The document discusses estimating the quantity of sewage that will flow through sewer pipes. It is theoretically equal to the water supply but there are additions and subtractions in practice. Additions include unaccounted private water sources and infiltration of groundwater into sewer pipes. Subtractions include water used for purposes other than sewage like watering gardens. The design sewage quantity is estimated by considering factors like population growth rates and per capita water consumption rates. Peak sewage flows also need to be estimated to size sewer pipes appropriately.

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1. INTRODUCTION TO SANITATION & SANITARY ENGINEERING
Objective of the chapter
At the end of successful completion, one can;
I. Identify the difference between conservancy and water carriage system of sanitation
II. Classify potential sources of wastewater
III. Know the systems of sewerage
IV. Identify the relative advantages and disadvantages of different sewerage systems
V. Identify component parts of wastewater collection system and
VI. Plan economically feasible sewerage system
1.1. Systems of Sanitation
The waste products of a society including the human excreta had been collected, carried and
disposed of manually to a safe point of disposal, by the sweepers, since time immemorial. This
primitive method of collecting and disposing of the society's wastes has now been modernized
and replaced by a system, in which these wastes are mixed with sufficient quantity of water and
carried through closed conduits under the conditions of gravity flow. This mixture of water and
waste products, popularly called sewage, thus automatically flows up to a place, from where it is
disposed of, after giving it suitable treatments; thus avoiding the carriage of wastes on heads or
carts.
The treated sewage effluents may be disposed of either in a running body of water, such as a
stream, or may be used for irrigating crops. This modern water-carried sewerage system has
completely replaced the old conservancy system of sanitation in the developed countries like
U.S.A. However, India being a developing country, still uses the old conservancy system at
various places, particularly in her villages and smaller towns. The metropolitan cities and a few
bigger towns of different countries, no doubt, have generally been equipped with the facilities of
this modern water carriage sewerage system.
The modern water-carried sewerage system is preferred to the old. Conservancy system, because
of its following advantages:
(i) The water carriage system is more hygienic, because in this system, the society's
wastes have not to be collected and carried in buckets or carts, as is required to be
done in the conservancy system. The free carriage of night soil in carts or as head load,
which is required in the conservancy system, may pose health hazards to The term
sewerage is applied to the art of collecting, treating and finally disposing of the
sewage. sweepers and other residents, because often possibilities of flies and insects
transmitting disease germs from these accessible carts to the resident's foods and

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eatables ; whereas, in modern sewerage system, no such danger exists, because the
polluted sewage is carried in closed conduits, as soon as it is produced.
(ii) In the conservancy system, the waste products are generally buried underground,
which may sometimes pollute the city's water supplies, if the water supply pipes
happen to pass through such areas or the wells happen to draw water through such
areas.
(iii) In the conservancy system of sanitation, the entire day's human feces are collected and
then disposed of in the morning, once a day, thus, from this type of latrines, pungent
smells may continue to pollute the surroundings for the entire day. But since in the
water, carried system, the human excreta is washed away as soon as it is produced, no
such bad smells are produced. Moreover, in the conservancy system of sanitation, the
waste waters from bath rooms, wash basins, kitchen sinks, etc.; is carried through open
road side drains, as this is supposed to be not so foul, since it does not contain human
excreta. But these road side drains are generally abused by children or adults for
passing their stools, particularly at night hours, thus creating foul and more unhygienic
conditions. No such problems exist in the water carriage system.
(iv)In water carriage system, the sewage is carried through underground pipes (popularly
called sewers) which owing to their being underground, do not occupy floor area on
road sides or impair the beauty of the surroundings. The road side drains carrying foul
liquid in the conservancy system, will no doubt pose such problems.
(v) The water-carried system may allow the construction of latrines and bath-rooms
together [popularly called water-closets (W.C)], thus occupying lesser space with their
compact designs. This system is also very helpful for multistoried buildings, where the
toilets, one above the other, can be easily constructed, and connected to a single
vertical pipe.
Inspire of these advantages of the modern water-carried system, it has not been possible to
completely replace the old conservancy system, mainly because huge capital funds are required
for the construction of such a system. Besides the huge initial investments, the MO expenses are
also high, which make it difficult to replace the simpler and cheaper conservancy system.
Moreover, for the functioning of sewerage system, ample amount of water must be made
available to the people, and hence, reliable and assured water supply must, first, be installed,
before installing the sewerage system.
1.2. Types and Sources of Sewage and Sewerage Systems
This modern water carriage sewerage system not only helps in removing the domestic and
industrial wastewaters, but also helps in removing storm water drainage. The run off resulting
from the storms is also sometimes carried through the sewers of the sewerage system, or more
generally is carried through separate set of drains (open or closed) directly discharging their
drainage waters into a body of water, such as a lake or a river. Since the rain run-off is not as

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foul as the sewage is, no treatment 'is generally required to be given to the drainage discharge.
When the drainage is taken along with sewage, it is called a combined system; and when the
drainage and sewage are taken independently of each other through two different sets of
conduits, it is called a separate system. Sometimes, a part of drainage water, especially that
originating from the roofs or paved courtyards of buildings, is allowed to be admitted into the
sewers ; and similarly sometimes, the domestic sewage coming out from the residences or
institutions, etc., is allowed to be admitted into the drains, the resulting system is called a
partially separate system.
Strictly speaking, it is generally advantageous and economical to construct a 'separate system' at
least in the bigger cities and towns. But in practice, it is generally not possible to attain a 'truly
separate system' because some rain water may always find its way into the sewers either through
wrong house sewer connections or through open manhole covers. Similarly, wherever the
authorities find insufficient sewer capacities, they divert part of the sewage into the storm water
drains, thus making most of our existing systems as 'partially separate' only.
Domestic sewage consists of liquid wastes originating from urinals, latrines, bathrooms, kitchen
sinks, wash basins, etc. of the residential, commercial or institutional buildings. This sewage is
generally extremely foul, because of the presence of human excreta in it.
Industrial sewage consists of liquid wastes originating from the industrial processes of various
industries, such as Dyeing, Paper making, brewing, etc. The quality of the industrial sewage
depends largely upon the type of industry and the chemicals used in their process waters.
Sometimes, they may be very foul and may require extensive treatment before being disposed of
in public sewers.
The sum total of domestic and industrial sewage may be termed as sanitary sewage or simply
sewage.
The run-off resulting from the rain storms was used to be called storm sewage, but the modern
approach is to call it storm drainage or simply drainage, so as to differentiate it from sewage,
which is much fouler as compared to drainage, and requires treatment before disposal
In the modern days, separate system is generally preferred to a 'combined system', although each
individual case should be decided separately on merits, keeping the following points into
consideration:
a) A separate system will require laying two sets of conduits, whereas, a combined system
required laying only one set of bigger sized conduits, thus making the former system
costlier. Moreover, the separate conduits cannot be laid in congested streets and
localities, making it physically unfeasible.
b) The sewer pipes in the combined system are liable to frequent silting during the non-
monsoon season (when the flows in them are quite less) unless they are laid at

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sufficiently steeper slopes, which, in turn, will make them deeper, requiring more
excavation and pumping, thereby making them costlier.
c) In a combined system, the less-foul drainage water gets mixed with the highly foul
sewage water, thus necessitating the treatment of the entire flow, needing more capacity
for the treatment plant, thereby making it costlier. Whereas, in the separate system only
sewage discharge is treated and the drainage discharge is disposed of without any
treatment
d) In case, flooding and backing up of sewers or drains occur due to excessive rains, more
foul and insanitary conditions will prevail in case of combined sewage than in the case of
storm drainage alone.
e) Since the sewer lines are generally laid deep and at steeper slopes, as compared to storm
water surface drains, pumping of sewage and often no pumping of drainage is required in
a separate system. Whereas, the entire discharge will have to be pumped if the sewage
and drainage discharges are mixed together; thereby making the combined system more
costly.
f) The economy of the two systems must be worked out for each individual project, and the
economical system should be adopted, if it is physically feasible.
1.3. Components of a Sewerage System
A sewerage system consists of a network of sewer pipes laid in order to carry the sewage from
individual homes to the sewage treatment plant. This network of sewers may consist of house
sewers (or individual house connections); lateral sewers; branch sewers (or sub mains); main
sewers (generally called trunk sewers); outfall *Since heavy rain storms concentrated for a
period of 3 months or so do occur, and there are poor water supplies here in India, the ratio of the
drainage to sewage works out to be as high as 20 to 30. Thus, during non-monsoon periods, only
1/20th or 1/30th of the designed discharge will be passing through the sewers, if the combined
system has been adopted. Sewer (the sewer which transports sewage to the point of treatment)
Manholes are provided in every sewer pipe at suitable intervals, so as to facilitate their cleaning
and inspection. In the sewers, which carry the drainage discharge either solely or in combination'
with sewage, inlets called catch basins are provided to permit entrance of storm water from street
gutters. In order to avoid the large scale pollution of the water sources and to keep them usable
for the downstream people, the original contaminated sewage is not allowed to be discharged
directly into the water sources. A complete treatment including screening sedimentation,
biological filtration (or activated sludge treatment), sludge digestion, etc. is therefore, given to
this extremely foul sewage, so as to bring down its BOD and concentrations of other constituents
to safer values, before discharging it into a national river resource. However, a recent use of
sewage is being made for irrigating crops. For this use also, the sewage has to be treated, so as to
bring down its constituents to permissible values, as per the requirements of LS. 3307-1965.
All these aspects are explained in details in subsequent chapters.

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1.4. Design and Planning of a Sewerage System
The sewerage system must be properly and skillfully planned and designed, so as to remove the
entire sewage effectively and efficiently from the houses, and up to the point of disposal. The
sewers must be of adequate size, so as to avoid their overflow and subsequent damages to
properties and health hazards. In order to provide economically adequate sized sewers, it is
necessary that the likely sewage discharge be estimated as correctly as possible. The sewer pipes
should then be designed to be laid on a slope that will permit reasonable velocity of flow. The
flow velocity should neither be so large, as to require heavy excavation and high lift pumping;
nor should it be so small, as to cause the deposition of solids in the sewer, bottoms.
The sewers are generally designed to carry the water from the basements, and should therefore,
be at least 2 to 3 m deep. As far as possible, they should be designed to flow under gravity with
1/2 or 3/4 full. Owing to the requirements of seeking gravity flow, the sewage treatment plant
should generally be located in a low lying area. The design of the treatment units also requires
good engineering skill. In order to provide adequate and economical treatment, it is necessary to
thoroughly study the constituents of the sewage produced in the particular project, and also the
quality and other characteristics of the body of water that will receive the sewage. The
permissible standards for effluents, and the possible uses of water downstream, should also be
studied. The legal bindings, if any, will also have to be taken into consideration, while deciding
upon the quantum of treatment required to be given. No fixed standards can be laid for fixing this
required treatment, as everything depends upon the exigencies of a particular project.
Since the treatment plant will have to be located at low level; the flood protection devices both
during construction and thereafter, should also have to be taken care of, by the design engineers.
SUMMARY
Systems of sanitation are Conservancy & water carriage the former is very old and non hygienic
where as water carriage system is hygienic and wastewater is conveyed to a central wastewater
treatment plant this can be separate, combined or partially separate. Each of the conveyance
systems has its own advantage and disadvantage attached to the way it functions. The potential
wastewater generation sources are residencies, industries commercial centers and institutions.
Sewerage system starts from this different sources and along the longitudinal direction to flow it
can have components like Manhole, drop manhole, clean-out street inlets etc. the more it
includes components and facilities based on the type of topography where sewerage is to be
constructed can make it the more expensive to implement.

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Activity Questions
1. Describe conservancy and water-carriage systems. What are the relative advantages and
disadvantages of the two systems?
2. Discuss briefly the necessity of replacing the conservancy system by the Water carriage
system of sanitation
3. Discuss the relative merits of the separate and the combined systems of sewage, and give
the conditions favorable for the adoption of each one of them
4. Differentiate between;
a) domestic industrial and sanitary sewage
b) combined and separate systems of sewage
c) sewage and drainage
5. Write short notes
(i) Financing the sewage projects
(ii) Types of sewages
(iii) Systems of sewerage

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2. DESIGN SEWAGE QUANTITY ESTIMATION
Objective of the chapter
At the end of successful completion, one can;
 Understand how to quantify sanitary sewage
 Identify the constraints that can affect design period of sewerage system
 Understand how to estimate waste generation rate and its timely fluctuations
 Precisely select the empirical relation to estimate peak drainage discharge
2.1. Estimating Dry-whether flow
The sewage discharge which has to pass through a sewer must be estimated as correctly as
possible; otherwise the sewers may either prove to be inadequate, resulting in their overflow, or
may prove to be of too much of size, resulting in unnecessary wasteful investments.
Theoretically speaking, the quantity of sewage (i.e., domestic sewage + industrial sewage) that is
likely to enter the municipal sewers under design should be equal to the quantity of water
supplied to the contributing area, from the water-works. But in actual practice, this is not the
precise quantity which appears as sewage, but certain additions and subtractions do take place
from it, as explained below:
1) Additions due to unaccounted private water Supplies
The accounted water supplied to the public through the public distribution system (the records of
which are easily available from the water-works office), is not necessarily the only water
consumed by the public. Some private wells and tube wells may sometimes be used by the public
for their domestic needs; and similarly, certain industries may utilize their own sources of water.
This extra quantity of water used by the town is generally small, unless there are large industrial
private water uses. This quantity can, however, be estimated by actual field observations.
2) Additions due to infiltration
Whenever, the sewer pipes are laid below the ground water-table, certain amount of ground
water generally seeps into them, through their faulty leaky joints or cracks formed in the pipes
due to bad materials or poor construction.
The quantity of the ground water entering these sewer pipes Depends mainly upon the height of
the water-table above the sewer invert level and the nature and extent of faults and fissures
present in the sewer pipes. However, if the ground water table is well below the sewer, the
infiltration can occur only after rain, when water is moving down through the soil. In that case,
the infiltration quantity will depend upon the permeability of the ground soil. Since these factors
cannot be precisely computed, the exact quantity of ground water infiltrating into the sewer pipes
cannot be estimated precisely. Only certain nominal allowance, based upon some experimental

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results, may be made on account of this factor. In U.S.A., an allowance varying from 11,000 to
2, 25,000 (average value = 1, 14,000) liters per day per kilometer length of sewer pipe, is
generally made in high water-table areas
No allowance for infiltration should, however, is made when sewers are provided with under-
drains which have free outlets.
Sometimes, the storm water drainage may also infiltrate into the sewers. This inflow cannot be
computed easily and generally left unaccounted without making any extra provision for it. This
additional water, if happens to enter the sewers, can be accommodated in the extra empty space
left at the top in the sewers, which are generally designed as running 3/4th full at maximum
designed discharge
3) Subtractions due to water losses.
The water lost, due to leakage in the distribution system and house connections of the water
supply scheme, does not reach the consumers, and hence, never appears as sewage.
4) Subtraction due to water not entering the sewerage 'system.
Certain amount of water may be used by the public and industries for such uses which may not
produce any sewage at all. For example, the water used in boilers for steam generation; the del'
sprinkled over the roads, streets, lawns and gardens; the water used for automobile washings; the
water consumed in industrial products, such as beverages, etc., the water used in air cooling etc.,
does not normally produce any sewage. Quantity of Sewage Produced. The net quantity of
sewage produced will be equal to the accounted quantity of water supplied by the water-works
plus the additions due to factors (1) and (2) minus the subtractions due to factors (3) and (4),
described above. The net value may vary between 70 to 130 per cent of the accounted water
supplied from the water-works.
However this value; generally taken as equal to 75 to 80% of the accounted water supplied from
the water works.
2.2. Design Periods for Different Components of Sewerage Scheme
A sewerage scheme involves the laying of underground sewer pipes and construction of costly
treatment units, which cannot be replaced or increased in their capacities easily or conveniently
at a later date. For example, addition of sewer pipes at a future date cannot be accomplished
without digging the roads and disrupting the traffic. In order to avoid such future complications,
and to take care of the future expansions of the city and consequent increase in the quantity of
sewage produced, it is necessary to design the various components of the scheme larger than
their present day requirements and of such sizes, as to serve the community, satisfactorily, for a
reasonable number of years to come. This future period for which the provision is made in
designing the capacities of the various components of the sewerage scheme is known as the

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design period. The design period should neither be too long nor it should be too short, and
moreover, it should not exceed the useful life of the component structures. The design period is
generally guided by the following considerations:
(i) Useful life of component structures, and the chances of their becoming old and obsolete.
Design period should not exceed those values.
(ii) Ease and difficulty, that is likely to be faced in expansion, if undertaken at future dates. For
example, more difficult expansions mean choosing a higher value of the design period.
(iii) Amount and availability of additional investment, likely to be incurred for additional
provisions. For example if funds are not easily available, then one has to keep a smaller design
period.
(iv) The rate of interest on the borrowings and the additional money invested. For example, if the
interest rate is small; a higher value of the design period may be economically justified, and
therefore, adopted.
(v) Anticipated rate of population growth, including possible shifts in communities, industries
and commercial investments. For example, if the rate of increase of population is less, a higher
figure for the design period may be chosen.
The following design periods are often used in designing the different components of a sewerage
scheme.
Table 2.1 Design Periods for Different Components of a Sewerage Scheme

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2.3. Future Forecasts and Estimating Design Sewage Discharge
The quantity of sewage that is likely to pass through a sewer (Q') at the end of the design period,
can be easily computed by multiplying the per capita production of sewage (q') by the expected
population at the end of the design period.
The per capita sewage which is produced (q') in a community can be easily estimated by
assuming it as 75 to 80 per cent of the per capital water supplied to the public (q). However, it
should also be kept in mind that the future increase in population may also increase the per capita
water demand, and consequently increasing the per capita production of sewage. The increase in
per capita water supply or sewage production with the increase in population obviously occurs
due to improved economical conditions in the city, implying higher standards of living and
greater consumption of water. In U.S.A., this increase in per capita water demand and sewage
production is generally assumed to be 5% of the percentage increase in population. However, for
normal Indian conditions, the following norms may be adopted:
Table 2.2 Variations in per capital water demand and sewage production with population case
study India.
The expected population at the end of the design period can be estimated by collecting the data
of the past populations of several decades from the Census Department, and then by
extrapolating the future population by using anyone of the different methods, such as:
o Arithmetical increase method;
o Geometrical increase method;
o Incremental increase method;
o Decreasing rate method;
o Simple graphical method;
o Comparative graphical method;

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o Master plan method;
o The apportionment method;
o The logistic curve method.
These methods for forecasting future populations have been described in details in water supply
modules determining the expected population as well as the per capita sewage contribution of the
town, by the end of the design period, the average quantity of sewage produced in liters/day
(then converted to cumecs) can be easily determined by multiplying both these figures.
2.4. Variations in Sewage Flow and their Effects on the
Components of a Sewerage Scheme
The per capita demand of waste production (q') so far discussed, are based upon annual defined
as annual average value is not sufficient, although design of various components of a sewerage
scheme; because there are wide variations in the actual flows that take place through the sewers
at a given time.
The f1ows in these sanitary sewers, though fluctuate seasonally, monthly, daily, as well as
hourly, with the water consumption*, yet they are sometimes delayed and less pronounced (Fig.
2.1) as they
Fig.2.1. Hourly variation of sewage flow compared to that of water supply
are damped because of the storage space in the sewers and because of the time required for the
sewage to reach the point of gauging. In other words, flattened, because it requires consider
point, and the high flows from various sections w various times of flow. Thus the time the flow
time in sewers and the type of district served. Hence, if the sewage is gauged near its origin, the
peak f1ow will be quite pronounced; whereas, if the sewage must travel a long distance before

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being gauged, the peak will be deferre Design of Various water (q) and the corresponding per
capital flow and are, therefore very useful, for the considerable sewage to fill the sewers to the
high flow will reach the gauging point as to when the peak flow occurs deferred. It, therefore,
follows, that the peak flows (expressed as number of times of their average values) will be much
greater for smaller lateral sewers, as compared to these for larger trunk sewers.
For areas of moderate sizes, such as involved for branch sewers, the maximum daily or hourly
sewage flows, can be expressed as:
Maximum daily flow = 2 times the average daily flow
Maximum hourly flow = 1.5 times the maximum daily
= 3 times the average daily
However, as pointed out earlier, the peak hourly flows will decrease, as the tributary area
increases. Therefore, the peak flow at the outfall of a city sewer system will be much less,
usually, about 1.5 times the average. The estimation of maximum hourly flows for different
types of sewers, within the city's sewerage system, are given below in table
Table 2.3 Hourly Variations in Sewage Flow
The sizes of the sewers can then be easily designed for carrying the computed maximum hourly
flows, with sewers running 3 /4th full
This peak sewage flow has been connected with the population by certain investigators by the
formula:
The minimum flow passing through a sewer is also an important factor in the design of the
particular sewer: because at low flow, the velocity will be reduced considerably, which may

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cause silting. Hence, the slope at which the sewer is to be laid has to be decided in accordance
with the requirement of minimum permissible velocity at the minimum flow.
The minimum flows occurring through the sewers during night hours will affect the laterals to a
maximum extent, and will affect the mains to a lesser extent. Thus, the minimum flows through
laterals, may be even lesser than 25 per cent of the average; while in the mains, they can be 50 to
70 per cent of the average. For 'moderate areas, such as involved for branch sewers, the
following minimum flows may be assumed:
2.5. Estimating the Peak Drainage Discharge
The sewers and the drains of a separate sewerage system should be designed to carry the
maximum sewage discharge and the maximum rain runoff, respectively. Were as, the sewers of a
combined sewerage system should be designed to carry the sewage discharge plus the rain
runoff. The sewers of a combined system should, therefore, in addition to passing this combined
maximum flow, should also be capable of passing the low sewage discharge during non-
monsoon periods, as dry weather flow, with minimum permissible velocities. The partially
separate sewers may be designed for carrying the sewage discharge plus part of the storm
drainage, particularly that coming from the roofs and courtyards.
In order to design the sewers and the drains properly, it is absolutely necessary to estimate the
sewage discharge and the urban storm drainage discharge that are likely to enter the sewers or
drains. The methods of estimating the maximum sewage discharge were discussed in the
previous chapter; and here we will discuss the methods of estimating the maximum rate of storm
run-off, popularly called peak drainage discharge.
2.6 The Run-off Process and Peak Run-off Rate
When a rain, falls n a certain area, a part of it is intercepted by the soil, a part of it is evaporated,
and the remaining water flows overland towards the valleys, as storm runoff.

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Since the storm runoff has to be removed through drains or through combined sewers, the
drainage engineer must evaluate the peak rate of run-off, which can be produced from a certain
catchment by the given rain, at any moment. Further, the more intense is the rain, the more will
be the peak run-off rate. Hence, a proper and economical value of rain frequency (or recurrence
interval**) must be chosen, which the drains must be designed. The frequency of rainfall to be
adopted in design should neither be so large, as to cause too heavy investments, nor should it be
so small, as to cause very frequent overflowing of the drains. For Delhi, the experts have
recommended a 2years rain frequency for designing smaller link drains, and 5 years Frequency
for designing all the major drains.
2.7 Estimating Peak Run-off
The peak rate of run-off that is produced from a particular catchment depends upon numerous
factors; such as, the type of precipitation, the intensity and duration of rainfall, the rainfall
distribution, the soil moisture deficiency, the direction of the prevailing storm, the climatic
conditions, the shape, size and type of catchment basin, etc. etc. Due to these 15 to 20 variables
involved in evaluating the run-off, it is not possible to precisely determine it, even with the help
of the most complicated mathematics, as all these variables are interdependent, and run off
cannot be easily expressed by an exact Equation. Hence, until about 40 years ago, the peak run-
off rate was used to be estimated by empirical formulas only, even in the developed countries
like U.S.A. Different empirical formulas were, therefore, developed¡¤ for different regions, by
the investigators, depending upon their actual experimental works. In recent years, however, a
rational method has been evolved to estimate the peak Drainage discharge.
This method, though called rational, is not rational in the sense that the results given by this
formula for larger areas (more than 500 hectares or so) are generally erroneous and misleading.
This method can be applied most precisely to smaller areas (preferably less than 50 hectares or
so). For large areas, empirical formulas are, however, continued to be used, although the most
modern method for computing urban storm drainage is by digital computer simulations. This is
an advance topic dealt under the subject of "Water Resources Systems Planning" and is beyond
the scope of the Undergraduate Courses. The rational formula and other empirical formulas for
determining peak drainage discharge are discussed here:
2.7.1 Computing the Peak Drainage Discharge by the Use of Rational Formula.
If a rainfall is applied to an impervious surface at a constant rate, the resultant runoff from the
surface would finally reach a rate equal to the rainfall. In the beginning, only a certain amount of
water will reach the outlet, but after some time, the water will start reaching the outlet from the,
entire area; and in this case, the run-off rate would become equal to the rate of rain The period
after which the entire area will start contributing to runoff is called the time of concentration.
The runoff resulting from a rain having a duration lesser than the time of concentration will not
be maximum, as the entire area will not contribute to run-off in this case Further, it has been

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established that the runoff is not maximum, even when the duration of the rain is more than time
of concentration, because in such a case, the intensity of rain reduces with the increase in its
duration. In other words, it has been established that the maximum runoff will be obtained from
rain having duration equal to the time of concentration, and this is called the critical rainfall
duration. Based upon these basic principles, the rational formula evolved, due to the efforts of
Fruhling of Germany, Kuichling America, and later Lloyd Davis of England. This formula states
that
Concentration in cm/hr
Coefficient of Runoff
The coefficient of runoff (K) is in fact, the impervious factor of runoff, representing, and the
ratio of precipitation to runoff. The value of K increases as the imperviousness of the area
increases**, thus tending to make K = 1 for perfectly impervious areas. It is generally taken as
equal to 0.9 for paved areas and 0.15 for lawns and gardens. The values of K can also be worked
out for different localities having different population densities. Various values of K which can
be of use in designing storm water drains are given in Tables 2.3 and 2.4.
Table 2.3 Values of Run-off coefficient (K) for various Surfaces

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Table: 2.4 values of run- off coefficient (K) for different types of localities

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Intensity of Rainfall

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The time of concentration
The time of concentration for a given storm water drain generally consists of two parts; viz.
The total time of concentration at a given point in the drain, for working out the discharge at that
point, can be easily obtained as
The intensity of rainfall during this much of time (for the given design frequency, of course) can
be easily obtained from the standard intensity duration curves or DAD curves.

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Figure Typical Intensity-Duration-Frequency (IDF) Curve
The value of intensity so obtained is still the rainfall intensity at the rain gauge station, and is
called the point rainfall intensity. In order to make it effective over the entire catchment area (in
which this rain gauge station lies), it is necessary to multiply it by a factor called dispersion
factor or areal distribution factor. The resultant value will be nothing but Pc, to be used in Eq.
(2.4). The areal distribution factor: the resultant value will be nothing but p; to be used in
equation (2.4) it is a well established fact that the intensity of rainfall recorded at a particular rain
gauge station in a catchment is not the same throughout the catchment. As the size of the
catchment increases, the average intensity of rainfall over the catchment as a whole goes on
decreasing compared to the point intensity recorded at a particular station. Therefore, the areal
distribution factor, also called, the dispersion factor, is always applied to the point rainfall for
working out the design rainfall intensity. In case of Delhi, it is seen that the intensity of rainfall
varies considerably from one part to another, and as such, the dispersion factor reduces
considerably with the increase in the catchment area, as shown in Table 3.3
Table 2.5 Values of Dispersion Factor for Delhi

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In the absence of standard intensity-duration curves, the value of c can also be determined in the
following two ways:
(i) The value of "one hour rainfall" of a given frequency at a given place can be found from the
charts,

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This value of "one hour rainfall" is multiplied by the areal distribution factor, so as to
The values of a and b have been found out by the Health Ministry of Britain as 75 and 10
respectively for T varying between 5 to 20 minutes ; and as 100 and 20 respectively for T
varying between 20 .to 100 minutes respectively. The formulas given by them, and generally
applicable in England, are, therefore, given as below:
Using Tc in minutes, in place of T in Eqn. (2.7) and (2.8), the values of p, i.e. Pc can be
evaluated.
Besides the above generalized equations, certain other empirical equations have been suggested
for determining rainfall intensity, as given below:

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(a) For localities where rainfall is frequent. .
The equations from (2.7) to (2.14) can, though be used for finding the value of Pc, yet they are
very empirical equations, and are not very reliable. They are, therefore, generally avoided in
designing storm water drains in modern days. They may, however, be used when absolutely no
rainfall records are available. .
2.7.2. Computing the Peak Drainage Discharge by the Use of Empirical Formulas
The Rational formula described above is also quite empirical in the sense that the value of K
considerably depends upon the judgment of the designer. Moreover, this method gives reliable
results only for smaller areas, and hence used only for the design of drains having catchments
less than 400 hectares or so. For the design of drains having larger catchments (say above 400
hectares or so), it is generally advisable to use the suggested empirical formula for the given
region.
Various empirical formulas for calculating storm water run-off have been suggested by various
investigators; some of these formulas are based on local conditions only, and can be adopted
only when certain specific requirements are specified. The other formulas are based on
experimental studies and results obtained over wide areas, and they can, therefore, be adopted for
many localities. Some of the leading empirical formulas are given below:

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(i) Burkli-Zieglerformula. This formula is the oldest empirical formula used for determining the
peak run off rate. It was devised by a Swiss engineer for local conditions, but was soon followed
in the entire U.S.A. In M.K.S. units, it states that
ii. Dickens¡¯ s formula. This formula is generally useful for Indian catchments and particularly
for northern India and states that,
The value of C must be ascertained for each catchment, and depends upon the nature of the
catchment and the intensity of rain fall. An average value of C equals to 11.5 is generally used
and it should be increased for hilly areas and vice versa. Secondly for the same type of
catchment, greater is the rain fall greater will be the value of C and vice versa.
iii. Ryve¡¯ s formula. This formula is almost similar to that of Dicken¡¯ s; the only difference is in
the value of the constants. It is generally applicable to south Indian catchments and states that

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Iv. Inglis Formula
This formula is applicable to the fan shaped catchments in old Bombay state of India.
It states that
Vi. Dredge or Burge¡¯ s formula. This formula is based upon Indian records