”
“SP”
100
31
481
164
430
128
64
15
169
34
2
31
10
1
1
7
147
33
5
2
2
5
142
16
9
2
18
4
1
-
1
53
14
3
-
3
2
-
1
27
2
1
1
1
34
4
3
4
4
2
1
-
19
3
2
-
1
2
2
-
1
13
3
2
-
2
25
5
1
4
9
2
-
12
3
2
-
1
1
-
6
14
4
1
5
2
-
1
-
1
4
3
1
2
7
1
-
2
1
20
5
2
3
1
16
4
3
1
4
3
-
1
2
4
-
2
2
8
3
8
-
2
2
4
-
31
40
25
3
1
164
200
103
12
1
128
206
80
12
4
15
39
10
-
34
114
21
1
-
Certain categories dominate - pits at the top of a line with no inlets, straight-through pits with
inlet and outlet pipes of the same size, and pits with one inlet. Due to the large numbers of
these, correct estimation of pressure changes is particularly important for these categories.
However, there are also a number of unusual pits in all examples except the conventional
subdivision "PL", so there is also a need to determine coefficients for non-standard pits.
10
In practice, designers tend to use fixed default values, which are probably overly conservative
in most cases. In the past, a kL coefficient of 0.15 was applied to sanitary sewers in the U.K.
(Howarth and Saul, 1984) and a kP coefficient of 1.5 has been applied to stormwater drainage
systems in Australia. Most Australian designers are reluctant to employ negative kP
coefficients.
As a further test, sensitivity analyses have been applied to the first two catchments listed in
Table 4. They were analysed using DRAINS with conservative assumptions on pit pressure
changes, without specifying any negative coefficients. The flowrates shown are the worst
cases derived for 12 design storms of different durations. Surface overflows from the pits,
which are the main factor of concern, have been estimated for average recurrence intervals
(ARIs) of 1, 10 and 100 years, at three locations in the catchment. The results, given in Table
5, show that in general, the overflows are not sensitive to the selection of pit pressure
changes. However, experience of other cases, particularly ones involving steep locations or
complex pipe layouts, indicates that pit pressure changes can be locally significant.
Table 5 Results of Sensitivity Analyses for Two Catchment Models
Description for the
"WS" Catchment
ARI (years)
Overflows with pit pressure
change coefficients halved (m3/s)
Base Case overflow rates
(m3/s)
Overflows with pit pressure
change coefficients doubled
(m3/s)
Description for the
"CR" Catchment
ARI (years)
Overflows with pit pressure
change coefficients halved (m3/s)
Base Case overflow rates
(m3/s)
Overflows with pit pressure
change coefficients doubled
(m3/s)
Overflow from a
relatively small
catchment through
properties
(m3/s)
1
10
100
Overflow from a
storage in a trapped
low point, with a
medium size
catchment (m3/s)
1
10
100
Overflow from a
zone where many
overflows and pipes
meet at a major
road (m3/s)
1
10
100
0.086
0.618
1.04
0.203
1.08
1.72
1.17
8.10
13.8
0.085
0.693
1.12
0.208
1.08
1.72
1.35
8.84
14.5
0.115
0.761
1.19
0.199
1.09
1.74
1.83
9.36
15.1
Overflow from small
catchment through
properties
(m3/s)
Overflow from
larger catchment
with several
branches (m3/s)
Flow contained in a
roofed channel at
the catchment outlet
(m3/s)
1
0.08
10
0.55
100
1.17
1
1.39
10
8.7
100
17.3
1
12.3
10
23.5
100
30.1
0.08
0.66
1.28
1.44
10.2
18.6
11.5
24.6
29.7
0.09
0.75
1.38
1.59
11.6
20.3
11.3
24.0
32.0
Generally, increasing the coefficients increases overflows by raising HGLs to the surface
more frequently and for longer durations during storm events. This is especially so for small
drainage systems. However, for larger systems that collect overflows from several locations,
the slower speed of travel of surface flows compared to pipe flows causes complex
behaviour, with peak flowrates sometimes decreasing as kP coefficients are increased.
11
A solution to uncertainties surrounding coefficients might seem to be to set these
conservatively high. While this might be acceptable for design, it is not appropriate for
analysis, as high coefficients might raise or lower overflows at various parts of a system,
depending on the various concentration times of hydrographs in pipes and on the surface.
9. Conclusions
•
Pit hydraulics are extremely complex. The results of the comparison of algorithms are
inconclusive, with no single method being superior. However, the information obtained
so far indicates that a viable algorithm can be developed. Further testing and
development is required.
•
The FHWA algorithm appears to provide a significant advance in the determination of
head losses and pit pressure changes in stormwater drainage and sewerage systems.
However, comparisons with alternative algorithms and experimental data indicate that
simpler methods appear to give results that are at least as good.
•
A general algorithm will have to allow for misalignment of the inlet and outflow pipes at
a pit. Previous studies have shown that the alignment or misalignment of pipes can make
large differences to head losses and pressure changes.
•
While essentially-empirical procedures may eventually provide adequate estimation
procedures for computer models, they will still be incomplete, and further experimental
modelling and development of theoretical concepts is necessary. This applies specially to
the investigation of dynamic effects in rapidly changing hydrographs passing through
complex pipe systems. Coefficients for energy losses and pressure changes that are
derived from steady flow tests will not always be accurate.
•
A survey of separate stormwater drainage systems in the Sydney Area reveals that certain
geometric arrangements predominate, but that a variety of unusual configurations can
occur when existing systems are partially reconstructed, or where special requirements
such as surcharge pits apply in design.
•
The sensitivity analyses reported in Table 5 show that the selection of coefficients is
complex, and that use of conservatively high coefficients will not necessarily increase
peak flowrates at all locations in a drainage system. There seems to be little justification
for avoiding the use of negative pit pressure change coefficients in design.
Acknowledgements
Special thanks are due to Clive Hare and Ray Parsell for their constructive comments on this
paper.
References
Ackers, P. (1959) “An Investigation of Head Losses at Sewer Manholes”, Civil Engineering
and Public Works Review, Vol. 54. No. 637
Arao, S. and Kusuda, T. (1999) “Effects of Pipe Bending Angle on Energy Losses at TwoWay Circular Drop Manholes”, Proceedings, 8th International Conference on Urban Storm
Drainage, Sydney
12
Archer, B., Bettess, F. and Colyer, P.J. (1978) Head Losses and Air Entrainment at
Surcharged Manholes, Report No. IT 185, Hydraulics Research Station, Wallingford
Black, R.G. and Piggott, T.L. (1983) “Head Losses at Two Pipe Stormwater Junction
Chambers”, Proceedings, 2nd National Local Government Engineering Conference,
Institution of Engineers, Australia, Brisbane
Bo Pedersen, F. and Mark, O. (1990) “Head Losses at Storm Sewer Manuals, Submerged Jet
Theory”, J. Hydraulics Division, ASCE, 116(11)
Calomino, F., Frega, G., Piro, P. and Gironda Veraldi, M. (1999) “Hydraulics of Drops in
Supercritical Flow”, Proceedings, 8th International Conference on Urban Storm Drainage,
Sydney
Chang, F. M., Kilgore, R. T., Woo D. C. and M. P. Mistichelli (1994) Energy Losses
Through Junction Manholes, Volume I: Research Report and Design Guide, Federal
Highway Administration, FHWA-RD-94-090, McLean, VA
Christodoulou, G.C. (1987) “Energy Loss at Drop Manholes”, Proceedings, 4th International
Conference on Urban Storm Drainage, IAHR, Lausanne
Christodoulou, G.C. (1991) “Drop Manholes in Supercritical Pipelines”, J. Irrigation and
Drainage Engineering, ASCE, 117 (1)
De Groot, C.F. and Boyd, M.J. (1983) “Experimental Determination of Head Losses in
Stormwater Systems”, Proceedings, 2nd Local Government Engineering Conference,
Institution of Engineers, Australia, Brisbane
Dick, T.M. and Marsalek, J. (1985) “Manhole Head Losses in Drainage Hydraulics”,
Proceedings, 21st IAHR Conference, Melbourne
GKY & Associates Inc, (1999) User’s Manual for HYDRAIN, Integrated Drainage Design
Computer System: Version 6.1, Federal Highway Administration, US Department of
Transportation, Washington, DC (manual and software downloadable from
www.fhwa.dot.gov/bridge/hyd.htm)
Hare, C.M. (1983) “Magnitude of Hydraulic Losses at Junctions in Piped Drainage
Systems”, Civil Engineering Transactions, Institution of Engineers, Australia, CE 25 (1)
(also published in 1981 at Conference on Hydraulics in Civil Engineering, Institution of
Engineers, Australia, Sydney)
Hare, C.M., O'Loughlin, G.G. and Saul, A.J. (1990) “Hydraulic Losses at Manholes in Piped
Drainage Systems”, Proceedings, International Symposium on Urban Planning and
Stormwater Management, Kuala Lumpur
Hare, C. and O'Loughlin, G.G. (1991) “An Algorithm for Pressure Head Change Coefficients
at Stormwater Manholes”, in Urban Drainage and New Technologies (UDT '91),
Dubrovnik, Elsevier, London
Howarth, D.A. (1984) The Hydraulic Performance of Scale Model Storm Sewer Junctions,
PhD Thesis, University of Manchester
Howarth, D.A. and Saul, A.J. (1984) “Energy Loss Coefficients at Manholes”, Proceedings,
3rd International Conference on Urban Storm Drainage, Goteborg
Jacobsen, P. and Harremoes, P. (1984) “The Significance of Head Loss Parameters in
Surcharged Sewer Simulations”, Proceedings, 3rd International Conference on Urban
Storm Drainage, Goteborg
Johnston, A.J. and Volker, R.E. (1990) “Head Losses at Junction Boxes”, J. Hydraulics
Division, ASCE, 116(3)
13
Kusuda, T. and Arao, S. (1987) “Energy Losses at Circular Drop Manholes”, Proceedings,
4th International Conference on Urban Storm Drainage, Lausanne
Kusuda, T., Arao, S. and Moriyama, K. (1993) “Energy Losses at Junctions and Transient
Flow in Sewer Networks”, Proceedings, 6th International Conference on Urban Storm
Drainage, Niagara Falls
Lindvall, G. (1984) “Head Losses at Surcharged Manholes with a Main Pipe and a Ninety
Degree Lateral”, Proceedings, 3rd International Conference on Urban Storm Drainage,
Goteborg
Lindvall, G. (1987) “Head Losses at Surcharges Manholes”, Proceedings, 4th International
Conference on Urban Storm Drainage, IAHR, Lausanne
Marsalek, J. (1981) Energy Losses in Straight-Flow-Through Sewer Junctions, Research
Report No. 111, Environment Protection Service, Ottawa
Marsalek, J. (1984) “Head Losses at Sewer Junction Manholes”, J. Hydraulics Division,
ASCE, 110(8)
Marsalek, J. (1985) Head Losses at Selected Sewer Manholes, Special Report No. 52,
American Public Works Association, Chicago (Report No. 85-15, National Water
Resources Institute, Burlington, Ontario)
Marsalek, J. (1988) “Head Losses at Sewer Junctions, in Civil Engineering Practice”,
Volume 2 (Hydraulics, Mechanics) edited by P.N. Cheremisinoff et al., Technical
Publishing Company, PN
Merlein, J. and Valentin, F. (1999) “Hydraulic Conditions and Energy Loss in Submerged
Manholes”, Proceedings, 8th International Conference on Urban Storm Drainage, Sydney
Mills S.J. and O’Loughlin, G. (1998) Workshop on urban piped drainage systems,
Swinburne University of Technology and University of Technology, Sydney, (Offered
many times between 1982 and 1998)
Mudgal, B. and Pani, B.S. (1993) “Head Losses in Sewer Manholes”, 6th International
Conference on Urban Storm Drainage, Niagara Falls
O’Loughlin, G. and Stack, B. (2001) DRAINS User Manual, Watercom Pty Ltd, Sydney
(downloadable on www.watercom.com.au)
Parsell, R. (1992) “Generalised Equations for Estimating Pressure Change Coefficients at
Stormwater Pit Junctions, International Conference on Urban Stormwater Management,
Institution of Engineers, Australia, Sydney
Sakakibari, T., Tanaka, S. and Imaida, T. (1996) “Energy loss at surcharged manholes model experiment”, Proceedings, 7th International Conference on Urban Storm Drainage,
IAHR, Hannover (also published in Water Science and Technology Vol. 36, No. 8-9, 1997)
Sangster, W.M., Wood, H.W., Smerdon, E.T. and Bossy, H.G. (1958) Pressure Changes at
Storm Drain Junctions, Engineering Series Bulletin No. 41, Engineering Experiment
Station, University of Missouri
Stein, S.M., Dou, X., Umbrell, E.R. and Jones, J.S. (1999) Storm Sewer Junction Hydraulics
and Sediment Transport, US Federal Highway Administration Turner-Fairbanks Highway
Research Centre, VA (available on www.tfhrc.gov/structr/hydrlcs/pdf/3.pdf)
Townsend, R.D. and Prins, J.R. (1978) “Performance of Model Sewer Junctions”, J.
Hydraulics Division, ASCE, 104(1)
U.S. Department of Transportation, Federal Highway Administration (1996) Urban
Drainage Design Manual, Hydraulic Engineering Circular No. 22, Office of Engineering,
Office of Technology Applications, Washington, DC
14
Yen, B.C. (2001) “Hydraulics of Sewer Systems”, Chapter 6 in Stormwater Collection
Systems Design Handbook, edited by L.W. Mays, McGraw-Hill, New York
XP Software (1999) XP-SWMM Reference Manual, Canberra
Bibliography
This includes additional references that have a bearing on pit pressure changes, or contain
original material on the subject. Some are unpublished research reports. The first author can
provide information on Australian sources to interested persons
Argue, J.R. (1986) Storm drainage design in small urban catchments : a handbook for
Australian Practice, Special Report No. 34, Australian Road Research Board, Vermont
South, Victoria
Ball, J.E. (1993) “Modelling of Unsteady Flow through Manholes”, 6th International
Conference on Urban Storm Drainage , Niagara Falls
Blaisdell, F.W. and Manson, P.W. (1963) Loss of Energy at Sharp Edged Pipe Junctions,
Technical Bulletin No. 1283, US Department of Agriculture, Washington
Blaisdell, F.W. and Manson, P.W. (1967) “Energy Loss at Pipe Junctions”, J. Hydraulics
Division, ASCE, 76
Catanzariti, G.A. and Kontominas, S. (1986) Energy Losses and Pressure Head Changes at
Storm Drain Junctions, Bachelor of Engineering Thesis, NSW Institute of Technology,
Sydney
Christodoulou, G.C. (1987) “Energy Loss at Drop Manholes”, Proceedings, 4th International
Conference on Urban Storm Drainage, IAHR, Lausanne
Freeman, K.F. and Marshall, G.R. (1984) Pressure Changes and Energy Losses in Drop
Pits, 8 volumes, Bachelor of Engineering Thesis, School of Civil Engineering, NSW
Institute of Technology, Sydney
Gayer, J.A. (1984) “On the Hydraulic Role of Manholes in Urban Storm Drainage Systems”,
Proceedings, 3rd International Conference on Urban Storm Drainage, Goteborg
Hager, W.H. (1989) “Transitional Flow in Channel Junctions”, J. Hydraulics Division,
ASCE, 115(2)
Hare, C.M. (1980) Energy Losses and Pressure Head Changes at Storm Drain Junctions,
Master of Engineering Thesis, NSW Institute of Technology, Sydney
Institution of Engineers, Australia Australian Rainfall and Runoff, A Guide to Flood
Estimation, 2 volumes, (edited by D.H. Pilgrim and R.P. Canterford), Canberra, 1987 (revised
into eight loose-leaf books, 1998)
Jenson, M. (1981) Hydraulic Energy Relations and Their Application to Ninety Degree
Junction, Series Paper No. 11, The Royal Veterinary and Agricultural University,
Copenhagen
Johnston, A.J., Pettigrew, M.R. and Volker, R.E. (1987) “Energy Losses at a Surcharged
Three Pipe Stormwater Pit”, 2nd National Conference on Hydraulics in Civil Engineering,
Institution of Engineers, Australia, Brisbane
Johnston, A.J., Volker, R.E. and Di Bella, C.J. (1990) “Factors Influencing Head Losses at
Junction Pits”, Conference on Hydraulics in Civil Engineering, Institution of Engineers,
Australia
15
Johnston, A.J. and Volker, R.E. (1990) “Head Losses at a Three Pipe Junction Box”, Civil
Engineering Transactions, Institution of Engineers, Australia, CE32 (3)
Jones, S. (1980) Pressure Changes in Urban Drainage Junctions, Undergraduate Project,
School of Civil Engineering, University of Technology
Liebman, H. (1970) “Der Einfluss von Einsteigschachten auf den Abflussforgang in
Abwasserkanalen” (Effects of Manholes on Flow Processes in Storm Drains), Wasser und
Abwasser in Forschung und Praxis, 2, Erich Schmid Verlag, Bielefeld
McEleney, A. (1989) Investigation of Energy Loss Coefficients at a Straight Through
Manhole, BE Project, Department of Civil Engineering, University of Manchester
McKenzie, G.J. (1993) Pressure Head Changes at Pit Junctions, Undergraduate Thesis,
School of Civil Engineering, University of Technology, Sydney
Marsalek, J. (1987) “Head Losses at Junctions of Two Opposing Lateral Sewers”,
Proceedings, 4th International Conference on Urban Storm Drainage, IAHR, Lausanne
Marshall, G.R. (1990) “A Tabulation of Pressure Changes and Energy Losses in Stormwater
Drop Pits”, Conference on Hydraulics in Civil Engineering, Institution of Engineers,
Australia
Pardee, L.A. (1968) Hydraulic Analysis of Junctions, Office Standard No. 115, Storm
Drainage Design Division, City of Los Angeles
Prins, R.J. (1975) Storm Sewer Junction Geometry and Related Energy Losses, MSc Thesis,
University of Ottawa
Ramamurthy, A.S., Carballada, L.B. and Tran, D.M. (1988) “Combined Open Channel Flow
at Right Angled Junctions”, J. Hydraulic Engineering, 114 (12)
Sangster, W.M., Wood, H.W., Smerdon, E.T. and Bossy, H.G. (1963) “Pressure Changes at
Open Junctions in Conduits”, Proceedings, ASCE, 85
16