Combined Sewer Papereoffprint

Hydraulic design and engineeringaspects of combined sewersAyanangshu Dey PhD, CEng, MICE, MASCE, MIWAPartner, AND Engineers & Associates, Kolkata, India

Several cities of India were developed in the colonial era and provided with a combined system for sanitation and

disposal of storm run-off. Further extension of the sanitation infrastructure had to involve a combined system in order

to be consistent or address other constraints, generally congestion. For example, Kolkata receives . 1600 mm of

average yearly rainfall, mostly from July to September. Storm run-off from any catchment is estimated to be about 80

to 120 times the corresponding sewage flow. Hence, only a small portion of the conduit’s capacity is used during the

dry period constituting the majority of the time (nine months). This paper summarises the rationale behind the

general hydraulic design philosophy pertaining to the expansion of such a combined sewerage system. The approach

uses differential values of Manning’s coefficient (n) dependent on flow depth and restricts adoption of the qactual/Qfull

ratio to 1?0 to address potential surcharge condition. A reasonable and approximate procedure of hydraulic design

using a circular conduit is described thereafter utilising basic design charts and simple logic functions. Lastly, a set of

design evaluation parameters are suggested for comparison and optimisation of such hydraulic design. These

parameters, once calculated for similar designs, can be mutually compared and used as indicators to assess the level of

optimisation achieved in any particular design.

NotationD inside diameter of conduit (mm)

De equivalent diameter (mm)

Di diameter of the ith sewer

d depth of partial flow in conduit (mm)

de equivalent depth of flow (mm)

di depth of flow in ith sewer (mm)

fPU pipe utilisation factor

Ie equivalent invert level (m)

Iiav average of upstream and downstream

inverts of ith sewer

L total length of network (m)

Li length of the ith sewer (m)

n Manning’s coefficient

n9 total number of links in the network

nd Manning’s coefficient at d (depth of flow)

P ratio of total cost of supply and laying of

pipe to supply cost of pipe

Q discharge in conduit (m3/s)

Qf, Qfull full discharge in sewer conduit (m3/s)

qa, qactual partial or actual discharge in sewer conduit

(m3/s)

R hydraulic radius at partial or actual dis-

charge condition in sewer conduit

Rf hydraulic radius at full discharge condition

in sewer conduit

S slope or hydraulic gradient (given as 1 over

length, i.e. m/m)

Se equivalent slope

Si slope of the ith sewer

V velocity in conduit (m/s)

Vf, Vfull velocity at full discharge condition in sewer

conduit (m/s)

va, vactual velocity at partial or actual discharge

condition in sewer conduit (m/s).

1. Introduction

Hydraulic design of sewer systems is commonly based on the

application of Manning’s equation for open channel flow. This

equation is universally accepted and used routinely by

practising engineers all across the globe. Manning’s formulae

are used for their simplicity in design and generally satisfactory

prediction of velocity and flow at varying flow depths.

However, this application is based on the assumption of

steady-state, uniform flow conditions: a situation which is

rarely the case.

Basic expressions of Manning’s formulae for circular conduits

when flowing full are given as

1. V~1

n(3:968|10{3)D2=3S1=2

and

Municipal Engineer

Hydraulic design and engineering aspectsof combined sewersDey

Proceedings of the Institution of Civil Engineers

http://dx.doi.org/10.1680/muen.12.00055

Paper 1200055

Received 12/10/2012 Accepted 11/02/2013

Keywords: hydraulics & hydrodynamics/municipal & public

service engineering/sewers & drains

ice | proceedings ICE Publishing: All rights reserved

1

Offprint provided courtesy of www.icevirtuallibrary.com Author copy for personal use, not for distribution

2. Q~1

n(3:118|10{6)D8=3S1=2

where V is velocity (m/s), n is Manning’s coefficient of

roughness, D is the inside diameter of conduit (mm), S is

slope or hydraulic gradient (given as 1/length, i.e. m/m), and Q

is discharge (m3/s).

In the majority of cases, circular conduits are designed and

optimised for partial flow conditions. Attempts have been

made by past researchers to analyse the hydraulics of partially

filled conduits (Giroud et al., 2000; Wong and Zhou, 2003;

Zaghloul, 1998) and find out explicit solutions corresponding

to the depth of flow (Barr and Das, 1986; Esen, 1993; Giroud

et al., 2000; Saatci, 1990, 1992; Wheeler, 1992).

From the above formulae, it is observed that if the diameter

and slope (i.e. D and S) of any conduit are known, its discharge

capacity and velocity (i.e. Qfull and Vfull) under full flow

condition can be calculated immediately. However, when a

conduit has to be designed for a given flow, often referred to as

the actual flow or qactual (qa), the process of finding the exact

solution to calculate the hydraulic parameters of the conduit is

not as direct, particularly for any large combined system

collection network. Akgiray (2004) indicated that, provided the

diameter (D), slope (S), and discharge are known, iterative

calculations are required to find the hydraulic properties such

as the depth of flow (d) and corresponding velocity (v).

However, he also mentioned that, with the aid of modern

software, such iterative calculations could be completed

quickly and precisely. On finding this d/D ratio and after the

adoption of suitable values for the diameter and slope,

subsequent calculations are performed.

In all practical cases the design of any circular conduit over a

given length is required to be done to convey a previously

estimated flow, i.e. qactual. The conduit is required to be

designed and optimised to convey this flow and, hence, it is the

latter situation that any sewerage and drainage engineer has to

deal with most of the time. Furthermore, on many occasions

Manning’s formulae are applied but neglecting the variation of

Manning’s coefficient (n) with depth of flow (Benefield et al.,

1984; Metcalf & Eddy Inc., 1981). Previously, Saatci (1990,

1992) and Giroud et al. (2000) proposed solutions over the

range 0 # d # 0?938D, which removed the need to use the

iterative approach. However, their solutions did not take into

account the variation of Manning’s coefficient with the ratio of

d/D. As early as 1946, T R Camp (Camp, 1946) reported

changes in values of n with flow depth; in other words, it was

suggested that n was a function of the d/D ratio. This

phenomenon pertains to a number of factors commonly found

in sewers. These include: corrosion of the conduit above the

normal water surface, solids deposition at the bottom of sewers

during extended low flow conditions, erosion of the conduit

surface by solids contained in the flow. Recent studies by

Akgiray (2004, 2005) put forward explicit formulae for partial

flow in conduits over the entire range of flow depth, i.e.

0 # d # 1?0D taking into account both constant and variable

n values over depth of flow.

Furthermore, Escritt (1984) indicated that turbulent flow in

pipes flowing full appeared to be different from that in an open

channel, suggesting the application of Manning’s equation for

estimating the full flow capacity of a pipe was somewhat

flawed. This can be attributed to a number of differences

between a true open channel for which Manning’s variation on

Chezy’s equation is applicable and a full pipe. One specific

deviation is the availability of a free water surface which

provides for the dissipation of energy by water surface waves,

undulations and eddies. Escritt (1984) suggested that there is a

direct connection between the dissipation of energy by waves

and the water surface over which it occurs. Subsequently, he

attempted to refine the hydraulic radius of conduit flow as the

flow area over the sum of the wetted perimeter and half the

width of the air–water surface. However, Manning’s coefficient

was assumed to be constant over flow depth (d) in such

analysis. His proposed set of hydraulic properties of circular

conduits is given in Table 1 (set 3), which Escritt reported to

have been based on numerous tests on partially filled small and

large conduits. The other sets of hydraulic parameters (i.e. sets

1 and 2) for circular conduits are adopted from India’s Central

Public Health and Environmental Engineering Organisation

Manual (CPHEEO, 1993).

Instead of an iterative solution, it is preferable to have an exact

or theoretical solution which can only be solved by employing

established and commercially available software packages.

However, time and scope for such an elaborate and exhaustive

design for a combined sewer network can be limited for some

projects. Hence, an alternative yet sound engineering proce-

dure for hydraulic design needs to be devised and made

standard guidelines for designers. An approximate method

using basic hydraulic charts, tables, and design guidelines will

prove to be a reasonable alternative for use in such cases. One

such attempt using the logic function of the Microsoft Excel

software is described in subsequent sections. Certain assump-

tions are made in such an approach, making it an approximate

procedure.

2. Aspects of design philosophy

The basic philosophy of the hydraulic design of a combined

sewerage system is that it be a consistent approach which is

well-justified from a technical standpoint and at the same time

practical for adoption. The existing Manual of Sewerage and

Sewage Treatment (CPHEEO, 1993) contains the key guide-

lines to be followed by practising engineers all across India.

Municipal Engineer Hydraulic design andengineering aspects ofcombined sewersDey

2


Other publications on recent trends in sewerage system and

sewage treatment continue to be published by the Ministry of

Urban Development, Government of India, pending a revised

edition of the sewerage manual. The requirement for a

comprehensive and exhaustive review of existing guidelines

and further recommendations is currently being felt by

engineers as well. The issues that need to be addressed urgently

by a newly revised document are, material selection for sewers,

methodology for advanced sewer installation, applicability of

material and methods under varied field conditions, sewer

appurtenant works, administrative framework for project

implementation, cost recovery, assessment of economic bene-

fits, and financial aspects.

A few of the critical design aspects are discussed here in view of the

limited available information on the subject. Recommendations

are put forward on these issues by analysing previous studies and

selecting the most applicable option. These issues are believed to

be among those playing a key role in design and optimisation of a

combined system.

2.1 qactual/Qfull ratio

In a combined sewerage system, there is always a chance that

the system might operate under flooded condition. This is a

result of it being designed for a specific storm event which

produces a design storm weather flow (SWF). However, for a

majority of the time, the sewer system handles primarily

domestic wastewater flow (i.e. dry weather flow or DWF). For

these systems, the SWF is sometimes significantly larger than

corresponding DWF and dominates the design. Flooding and

subsequent surcharging due to run-off events that are greater

than that used for design, do occur at times. Such combined

systems are also prone to siltation as it would be difficult (if not

hydraulically impossible) to maintain self-cleansing velocity in

sewers during minimum flow (DWF) condition. Their opera-

tion also becomes very much dependent on periodic and

regular de-silting.

From the hydraulics of a circular conduit, maximum flow

occurs over flow depth (d) of 0?83 and 1?0D (Table 1, including

all three sets of data). The three sets of conditions (Table 1)

refer to: (1) no variation in the value of n over depth of flow;

(2) including the variation in the value of n over depth of flow;

and (3) as evaluated by Escritt (1984) by his modified definition

of hydraulic radius mentioned earlier. Over this range of flow

depth, actual discharge was found to be more than the

discharge capacity (Qf) of the conduit (i.e. qactual/Qfull . 1?0)

while flowing full. It should be noted that adoption of a

constant value of n continues to be a common practice in

design.

Considering linear interpolation between points, namely the d/D

ratio from 0?8 to 0?9, for the first two data sets in Table 1, it can

be calculated that qactual becomes equal to Qfull at d/D ratios of

approximately 0?83 and 0?88, respectively. Escritt (1984)

referred to previous estimates that indicated that, at a d/D ratio

of 0?94, qactual discharge in the conduit would be about 1?0757

times its Qfull discharge. However, on analysing Escritt’s

equation, Akgiray (2004) concluded that the ratio of qactual/

Qfull was 1?022 at a d/D ratio of 0?9728. This was the reason why

Ratio of

d/D

Set (1): for constant

n value

Set (2): for n variable with depth

of flow (d)

Set (3): values as suggested

by Escritt (1984)

va/Vf qa/Qf n/nd va/Vf qa/Qf Aa/Af va/Vf qa/Qf

1?00 1?000 1?000 1?00 1?000 1?000 1?000 1?000 1?000

0?90 1?124 1?066 1?07 1?056 1?020 0?948 1?039 0?985

0?80 1?140 0?968 1?14 1?003 0?890 0?858 1?019 0?874

0?70 1?120 0?838 1?18 0?952 0?712 0?748 0?977 0?730

0?60 1?072 0?671 1?21 0?890 0?557 0?627 0?917 0?575

0?50 1?000 0?500 1?24 0?810 0?405 0?500 0?843 0?421

0?40 0?902 0?337 1?27 0?713 0?266 0?374 0?752 0?281

0?30 0?776 0?196 1?28 0?605 0?153 0?252 0?643 0?162

0?20 0?615 0?088 1?27 0?486 0?070 0?142 0?510 0?073

0?10 0?401 0?021 1?22 0?329 0?017 0?052 0?337 0?018

d, depth of flow; D, diameter of conduit; nd, value of n at depth of flow (d); va, actual velocity; Vf, velocity at full flow in conduit; qa,actual flow; Qf, full flow in conduit; Aa, actual area of flow; Af, area at full flow in conduit.

Table 1. Tabular representation of hydraulic properties of circular

conduits


3


the same did not show up in the set 3 values of Table 1.

Adopting linear interpolation with Escritt’s values (set 3 in

Table 1), it was calculated that, at a d/D ratio of about 0?93,

qactual equals Qfull.

However, the formula for conduit flow as suggested by Escritt

does not contain any Manning’s coefficient and therefore also

ignores its variation with depth of flow. Akgiray (2004)

analysed the explicit solutions of partially flowing circular

conduits as proposed by him with three separate approaches:

constant value of n, alternative hydraulic radius suggested by

Escritt (1984), and variation of the value of n with depth of

flow (Camp, 1946). Akgiray concluded that these last two

approaches gave nearly the same results over the range

0 # d # 1?0D, giving Qfull values that were about 20–30%

less than that obtained with constant value of n and adopting

the conventional definition of hydraulic radius.

From a designer’s standpoint and incorporating some reason-

able level of approximation, it is suggested that the most

conservative approach to design of a combined sewer would be

to adopt a variable value of n (set 2 in Table 1) and at the same

time restrict qactual to Qfull ratio to 1?0; in other words putting a

ceiling of Qfull value on qactual. This argument for circular sewers

will also be applicable for ovoid sections. Bijankhan and

Kouchakzadeh (2011) showed that, for an ovoid sewer, the d

value at which qactual/Qfull 5 1?0 occurs was at 0?84D. Such a

point (qactual 5 Qfull) in the case of both circular and ovoid

sections also indicates that this point coincides with both R/Rf

(R and Rf are the hydraulic radii at flow depth d and full flow

conditions, respectively) and v/Vf (v and Vf are velocities at flow

depth d and full flow conditions, respectively) being maximum.

Such a criterion of basic sewer hydraulics might be extended for

other conduit sections; for example, elliptical, horse-shoe, and

semi-elliptical. In summary, there exists a range of flow depth in

the top portion of such conduit sections for which qactual exceeds

Qfull. Such flow estimation, apart from being relevant for new

design, is also applicable for re-sectioned circular and non-

circular conduits in sewer rehabilitation projects for conserva-

tive system planning.

Each link of sewer will then be designed to convey flows equal

to or less than their corresponding discharge capacity under

surcharge condition. This would infuse a conservative

approach to design and effective utilisation of sewers either

under flooded conditions or during maximum flow. In the

suggested procedure for hydraulic design of sewers presented

under section 3, the second set of values given in Table 1 have

been used.

2.2 Variable value of n

Literature provides only limited justification as to whether to

incorporate variation in the value of n with flow depth for

hydraulic design of a combined system under Indian condi-

tions. The current sewerage manual (CPHEEO, 1993), contains

relevant charts (Figure 1) and tables (set 1 and 2 in Table 1) for

using variations in the value of n but is silent on properly

encouraging its use and justification. As a result, it has become

a common and conventional practice to adopt a constant value

of n for design purposes and ignore the critical issue of

differential values over the range of flow depth, i.e.

0 # d # 1?0D.

For any combined system, consideration should be given to the

fact that, for the majority of the time (during dry weather),

sewage flow takes place over a small section of the combined

sewer. Actual capacity of these sewers only comes into play

during monsoon period when combined flow (DWF + SWF) is

conveyed. Hence, it would be reasonable to presume that there

would be a difference in n values of surfaces over which these

distinctively different quanta of flows occur. Hence, it is

considered logical and prudent to adopt differential values of

Manning’s coefficient for a conservative design instead of the

conventional approach of assuming constant n, all through the

conduit diameter.

2.3 Sewer transition

This is one very critical aspect to ensure proper hydraulics in

the collection network. For a specific reference, Kolkata’s

original underground combined sewerage network was devel-

oped over the years 1858 to 1875. As early as 1916, Goode

(2005) reported a serious defect in the system as sewer

transitions from smaller to larger diameters were made without

providing any drop. The branches and main sewers were built

by matching their inverts. Thus, full flow capacity of down-

stream sewers could not be fully utilised without causing a

1.00qa/Qf for constant n value

qa/Qf for variable n valueva/Vf for constant n value

va/Vf for variable n value

0.00

1.00

Hydraulic elements, va/Vf and qa/Qf

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

1.10

0.10

0.90

0.80

0.70

0.60

0.50

0.40

0.30

Rat

io o

f dep

th to

dia

met

er, d/D

0.20

Figure 1. Hydraulic-elements graph for circular sewers. (plotting

set 1 and 2 in Table 1)


4


certain amount of flooding on smaller diameter upstream

sewers.

In developing a new sewer system, transition from smaller to

larger diameters of the sewer needs to be done by matching the

top or soffits of corresponding sewers. For an extremely flat

terrain such as that in Kolkata, this practice will incur

additional invert depth as designers’ might prefer to restrict

the depth of the sewer invert up to a predetermined level to

facilitate installation. Invert matching may also arguably be

supported by prevailing soil condition, locations having acute

space constraints, or expected flooded condition causing full

flow in conduits. However, from a hydraulic standpoint it is

absolutely essential that the free-flowing water level of

branches and laterals are not restricted at junctions by the

maximum water level in main sewers, even if this calls for some

additional excavation depth.

Otherwise, when a long stretch of sewer is considered in a flat

terrain, it is pertinent to assume that its inverts would be less

over the initial stretches and gradually increase on the

downstream side. Hence, inverts of branch sewers culminating

in the main sewer over initial stretches might have to be

matched with its inverts in order to restrict the excavation

depth. However, over middle and terminal stretches, it may

very well be possible to match the soffits of sewer branches

meeting this sewer with its corresponding soffits so that

suitable hydraulic drops at these sewer junctions can be

provided (Figure 2).

Keeping such provision for incoming branches can eventually

reduce required depth of excavation and at the same time

facilitate better hydraulics at peak flow condition. Basically,

some level of physical drop at the junction of branches and the

main sewers should be kept in working out the hydraulic

design, and such design needs to be performed not by a generic

approach but by a more specific one in order to achieve

effective design.

2.4 Screening manhole

Expansion of a sewerage system into unsewered areas is usually

done in phases. Most of the time, it is observed that the

collector and interceptor sewers of any system are designed

and constructed ahead of branches, sub-laterals, and tertiary

level sewers which constitute the complete collection network.

It is likely that, when these facilities become ready for

commissioning, corresponding upstream components might

be under construction. Furthermore, in all probability,

existing surface drains, catering to drain the combined flow

from a catchment, will be connected to the newly constructed

underground sewer system to provide immediate relief to the

population from water logging. These surface drains will later

be dismantled once a permanent underground collection

network is completed.

Surface drains are mostly open over large stretches, and solid

waste is either indiscriminately dumped or street littering

eventually ends up in them. This chokes up the natural flow of

conduits during the dry season. It is clear that, if these drains

are connected to sewers without any arrangement for screen-

ing, it will inevitably clog these lines. This will disrupt natural

flow in sewers and cause severe deterioration in their carrying

capacity. This problem may become compounded over time if

this accumulated silt and waste are not regularly removed from

the sewers. In the majority of cases, a screening arrangement

cannot be provided at the outlets of the surface drains (opening

into these sewers) due to acute space constraints.

To safeguard these sewers from undesired solid waste

dumping, it is suggested that online screening be provided

inside some manholes at strategic locations. These will be

designated as ‘screening manholes’ and will house a detachable

manual screen fitted perpendicularly to the direction of flow,

an operating platform, preferably two access hatches, and

other facilities (Figure 3). The screen can be of stainless steel to

avoid corrosion under extended use. A screening manhole will

help in sewer maintenance by arresting the debris at some

specific locations, which would otherwise have been distributed

all over the length of the sewers, making its removal difficult.

The periodicity of cleaning of such manholes would depend on

the amount of debris accumulated over a stipulated time, field

conditions and might vary from one location to another.

Ground level

Access manhole

Manhole invert

Incoming sewers

Outgoing sewer

Figure 2. Typical detail of sewer transition


5


2.5 De-silting work

The development of a combined sewerage network where there

is a very large difference between estimated DWF and SWF,

would perpetually have a siltation problem. If circular conduits

are used, their dimensions are primarily selected so these are able

to convey maximum flow. This in turn eliminates the possibility

of maintaining self-cleansing velocity at nominal DWF, causing

siltation all over the dry period. Although egg-shaped brick

sewers were used during the initial stages in the late nineteenth

century (Goode, 2005), oval-shaped sewers are neither readily

available in India nor preferred by the executing agencies

responsible for procurement and other contractual issues. As

such, their use is restricted to rehabilitation of old sewers and

not in the design of new ones. Regular and adequate de-silting

becomes quite a challenge and remains the only option for

keeping the sewers in adequate serviceable conditions. This is a

continuous process and should be made exhaustive and

continued all over the year to offset the siltation problem.

3. Method statement for hydrauliccalculations

A description of the method of performing hydraulic calculations

of a gravity sewerage network is presented here. As earlier

justified, this approach uses set 2 design data (Table 1) of

hydraulic properties of circular conduits. Linear interpolation of

intermediate values given in the above table is performed to work

out ratios corresponding to intermediate values of qa/Qf and v/Vf.

A representative layout of a combined sewerage system is

shown in Figure 4. This constitutes a reasonably long and

continuous stretch of lateral or secondary sewer, a branch or

tertiary sewer converging with it, and its ultimate culmination

into a trunk (primary) sewer. This network is used to

Ground level

Access manholes

Bar screen Operating platform

Outgoing sewerIncoming sewerhf

Figure 3. Arrangement of screening manhole. hf is the total head

loss for full flow condition, provided as the drop between incoming

and outgoing manhole inverts

8

67

5

Trun

k Se

wer

4Lateral Sewer

32

1

Sub-

late

ral

Figure 4. Sample layout of a combined sewerage network


6


demonstrate sample hydraulic calculations of a gravity sewer

system ignoring other laterals and branches. The node numbers

are indicated as appropriate and referred to in the design. The

lateral sewer originates at node 1 and connects to trunk sewer

at node 7, and a branch sewer starts from node 8 and joins with

this lateral at node 4. Only a few of the strategic manholes are

shown on this layout. Intermediate manholes are omitted for

clarity; however, these are considered in the design to make it

as exhaustive as possible.

A sewer connecting an upstream manhole to a downstream one

is referred to as a link, and a sewer line comprises a collection

of several such links. The estimated flow in each link

contributed by their respective catchments were ascertained

as given. Hydraulic design of this network needs to be

performed keeping the maximum depth of sewer invert to

4?0 m due to acute space constraints, soil and groundwater

conditions, and safety of adjoining structures. Furthermore, all

individual links will be designed with a design philosophy of

qactual # Qfull, as mentioned and justified earlier.

At first for any link, diameter and slope are selected and the

resulting full discharge capacity (Qfull) and velocity (Vfull) for

that link are calculated. This is matched against the estimated

flow (qactual) that the particular link will be required to carry.

The ratio of qactual/Qfull is then calculated. From Table 1, the

corresponding values of vactual/Vfull and d/D ratios are

calculated by linear interpolation for intermediate values.

Multiplying this vactual/Vfull ratio by Vfull gives the value of

vactual. If required, the diameter is suitably selected against the

slope provided. After selecting the diameter, the slope of the

link is meticulously adjusted to meet the stipulated criterion of

qactual/Qfull # 1?0 to optimise the slope as much as possible.

Once the slope of the link has been ascertained, sewer inverts,

depths of inverts and excavation depths can be calculated.

These values and some other parameters are checked against

their permissible corresponding values (e.g. minimum clear

cover, maximum invert depth). If these are found to be

satisfactory and met certain stipulations, the design of this

particular link becomes final. However, the design can always

be reviewed later to suit either any additional requirement or

overall optimisation of the network or both. This process is

repeated for each of these links. Some decisions are also

dependent on any incoming sewer invert, its diameter, and

several other factors.

A snapshot of the proposed design output using MS Excel

(Microsoft Corporation, Redmond, WA, USA) is given in

Figure 8 (see appendix) and a step-by-step numerical sample

calculation is given in Table 3 (see appendix). Turbulence and

hydraulic losses are expected at locations where incoming flow

will be mixing with the flow in laterals, and at appurtenant

structures. However, such losses are considered to be minor

without having any significant impact on the overall hydraulics

of sewers; hence they are neglected in the design. In this

hydraulic analysis, the diameters of the sewers are defined as

the internal diameter of the RCC (reinforced cement concrete)

pipe barrel.

4. Hydraulic design of a combined systemThe design of a combined sewerage system is usually aimed at

striking the most effective balance between the diameters of the

conduits used and the depths of the sewer inverts. Direct

construction cost and indirect social cost associated with the

laying of sewers at large depths in the congested urban areas

normally found in Kolkata (or any other congested Indian

cities) are high enough to offset the material cost of the sewer

conduit. As an estimate, say ratio P depicts the ratio of total cost

of supply and laying of RCC (class NP3) pipe to the supply cost

of pipe under Kolkata conditions. Then it is calculated that, at

present, the value of ratio P can vary from 3?3 to 2?4, which

means that the complete installation cost of 300 to 1200 mm

diameter RCC sewers installed between a 1?5 and 4?5 m sewer

invert can be as high as 3?3 to 2?4 times the pipe supply cost

(Figure 5), respectively. Accordingly, in finalising any sewerage

and drainage design in congested urban areas, the diameters of

sewers are weighed against their inverts to satisfy both space

requirements for laying such sizes of sewers and also the

feasibility of construction at corresponding depths.

In handling large and complicated sewerage networks, it is

always preferable to have a link-by-link analysis for better

design control rather than have a generic approach of stipulating

certain parameters applicable to all links in the network. The

detailed hydraulic design of each link of the combined flow

network is absolutely essential as opposed to a design adopting

longer stretches (i.e. stretches with two or more links). Not only

3.0

2.0 60

40

20

0

80

100

Rat

io P

1.0

0.0

Per

cent

age

mat

eria

l cos

t

300

900

Ratio P

Sewer diamater, mm

% Material cost

800

700

600

500

400

1000

1200

1100

Figure 5. Variation of material cost and total pipe installation cost.

It is assumed that sewers #600 mm are laid within 2?5 m invert

depth and those #1200 mm within 4?5 m invert depth


7


does such a design approach determine the hydraulic properties

of all pipes and related pertinent structures, but more

importantly the entire sewerage system can be better optimised

by individual calculations for each such link.

There remains the possibility that the combined system would be

required to operate under flooded conditions. For large

differences between SWF and DWF (as in the case of

Kolkata), the combined system will primarily behave as a

drainage system. As for the hydraulics of a circular sewer,

maximum discharge occurs between 0?83D and 1?0D depth of

flow. Over this range, the actual discharge capacity is found to

be more than the discharge capacity of the same sewer under

flooded condition (i.e. qactual/Qfull 5 1?0 or qactual . Qfull),

regardless of diameter. For conservative hydraulic design,

efforts should be made during hydraulic analysis of combined

sewers to keep the qactual/Qfull ratio equal or below 1?0 for all

stretches. Hence, sewers are dimensioned to convey flows equal

to or less than their corresponding discharge capacity under full

flow condition. The difference between depth of flow and

conduit diameter provides a minor amount of ‘safety’ margin

and some amount of sewer ventilation. This would ensure

effective utilisation of sewers under a flooded condition

conveying the maximum flow.

In developing this design, minimum clear cover over pipe barrels

is kept at 1?0 m as stipulated by the sewerage manual

(CPHEEO, 1993) and suitable protection needs to be provided

if this becomes less. The invert of starting manhole at node 1 has

to be adequately low to ensure proper draining of its catchment.

Furthermore, the maximum depth of the invert is restricted to

4?0 m in view of space constraints and to safeguard existing

buildings in close proximity to the alignment. Each link is a

separate hydraulic element and designed to convey its estimated

flow against these stipulated hydraulic criteria. Minor losses at

junctions and drops are assumed to be negligible.

This layout thus represents a small portion of a large network, yet

the same design procedure is applicable following a part-to-whole

design approach. For this lateral, at first tentative but fair

estimates of diameters and slopes in various stretches are made.

The resulting minimum cover and depth of inverts are checked

against the stipulated values. Then, fine tuning of the design is

carried out by meticulously adjusting the slope of every link to

make it just enough to match the qactual/Qfull ratio of #1?0 as much

as possible and practicable while adhering to other conditions.

Later, the same approach is repeated to design the branch sewer.

Hydraulic design of any sewerage network can be optimised

following this procedure. This applies to smaller and even large

and more complicated networks as well. The single longest

stretch of main sewer is designed first and its hydraulics is

worked out. Subsequently, all its laterals and branches can be

taken up one by one to work out their design in reverse as the

inverts of these branches (at their connecting points on the

main sewer) become available as soon as the inverts of the

main sewer are calculated. Hence, the hydraulics of the laterals

and branches can effectively be calculated backwards. Fine-

tuning and minor adjustments to suit the site conditions and

any specific design requirements can always be done later

taking one particular stretch at a time.

5. Hydraulic design evaluation parameters

Hydraulic design of a gravity sewer system fundamentally

attempts to optimise the diameters of conduits and their invert

depths. The basic factor dictating such optimisation is the fact

that the material cost of the conduit is found to be nominal in

comparison with its installation cost at the design invert depth.

Several other factors also play critical roles in developing the

design philosophy: for example, defining the correct flow,

maximum depth of invert, groundwater table, space con-

straints, attainment of self-cleansing velocity, sewer ventila-

tion, possible flooding condition, environmental aspects, and

social issues.

Once the hydraulic design of any gravity system has been

finalised, it is necessary to ascertain not only whether all design

considerations were duly satisfied but also to what extent they

were met. This would eventually lead to comparative analysis

of that design with some stipulated parameters or if required

with some other similar designs. A set of such evaluation

parameters have been worked out; in the following subsections

they are proposed and elaborated for such an assessment.

5.1 Equivalent diameter

Different diameters adopted in various stretches of the network

have been reduced to a parameter referred to as the equivalent

diameter (De). It is the summation of individual diameters of

stretches with their corresponding lengths over total length of

network and is expressed by

3. De~1

L

Xn

i~1

DiLi

where De is the equivalent diameter (mm), L is the total length

of the network (m), n is the total number of links in the

network, Di and Li are the diameter and length of the ith sewer,

respectively.

The equivalent diameter can be regarded as a measure of

diameter optimisation for any network design. In any given

network, for two separate hydraulic designs (done as per

minimum and maximum depth of invert criteria) two

corresponding values of De can be calculated. A lower value

of De would indicate that particular design is better optimised


8


from the standpoint of using lower conduit diameters under

the same design criteria.

5.2 Pipe utilisation factor

The pipe utilisation factor (fPU) is the ratio of the equivalent

depth of flow (de) and the equivalent diameter (De), given by

the following expression

4. fPU~de

De

with De and de measured in millimetres. The equivalent depth

of flow (de), like De, is the summation of the depth of flows in

individual stretches multiplied by their corresponding lengths

divided by the total length of the network and is given by

5. de~1

L

Xn

i~1

diLi

where di is depth of flow (mm) in the ith sewer. The various

depths of flow in different sewers are thus condensed to a single

depth of flow (de).

When the sewer diameters and their flow depths are reduced to

single values of De and de, then based on the previously presented

justification, the pipe utilisation factor, fPU, should be adjusted to

approach 0?88 (see Table 1, set 2, at d/D 5 0?88, qactual 5 Qfull

for variable n value) but never allowed to cross this value for

conservative design. Furthermore, in evaluating the hydraulic

design of the system, the depth of flow in each hydraulic element

or sewer is meticulously adjusted by altering its slope to bring it

as close as possible to this value, namely d/D 5 0?88. The

closeness of this parameter to that value will indicate both the

level of design optimisation and also its conservativeness from

the standpoint of possible surcharge in the system.

5.3 Equivalent slope

The slope provided in the sewers is given in 1/length format, for

example, 1/100 or 0?01 or 1%. The different slopes provided in

stretches of any network are reduced to an equivalent slope

(Se) that is expressed as

6. Se~1

L

Xn

i~1

SiLi

Evaluation parameter Design 1 Design 2 Remarks

Equivalent diameter, De: mm 945 850 Higher value indicates high equivalent

diameter of sewer used in design signifying

higher cost of pipe procurement. In this

case, design 2, having lower De value, is

concluded to have used less pipe diameter

than design 1.

Pipe utilisation factor, fPU 0?76 0?87 Proximity of this value to 0?88 would

indicate how efficiently proposed pipe

diameters are utilised. Here, design 2,

having approached this value more,

becomes a preferred design over 1.

Equivalent slope of invert, Se 1 in 962 (0?00104) 1 in 614 (0?00163) Higher value of Se is an indication of

increased excavation and pipe laying cost.

Higher value for design 2 also alludes to

higher Ie as calculated below.

Equivalent depth of invert, Ie: m 2?389 2?761 This value needs to be weighed against the

first parameter value. A lower value of this

parameter will indicate less excavation cost.

Stipulated maximum depth of invert was

4?0 m. Marginal increase in Ie (for design 1)

will result in significant savings in pipe

material cost, hence to be selected.

Table 2. Comparison of hydraulic designs


9


where Si and Li are the slope and length of the ith sewer,

respectively.

A lesser equivalent slope of two similar hydraulic designs

would signify a reduced depth of invert for the corresponding

one. Understandably though, this parameter will be inversely

proportional to equivalent diameter (De) and directly propor-

tional to the next parameter, equivalent invert (Ie).

5.4 Equivalent invert depth

Similar to the above parameter, equivalent invert level (Ie) can

be calculated as

7. Ie~1

L

Xn

i~1

LiIavi

where Ie is the equivalent depth of the sewer invert (m), Li is the

length of the ith sewer, and Iavi is the average of the upstream

and downstream inverts of the ith sewer.

This is also a comparison parameter and the greater the value,

the steeper is the equivalent slope of the network, signifying

higher excavation. This parameter will be inversely propor-

tional to the equivalent diameter (De) and directly proportional

to the previous parameter, equivalent slope (Se), as mentioned

earlier.

Separate designs of the same network can be evaluated by

comparing these parameters. A single design can be adjusted to

make these parameters converge to stipulated values for

optimisation. This process can be extended to compare the

design of two separate networks which are similar with regard to

existing terrain, development pattern, design philosophy, soil

conditions, and so on. An example showing the usefulness of

these parameters for comparative analysis is given in Table 2.

Here, two separate designs of a single network are now compared

in the light of suggested evaluation parameters. The network is

about 7 km in length comprising main sewers, laterals and

branches, with given flows in every link. The network is a

reasonably representative sample for such a comparative analysis.

The terrain is generally flat with ground levels varying within 1?5

to 2?0 m across 1 km. Minimum clear cover (1?0 m) and

maximum invert depth (4?0 m) criteria are same for this design,

which forms the basis of comparison. Evaluation parameters are

given in Table 2 and compared, and adoption of a better design

option is justified in terms of these parameter values.

6. Conclusions

A meaningful and relevant hydraulic design philosophy to be

adopted for a combined sewerage network is discussed above.

This directly relates to and takes cognisance of previous studies

done in analysing the hydraulics of partially flowing circular

conduits. Furthermore, the theoretical and practical design

considerations proposed here can very well be applicable for

designing sewerage and drainage infrastructure for cities with

similar physical and historic settings in India and inter-

nationally, and can also be extended to sewer rehabilitation

works. The following critical issues for hydraulic design of a

combined sewerage network were identified.

& Variation of Manning’s coefficient with flow depth needs to

be considered specifically for combined flow as it would be

justified to consider variable n value in conduits conveying

two very different quanta of flows over corresponding

periods of their occurrence. Use of applicable hydraulic

charts should be made mandatory for a conservative design

approach.

& Regardless of diameter, hydraulic design of a gravity sewer

system should be done restricting qactual/Qfull ratio to equal

or be below 1?0 for all sewers under consideration.

Hydraulic calculations are required to be performed

adopting charts for an n value varying with flow depth and

over a range of d/D ratio from 0?1 to 0?88. This ceiling in

adoption of flow depth will provide sewer ventilation and

more importantly a minor amount of ‘safety’ on account of

actual flow deviations from estimated figures, possible

siltation in the sewer, and actual construction slope. This

will also ensure effective utilisation of sewers under flooded

conditions during maximum flow. Such a stipulation is also

applicable for non-circular sewer hydraulics and finds its

relevance when century-old non-circular brick sewer reha-

bilitation works are undertaken in colonial cities with

combined drainage systems (Figure 6).

& Sewer transition by matching the soffit levels of corre-

sponding sewers (and definitely not inverts) and the

introduction of online screening manholes at strategic

locations will prove to be useful to ensure better system

hydraulics and facilitate future maintenance of the system,

respectively.

& A set of evaluation parameters have been suggested to

compare similar hydraulic designs of combined sewers with

an aim to standardising such designs, for example,

equivalent diameter (De), pipe utilisation factor (fPU), and

equivalent invert depth (Ie) being the most important ones.

These parameters can very well assess the efficiency of a

hydraulic design produced by comparing these with pre-

determined values or corresponding parameter values of

similar and comparable designs. Such an optimisation

approach is pertinent for any gravity sewer network system.

A reasonably practical and complete procedure for hydraulic

design of a combined sewerage system has been described.

Such calculations are based on design philosophy as described

above. Although approximate, the assumptions are rational

and based on standard hydraulic charts and guidelines. This


10


can prove to be useful for designing and detailing either

combined or separate gravity sewer networks.

Faulty, inconsistent and ad hoc design concepts and con-

siderations can potentially jeopardise the philosophy and basic

engineering of sewer hydraulics and subsequent operation of

such an extremely important infrastructure facility especially

under the Indian scenario. This can potentially give rise to

optimistic and under-designed drainage system leading to

flooding of streets (Figure 7). Sewerage and drainage infra-

structure development needs to be carried out following a

standard set of design parameters and specially stipulated

guidelines. Procedures and parameters should be available to

assess the efficacy of design against some standard preset

values. This will eventually ensure consistency in design and

response of various systems under operation. This current

paper is an attempt towards that direction.

AcknowledgementThe author would like to extend his sincere appreciation to

Professor Dr Omer Akgiray (Department Head, Department

of Environmental Engineering, Marmara University, Istanbul,

Turkey), Professor Dr Dennis D. Truax (Department Head,

Department of Civil and Environmental Engineering,

Mississippi State University, USA), Nilangshu Bhusan Basu

(Principal Chief Engineer, Department of Planning and

Development, Kolkata Municipal Corporation, India) and

Parthajit Patra (Consultant, Asian Development Bank) for

their encouragement and support. The contribution of the

author’s past colleagues in development of the hydraulic design

model for sewers in MS Excel is gratefully acknowledged.

Appendix 1

Sample calculations with numerical example

A combined sewer system is designed to carry the combined

flow of SWF and peak DWF. In this hydraulic analysis,

diameters of sewers have been adopted as internal diameter of

the barrel of the RCC pipe, with an n value of 0?013. Columns

in Figure 8 are numbered serially and values given in these

columns for the highlighted row were worked out as a

numerical sample calculation. Table 3 shows sample hydraulic

calculations for a combined sewerage network.

Figure 6. Brick sewer rehabilitation by glass-reinforced plastic

lining. Photograph: courtesy of the Department of Planning and

Development, Kolkata Municipal Corporation

Figure 7. Typical flooding of manhole in urban area. Photograph:

courtesy of the Department of Planning and Development, Kolkata

Municipal Corporation


11


Des

ign

flow

, m

3 /s

Upstream

Downstream

Sewage

Storm Run-off

Upstream

Downstream

"qactual"

Upstream

Downstream

Upstream

Downstream

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

11

1/1

0.1

386.

35.

265

5.38

00.

390

700

550

180.

395

1.03

0.98

81.

070.

8861

33.

500

3.46

71.

765

1.91

32.

050

0.98

01/

11/

11/

20.

138

4.4

5.38

05.

573

0.38

870

055

019

0.39

51.

030.

983

1.07

0.87

610

3.46

73.

433

1.91

32.

140

2.19

81.

128

1/2

1/2

1/3

0.2

391.

65.

573

5.61

20.

396

700

530

110.

402

1.05

0.98

31.

090.

8761

03.

433

3.41

22.

140

2.20

02.

425

1.35

51/

31/

31/

40.

238

9.5

5.61

25.

955

0.39

470

053

021

0.40

21.

050.

978

1.09

0.87

607

3.41

23.

372

2.20

02.

583

2.48

51.

415

1/4

1/4

1/5

0.4

398.

95.

955

6.18

90.

403

700

510

110.

410

1.07

0.98

31.

110.

8761

03.

372

3.35

12.

583

2.83

82.

868

1.79

81/

51/

51/

60.

942

9.8

6.18

96.

310

0.43

570

045

016

0.43

71.

130.

996

1.19

0.88

617

3.35

13.

315

2.83

82.

995

3.12

32.

053

1/6

1/6

1/7

0.9

428.

66.

310

6.11

20.

434

700

450

120.

437

1.13

0.99

31.

190.

8861

63.

315

3.28

92.

995

2.82

33.

280

2.21

01/

71/

72

1.3

449.

16.

112

6.38

30.

455

700

400

130.

463

1.20

0.98

21.

250.

8761

03.

289

3.25

62.

823

3.12

73.

108

2.03

82

22/

11.

344

7.2

6.38

36.

028

0.45

380

082

017

0.46

20.

920.

981

0.96

0.87

696

3.15

63.

135

3.22

72.

893

3.52

22.

332

2/1

2/1

2/2

1.8

475.

06.

028

6.16

50.

482

800

740

210.

486

0.97

0.99

01.

010.

8870

23.

135

3.10

72.

893

3.05

83.

188

1.99

82/

22/

22/

32.

048

1.9

6.16

55.

898

0.48

980

072

013

0.49

30.

980.

991

1.02

0.88

702

3.10

73.

089

3.05

82.

809

3.35

32.

163

2/3

2/3

2/4

2.3

502.

65.

898

6.07

70.

510

800

650

180.

519

1.03

0.98

31.

070.

8769

73.

089

3.06

12.

809

3.01

63.

104

1.91

42/

42/

42/

52.

350

0.1

6.07

75.

435

0.50

880

066

021

0.51

51.

020.

986

1.07

0.87

699

3.06

13.

029

3.01

62.

406

3.31

12.

121

2/5

2/5

2/6

3.3

554.

45.

435

5.38

70.

563

800

540

140.

569

1.13

0.99

01.

180.

8870

13.

029

3.00

32.

406

2.38

42.

701

1.51

12/

62/

62/

73.

656

5.1

5.38

75.

287

0.57

480

052

016

0.58

01.

150.

990

1.20

0.88

702

3.00

32.

973

2.38

42.

314

2.67

91.

489

2/7

2/7

33.

757

1.5

5.28

75.

332

0.58

180

051

018

0.58

61.

160.

992

1.22

0.88

703

2.97

32.

937

2.31

42.

395

2.60

91.

419

33

3/1

3.8

575.

15.

332

5.63

70.

585

900

950

210.

588

0.92

0.99

50.

970.

8879

32.

837

2.81

52.

495

2.82

22.

795

1.49

53/

13/

13/

23.

857

2.4

5.63

75.

660

0.58

290

095

021

0.58

80.

920.

991

0.96

0.88

790

2.81

52.

793

2.82

22.

867

3.12

21.

822

3/2

3/2

3/3

4.4

599.

85.

660

5.90

60.

610

900

860

330.

618

0.97

0.98

81.

010.

8878

82.

793

2.75

52.

867

3.15

13.

167

1.86

73/

33/

33/

44.

459

6.9

5.90

65.

265

0.60

790

086

022

0.61

80.

970.

983

1.01

0.87

785

2.75

52.

729

3.15

12.

536

3.45

12.

151

3/4

3/4

3/5

4.6

603.

85.

265

5.06

90.

614

900

860

210.

618

0.97

0.99

51.

010.

8879

32.

729

2.70

52.

536

2.36

42.

836

1.53

63/

53/

53/

64.

660

1.4

5.06

95.

218

0.61

290

086

018

0.61

80.

970.

991

1.01

0.88

790

2.70

52.

684

2.36

42.

534

2.66

41.

364

3/6

3/6

45.

765

8.1

5.21

85.

169

0.66

490

071

016

0.68

01.

070.

977

1.11

0.87

780

2.68

42.

661

2.53

42.

508

2.83

41.

534

2.96

14

44/

19.

887

8.6

5.16

94.

597

0.89

710

0070

026

0.90

71.

150.

990

1.20

0.88

877

2.56

12.

524

2.60

82.

073

2.92

31.

493

4/1

4/1

4/2

9.9

878.

14.

597

5.27

30.

897

1000

700

270.

907

1.15

0.98

91.

200.

8887

62.

524

2.48

62.

073

2.78

72.

388

0.95

84/

24/

24/

39.

987

7.7

5.27

35.

178

0.89

710

0070

026

0.90

71.

150.

989

1.20

0.88

876

2.48

62.

448

2.78

72.

730

3.10

21.

672

4/3

4/3

4/4

10.1

881.

95.

178

5.29

90.

901

1000

700

290.

907

1.15

0.99

41.

210.

8888

02.

448

2.40

72.

730

2.89

23.

045

1.61

54/

44/

44/

510

.489

1.3

5.29

95.

334

0.91

110

0068

017

0.92

01.

170.

990

1.22

0.88

877

2.40

72.

382

2.89

22.

952

3.20

71.

777

4/5

4/5

4/6

11.1

924.

75.

334

5.16

20.

945

1000

640

340.

948

1.21

0.99

71.

260.

8888

22.

382

2.32

92.

952

2.83

33.

267

1.83

74/

64/

64/

711

.493

3.9

5.16

25.

410

0.95

510

0062

025

0.96

31.

230.

991

1.28

0.88

878

2.32

92.

289

2.83

33.

121

3.14

81.

718

4/7

4/7

4/8

11.6

942.

45.

410

5.41

50.

964

1000

610

250.

971

1.24

0.99

21.

290.

8887

92.

289

2.24

83.

121

3.16

73.

436

2.00

6

Depth of Flow, mm

Clear cover above Pipeline, m

Incoming Invert, m

Depth of Excavation, m

Dep

th o

f Inv

ert,

m

Qfull "Q" in m3/s

Vfull (m/sec) "V"

Sew

er In

vert

Le

vel,

m

Ratio of qactual/Qfull

Vactual (m/sec) "v"

Link

Man

hole

Gro

und

Leve

l, m

Diameter, mm

Slope 1 in

Length, m

Estim

ated

Flo

w,

lps

Ratio of "d/D"

Fig

ure

8.

Snapsh

ot

of

the

pro

pose

ddesi

gn

outp

ut

usi

ng

MS

Exc

el


12


Column

no. Information/calculations

(1) 3/6 the no. of the link

(2) 3/6 is upstream manhole/node no.

(3) 4 is downstream manhole/node no.

(4) estimated peak sewage flow for this link is 5?7 l/s

(5) estimated storm water run off for this link is 658?1 l/s

(6) 5?218 m is existing ground level at manhole 3/6

(7) 5?169 m is existing ground level at manhole 4

(8) design flow for this link is calculated by adding columns (4) and (5) 5 5?7 + 658?1 5 663?8 l/s < 0?664 m3/s

(9) diameter of sewer (D) adopted is 900 mm

(10) slope of sewer is taken as 1 in 710

(11) length of this link is 16 m

(12) full capacity of sewer is calculated as Qfull 5 (1/0?013)(3?118 6 1026)(9008/3)(1/710)1/2 5 679?6 l/s < 0?680 m3/s

(13) velocity at full flow is calculated as Vfull 5 (1/0?013)(3?968 6 1023)(9002/3)(1/710)1/2 5 1?068 m/s < 1?07 m/s

(14) ratio of qactual and Qfull is calculated as qactual/Qfull 5 0?664/0?680 5 0?977

(15) from Table 1, ratio of Vactual/Vfull, corresponding to the calculated value of qactual/Qfull (i.e. 0?985), is worked out as

follows considering linear interpolation between terminal values, Vactual/Vfull 5 [1?056 2 (1?020 2 0?977)

{(1?056 2 1?003)/(1?020 2 0?890)}] 5 1?038; this ratio is then multiplied by the value of Vfull in column (13) to obtain

Vactual 5 1?038 6 1?068 5 1?112 m/s < 1?11 m/s

(16) from Table 1, ratio of d/D, corresponding to the calculated value of qactual/Qfull (i.e. 0?985), is worked out as follows

considering linear interpolation between terminal values, d/D 5 [0?90 2 (1?020 2 0?977){(0?90 2 0?80)/

(1?020 2 0?890)}] 5 0?867 < 0?87

(17) depth of flow (d) is calculated by multiplying this value with sewer diameter in column (9)

d 5 0?867 6 900 5 780 mm

(18) upstream sewer invert is calculated similarly in previous row as 2?684 m

(19) downstream sewer invert is calculated by deducting the drop between two terminal manholes of this link from

upstream invert as in column (18) 5 2?684 2 (16/710) 5 2?661 m

(20) depth of upstream invert is worked out by deducting value in column (18) from existing ground elevation in column (6)

5 5?218 2 2?684 5 2?534 m

(21) depth of downstream invert is worked out by deducting value in column (19) from existing ground elevation in column

(7) 5 5?169 2 2?661 5 2?508 m

(22) depth of excavation for upstream manhole is calculated by adding pipe thickness (100 mm), thickness of PCC cradle

below pipe barrel (125 mm), and depth of brick flat soling (75 mm) to depth of invert as found in column (20)

5 2?534 + 0?100 + 0?125 + 0?075 5 2?834 m

(23) clear cover over pipe barrel is calculated by deducting pipe diameter in column (9) and pipe thickness (100 mm) from

depth of upstream sewer invert as in column (18)

5 2?534 2 0?900 2 0?100 5 1?534 m

(24) invert level of incoming sewer converging to this manhole 4 is 2?961 m

Table 3. Step-by-step numerical sample calculation


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