module I.docx

WATER SUPPLY AND TREATMENT ENGINEERING, 18CV46
EPCET, CIVIL DEPARTMENT Page 1
MODULE I
1.1 NEED FOR PROTECTED WATER SUPPLY
 The lack of easy access to safe and adequate water supply and absence of sanitation
facilities are considered to be responsible for heavy loss of human lives by ill health
through water-borne diseases and also lead to the loss of valuable working days.
 The water when exposed to the atmosphere contains many impurities and pathogenic
organisms which are harmful to any living organism. The pathogenic organisms do not
multiply in water but water is considered as a carrier for bacteria. Due to these water
borne diseases like typhoid, Asiatic cholera, Amoebiasis, glavdists etc may spread.
Certain other diseases like goiter, dental fluorosis, skeletal fluorosis are caused due to
chemical impurities present in water. If untreated water is consumed by living organisms,
it is likely to cause serious harm to their health. Hence in order to make water potable and
free from various impurities, the purification methods are found out like disinfection
process, filtration If we control the purity of water completely, the chances of outbreak
of water borne diseases will be much less.
 The soul of purification process of present day water supply schemes is the filtration. It is
preceded by pre-filtration purification methods and followed by post-filtration
purification methods. The former methods make the water fit for filtration and the latter
methods treat the impurities which have not been removed with the help of the process of
filtration.
 Therefore in order to ensure the availability of sufficient quantity of good quality water, it
becomes almost imperative in a modern society to plan and build water supply schemes
which may provide potable water to the various sections of community in accordance
with their demand and requirements. Such a scheme shall not only help in supplying safe
wholesome water to the people for drinking, cooking, bathing, washing etc so as to keep
the diseases away and thereby promoting better health but would also help in supplying
water for fountains, gardens etc and thus help in maintaining better sanitation and
beautification of surroundings, thereby reducing environmental pollution.
1.2 DEMAND OF WATER
 A small quantity of water is required by a man under normal conditions for his personal
use. An average person may consume no more than 5 to 8 litres a day in liquid and solid
foods, including 3 to 6 liters in the form of water, milk and other beverages.
While planning a water supply scheme it is necessary to find out not only the total yearly water
demand but also to assess the required average rates of flow (or draft) and the variations in these
rates.
The following quantities are therefore generally assessed and recorded

(i) Total annual volume (V) in liters or million liters
(ii) Annual average rate of draft in liters per day, i.e. V/365
(iii) Annual average rate of draft in liters per day per person (i.e. liters per capita per day
or lpcd), called per capita demand (q)
(iv) Average rate of draft in liters per day per service,i.e.
V x 1
365 No. of persons
(v) Fluctuations in flows expressed in terms of percentage ratios of maximum or
minimum yearly, monthly, daily or hourly rates to their corresponding average
values.
1.3 TYPES OF WATER DEMANDS
1) DOMESTIC DEMAND
This includes the water required in private buildings for drinking, cooking, bathing, lawn
sprinkling, gardening, sanitary purposes etc. The IS:1172-1993 infact lays down a limit
on domestic water consumption between 135 to 225 l/h/d.
In a developed and an effluent country like U.S.A, this figure usually goes as high as 340
l/h/d. This is because more water is consumed in rich living in air-cooling, air-
conditioning, bathing in bath-tubs, dish washing of utensils, car washing, home laundries,
garbage grinders etc.
The total domestic water consumption usually amounts to 50 to 60 % of the total water
consumption.
Total domestic water demand = total design population x per capita domestic
consumption

2) INDUSTRIAL DEMAND
The industrial water demand represents the water demand of industries which are neither
existing or are likely to be started in future, in the city for which water supply is being
planned. This quantity will thus vary with the number and type of industries . The
ordinary per capita consumption on account of industrial needs of a city is generally
taken as 50 litres/person/day, which may suffice only to meet the water demand of small
scattered industries, without catering to larger industries. The requirement of industrial
water demand will have to be approximated on the basis of the nature and magnitude of
each industry and the quantity of water required per unit of production. The potential for
industrial expansion should also be investigated so the availability of water supply may
attract such industries and add to economic prosperity of the community.

In industrial cities, the per capita water requirement may finally be computed to be as
high as 450 litres/person/day or so as compared to the normal industrial requirement of
50 litres/person/day.
3) INSTITUTIONAL AND COMMERCIAL DEMAND
The water requirements of institutions such as hospitals, hotels, restaurants, schools and
colleges, railway stations, offices, factories etc. should also be assessed and provided.
This quantity will certainly vary with the nature of the city and with the number and types
of commercial establishments and institutions present in it. On an average, a per capita
demand of 20 litres/head/day is usually considered to be enough to meet such commercial
and institutional water requirements, although of course, this demand may be as high as
50 l/h/d for highly commercialized cities.

4) DEMAND FOR PUBLIC USE
This includes the quantity of water required for public utility purposes, such as watering
of public parks, gardening, washing and sprinkling on roads, use in public foundations
etc. For most of the water supply schemes in India, a nominal amount not exceeding 5 %
of the total consumption may be added to meet this demand on arbitrary basis. A figure
of 10 l/h/d is usually added on this account while computing total water requirement.
5) FIRE DEMAND
In thickly populated and industrial areas, fires generally break out and may lead to
serious damages, if not controlled effectively. Fire fighting personnel require sufficient
quantity of water so as to throw it over the fire at high speeds. The quantity of water
required for extinguishing fires should be easily available and kept always stored in
storage reservoirs. Fire hydrants are usually fitted in the water mains at about 100 to 150
m apart, and fire fighting pumps are immediately connected into them by the fire brigade
personnel as soon as a fire breaks out. These pumps then throw water on the fire at very
high pressures, so as to bring it under control. The minimum water pressure available at
fire hydrants should be of the order of 100 to 150 KN/m2 ( 10 to 15 m of water head) and

should be maintained even after 4 to 5 hours of constant use of fire hydrant. As far as
Indian conditions are concerned, a moderate allowance of one litre per head per day for
fire demand will be sufficient.
In a moderate fire break out, 3 jet streams are simultaneously thrown from each
hydrant; one on the burning property, and one each on adjacent property on either side of
the burning property. The discharge of each stream should be about 1100 litres/minute.
Total amount of water required = number of fires x discharge x time of each fire….(1)
The per capita fire demand is thus generally ignored while computing the total per capita
water requirement of a city. However for cities having populations exceeding 50,000, the
Water required in kilo litres may be computed by using the relation.
Kilo litre of water required = 100√P ……………………………………………..(2)
P = population in thousands
While designing public water supply schemes, the rate of fire demand is
sometimes treated as a function of population and is worked out on the basis of certain
empirical formulas, which are given below.
I. KUICHLING’S FORMULA
Q = 3182√P……………………………………………………………..(3)
Q = Amount of water required in litres/minute
P = Population in thousands
II. FREEMAN FORMULA
Q = 1136[
P
10
+ 10]……………………………………………………(4)
III. NATIONAL BOARD OF FIRE UNDER WRITERS FORMULAS
According to the recommendations given by the board (American Insurance
Association), the fire requirements are as follows:
a) For a central congested high valued city
(i) When population is less than or equal to 200000
Q = 4637√P[1− 0.01√P]……………………………(5)
(ii) When population is more than 2 lakhs, a provision of 54,600
litres/minute may be made with an extra additional provision of
9100 to 36400 litres/minute for a second fire.

b) For a residential city
The required draft for fire-fighting may be as follows:
(i) Small or low buildings = 2200 litres/minute
(ii) Larger or higher buildings = 4500 litres/minute
(iii) High value residences, apartments, tenements = 7650 to 13500
litres/minute
(iv) Three storeyed buildings in densely built up sections = up to
27000 litres/minute
IV. BUSTON’S FORMULA
Q = 5663√P………………………………………………………….(6)
The formulas (3),(4) and (5) give higher results
All the above formulas suffer from the drawback that they are not related to the
type of district served. They give equal results for Industrial as well as non-
Industrial areas.
1.4 FACTORS AFFECTING PER CAPITADEMAND
Per capita demand – It is the annual average amount of daily water required by one person and
includes the domestic use, industrial and commercial use, public use, wastes, thefts etc.
Per capita demand (q) in litres /day / head =
Total yearly water requirement of the city in litres (V)
365 ×design population
The annual average demand for water (i.e. per capita demand) considerably varies for different
towns or cities. This figure generally ranges between 100 to 360 litres/capita/day for Indian
conditions.

Factors affecting per capita demand are discussed below.
SIZE OF THE CITY
Per capita demand for big cities is generally large as compared to that for smaller towns. This is
because of the fact that in big cities, huge quantities of water are required for maintaining clean
and healthy environments. Similarly in a big city commercial and industrial activities are
generally more thus requiring more water. Affluent rich living in air cooled homes may also
increase the water consumption in cities.
On an average, the per capita demand for Indian towns may vary with the population as shown in
table below.
The fluctuation in demand depends upon the size of the city. In a large city the fluctuations in
demand may be narrow. The fluctuation in use in an industrial community is normally much
smaller than in a residential community.
AGE OF COMMUNITY
Older, more stable communities use less water than rapidly developing communities where new
homes are being constructed and owners are planting new lawns.
CLIMATIC CONDITIONS
At hotter and dry places, the consumption of water is generally more, because more of bathing,
cleaning, air coolers, air conditioning, sprinkling in lawns, gardens, roofs etc are involved.
Similarly in extremely cold countries, more water may be consumed, because the people may
keep their taps open to avoid freezing of pipes and there may be more leakage from pipe joints,
since metals contract with cold. Extremes of heat and cold cause variations in demand.

TYPES OF GENTRY AND HABITS OF PEOPLE
Rich and upper class communities generally consume more water due to their affluent living
standards. Middle class communities consume average amounts, while the poor slum dwellers
consume very low amounts. The amount of water consumption is thus directly dependent upon
the economic status of the consumers.
INDUSTRIAL AND COMMERCIAL ACTIVITIES
The pressure of industrial and commercial activities at a particular place increases the water
consumption by large amounts. Many industries require really huge amounts of water (much
more than the domestic demand) and as such increase the water demand considerably. Industrial
water demand is having no direct connection with the population or the size of the city, but more
industries are generally situated in big cities.
QUALITY OF WATER SUPPLIES
If the quality and taste of the supplied water is good, it will consumed more, because in that case,
people will not use other sources such as private wells, hand pumps etc. Similarly certain
industries such as boiler feeds etc which require standard quality waters will not develop their
own supplies and will use public supplies, provided the supplied water is up to their required
standards. Poor quality water results in reduction in use.
PRESSURE IN THE DISTRIBUTION SYSTEM
If the pressure in the distribution pipes is high and sufficient to make the water reach at 3rd or
even 4th storey, water consumption shall definitely be more. This water consumption increases
because of 2 reasons.
People living in upper storeys will use water freely as compared to the case when water is
available scarcely to them.
The losses and wastes due to leakage are considerably increased if this pressure is high. {If the
pressure increases from 20 m head of water (i.e. 200 KN/m2 ) to 30 m head of water (i.e. 300
KN/m2), the losses may go up by 20 to 30 %.}

DEVELOPMENT OF SEWERAGE FACILITIES
The water consumption will be more, if the city is provided with flush system and water
consumption shall be less if the old conservation system of latrines is adopted.
SYSTEM OF SUPPLY
The water may be supplied either continuously for all the 24 hrs of the day, or may be supplied
only for peak periods during the morning and evening. The second system, i.e. the intermittent
supplies may lead to some saving in water consumption due to losses occurring for lesser time
and a more vigilant use of water by the consumers. Intermittent supply will reduce rate of
demand. But at many places, the intermittent supplies may not give much savings over the
continuous supplies because of the following reasons.
In intermittent supply system, water is generally stored by consumers in tanks, drums, utensils
etc. for non-supply periods. This water is thrown away by them even if unutilized as soon as the
fresh supply is restored. This increases the wastage and losses considerably.
People have a general tendency to keep the taps open during non-supply hours, so that they come
to know of it as soon as the supply is restored. Many a times water goes on flowing unattended
even after the supply is restored thus resulting in wastage of water.
COST OF WATER
If the water rates are high, lesser quantity may be consumed by the people. This may not lead to
large savings as the affluent and rich people are little affected by such policies.
POLICY OF METERING AND METHOD OF CHARGING
Water tax is generally charged in 2 different ways
On the basis of meter reading (meters fitted at the head of the individual house connections and
recording the volume of the water consumed)
People use only that much of water as much is required by them. Although metered supplies are
preferred because of lesser wastage, they generally lead to lesser water consumption by poor and
low income groups, leading to unhygienic conditions. Moreover meters put necessary hindrance
to the flow resulting in loss of pressure and increased cost of pumping.
 On the basis of certain fixed monthly flat rate

When the supplies are unmetered and the charges are fixed, people generally do not practice
economy in the use of water because they think they have to pay only a fixed amount
irrespective of the quantity of water used by them. They are therefore liberal in consuming water
and many a times leave their taps flowing unused. All this leads to high wastage and high
consumption of water.
1.5 .VARIATIONS IN DEMAND OF WATER
Per capita demand is defined as the annual average daily consumption per person.
There are wide variations in the use of water in different seasons, in different months of the year,
in different days of the month, in different hours of the day and even in different minutes of the
hour.
Seasonal variations occur due to large use of water in summer season, lesser use in
winter and much less in rainy season. These variations may also be caused by seasonal use of
water in industries such as processing of cash crops at the time of harvesting etc. Day to day
variations reflect household and industrial activity. Water consumption is generally more on
Sundays and holidays. There are variations in hour to hour demand. Consumption in the early
hours of morning (0 to 6 hrs ) is generally small, increases sharply as the day advances, reaching
a peak value between 8 to 11 AM, then decreases sharply up to about 1 PM, remains constant up
to about 4 PM, again increases in the evening reaching a peak between 7 to 9 PM, finally falling
to a low value in the late hours of night. The night flow (excluding industrial consumption)
generally represent the magnitude of losses and wastes since there is no appreciable domestic
consumption during this time.
In the above figure, average demand is shown by dotted line. The area below the dotted line
shows surplus water and the area above the dotted line indicates the shortage of water. Excess
water stored during slack demand period is to be consumed in peak demand period. The excess

water is to be stored in tanks or reservoirs specially constructed for this purpose. In most of the
Indian cities, peak demand occurs in the morning and evening.
Suitable allowance must also be made for sudden and heavy drafts required for fire fighting.
Smaller the town, the more variable is the demand.
Maximum seasonal consumption = 130 % of annual average daily rate of demand…..(6 a)
Maximum monthly consumption = 140 % of annual average daily rate of demand……(6 b)
Maximum daily consumption = 180 % of annual average daily consumption………….(6 c)
Maximum hourly consumption = 150 % of average for the day………………………(6 d)
1.5.1 EFFECT OF VARIATIONS IN DEMAND ON THE DESIGN CAPACITIES OF
DIFFERENT COMPONENTS OF A WATER SUPPLY SCHEME
(i) Source of supply: wells may be designed for maximum daily consumption or
sometimes for average daily consumption.
(ii) Pipe mains: taking the water from the source upto the service reservoir may be
designed for maximum daily consumption.
(iii) Filter and other units: designed for maximum daily draft
(iv) Pumps: designed for maximum daily draft plus some additional reserve for break-
down and repairs
(v) Distribution system( includes the pipe carrying water from service reservoir to
distribution system): designed for maximum hourly draft of the maximum day
(vi) Service reservoir: designed to take care of the hourly fluctuations, fire demands,
emergency reserve, and the provision required when pumps have to pump the entire
day’s water in fewer hours than 24 hours. Only 2 hours storage may be considered
for fire allowance.
1.6 PEAK FACTOR
The maximum demands (monthly, daily or hourly) are generally expressed as ratios of their
means. These ratios may vary considerably for different communities. The following figures are
generally adopted.
a) Maximum daily consumption is generally taken as 180 percent of the average
Therefore maximum daily demand = 1.8 (i.e; 180 percent)× average daily
demand = 1.8 q……………………………………………………(6 e)
b) Maximum hourly consumption is generally taken as 150 percent of its average.
Therefore maximum hourly consumption of the maximum day i.e; peak demand
= 1.5 (i.e; 150 percent) × average hourly consumption of the max. day…………….(6 f)

= 1.5 × (
maximum daily demand
24
)………………………………………………………(6 g)
Substituting equation (6 e) in equation (6 g)
Therefore maximum hourly consumption of the maximum day i.e; peak demand
=1.5 × (
maximum daily demand
24
) = 1.5 × (
1.8 q
24
) = 2.7 (
q
24
)
= 2.7(annual average hourly demand)…………………………………………(6 h)
Many a times, the following formula given by Goodrich is also used for finding out the ratios of
peak demand rates to their corresponding means:
p = 180 t−0.10
…………………………………………………………………………(6 i)
p = percent of the annual average draft for the time t in days
T = time in days from
1
24
to 365
When t = 1 day ( for daily variations)
Substituting t=1 in equation (6 i)
p = 180 t−0.10
= 180 × 1−0.10
= 180
Hence
max.daily demand
average daily demand
= 180 %.........................................................................(6 j)
When t = 7 day ( for weekly variations)
Substituting t = 7 in equation (6 i)
p = 180 t−0.10
= 180 × 7−0.10
= 148 %
Hence
max.weekly demand
average weekly demand
= 148 %...................................................................(6 k)
When t = 30 days ( for monthly variations)
Substituting t = 30 in equation (6 i)
p = 180 t−0.10
= 180 × 30−0.10
=128 %
Hence
max monthly demand
average monthly demand
= 128 %..........................................................................(6 l)
The GOI manual on water supply has recommended the following values of the peak factor,
depending upon the population:

Evidently, the peak factor tends to reduce with increasing population, since the different habits
and customs of several groups in larger population, tend to minimize the variation in demand
pattern.
1.7 DESIGN PERIOD
A water supply scheme includes huge and costly structures (such as dams, reservoirs, treatment
works, penstock pipes etc) which cannot be replaced or increased in their capacities , easily and
conveniently.

For example water mains including the distributing pipes are laid underground and cannot be
replaced or added easily without digging the roads or disrupting the traffic. In order to avoid
these future complications of expansions, the various components of a water supply scheme are
purposely made larger so as to satisfy the community needs for a reasonable number of years to
come. This future period or the number of years for which a provision is made in designing the
capacities of the various components of the water supply scheme is known as design period. The
design period should neither be too long nor should it be too short. The design period cannot
exceed the useful life of the component structure.
Water supply projects under normal circumstances may be designed for a design period
of 30 years. The design period recommended by the GOI manual on water supply for designing
the various components of a water supply project are given in table below.
1.8 FACTORS GOVERNINGDESIGNPERIOD
(i) Useful life of component structures and the chances of them becoming old and obsolete.
Design period should not exceed those respective values.
(ii) Ease and difficulty that is likely to be faced in expansions, if undertaken at future dates.
For example, more difficult expansions means 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 the funds are not available, one has to keep a smaller design
period.

(iv)The rate of interest on the burrowing and 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 establishments. For example, if the rate of increase of
population is less, a higher figure for the design period may be chosen.
1.9 FACTORS RESPONSIBLE FOR CHANGES IN POPULATION
 BIRTH
Birth rates may decrease due to excessive family planning practices and legalized
abortions. Spread of education and development of extra recreational facilities for the
people, also tend to reduce the birth rates.
 DEATH
The death rates may decrease with the development and advancement of medical
facilities, thereby controlling infant mortality rates and adult death rates due to control of
infections and other diseases.
 MIGRATIONS
The migrations are dependent upon the industrialization and commercialization of the
particular cities or towns. People generally migrate from villages to cities and towns,
where more opportunities for earning livelihood are available. The migration rates,
therefore tend to increase sharply with the development of industries and commerce in
the city or in the nearby areas. The migration rates may decrease when migration
restrictions are imposed.
All the 3 factors are influenced by social and economic factors and conditions
prevailing in the various communities. Besides these factors, some other factors like
wars, natural havocs and disasters may also bring about sharp reductions in population.
All these varying influences make the task of predicting future population very
difficult and highly unexact, as it is very difficult and time consuming, especially for the
engineers, to evaluate all these economic and social factors. It is therefore, more common
to rely upon mathematical formulas and graphical solutions based upon previous
population records.

1.10DIFFERENT METHODSOF POPULATION FORECASTING
1. ARITHMETIC INCREASE METHOD
This method is based upon the assumption that the population increases at a
constant rate i.e. the rate of change of population with time (i.e. dP /dt ) is
constant.
dP
dt
= constant = K
dP = K dt
∫ dP = K ∫ dt
t2
t1
P2
P1
…………………………………(7)
P2 − P1 = K (t2 − t1)…………………………………(8)
Suffixes 1 and 2 represent the last and first decades or census respectively. Thus t2 − t1 =
Number of decades
The population data for the last 4 to 5 decades is obtained and the population increase per decade
(x) is calculated; the average of which ( x
̅ )is then used as the design growth rate for computing
future population.
P1 =Population after 1 decade from present
P1 = P0 + 1x
̅…………………………………………………………………….(9)
P2 = Population after 2 decades from present
P2 = [P0 + 2x
̅]…………………………………………………………………….(10)
P3 = [P2 + 1x
̅] ……………………………………………………………………(11)
P3 = [P0 + 3x
̅]…………………………………………………………………(12)
Pn = [P0 + nx
̅]…………………………………………………………………(13)
Pn = Forecasted population after n decades from the present
P0 = Population at present
n = Number of decades between now and future
x
̅ = Average (arithmetic mean) of population increases in the known decades.

I. GEOMETRIC INCREASE METHOD (UNIFORM INCREASE METHOD)
In this method , the per decade percentage increase or percentage growth rate (r)
is assumed to be constant, and the increase is compounded over the existing
population every decade.
The above geometric increase can be expressed as
P1= Population after 1 decade
P1 = P0 +
r
100
P0 = P0 (1 +
r
100
)…………………………………..(14)
Where r is in percent
P2 = P1 +
r
100
P1 = P1 (1 +
r
100
) = P0 (1 +
r
100
)
2
………………….(15)
P3 = P2 +
r
100
P2 = P2 (1 +
r
100
) = P0 (1 +
r
100
)
3
………………….(16)
Pn = P0 (1 +
r
100
)
n
…………………………………………………….(17)
P0 = Initial population i.e. the population at the end of last known census
Pn = Future population after n decades
r = Assumed growth rate (%)
Assumed growth rate can be computed in several ways
 r = √
P2
P1
t
− 1………………………………………..(18)
P1 = Initial known population
P2 = Final known population
t = number of decades between P1 and P2
 Compute the average of the percentage growth rates of the several
known decades of the past

The growth rates; i.e;
increase in population
original population
× 100 are computed for
each known decade and their average may be taken as the
assumed constant per decade increase (r).
The average may again be either the arithmetic average i.e;
r1+r2 +r3…………..rt
t
…………………………………………….(19)
or the geometric average i.e; √r1 × r2 × r3 … …. . rt
t
……….(20)
The design engineers in the field generally consider the arithmetic
mean here, because it is slightly higher than the geometric mean
and hence gives conservative higher value of forecasted
population. However the “GOI Manual on water and water
treatment” recommends the use of geometric mean here.
II. METHOD OF VARYING INCREMENT OR INCREMENTAL INCREASE
METHOD
In this method, the per decade growth rate is not assumed to be constant as in the
arithmetic or geometric progression methods; but is progressively increasing or
decreasing depending upon whether the average of the incremental increases in
the past data is positive or negative.
The population for a future decade is worked out by adding the mean
arithmetic increase (x
̅) to the last known population as in arithmetic increase
method and to this is added to the average of the incremental increases (y
̅), once
for the first decade, twice for the second decade, thrice for the third decade and
so on.
The method, thus assumes that the growth rate in the first decade is at (x
̅ + y
̅), in
the second decade at (x
̅+ 2y
̅), and in the nth decade at (x
̅ + ny
̅). Thus the growth
rate is assumed to be varying.
P1 = population after 1 decade from the present (i.e; last known census)
P1 = Po + (x
̅ + 1y
̅)………………………………………………………..(21)
P2= population after 2 decades = P1 + (x
̅ + 2y
̅) = Po + (x
̅ + 1y
̅) + (x
̅ + 2y
̅)
P2 = Po + 2x
̅ + 3y
̅……………………………………………………..(22)
P2 = [Po + 2x
̅ + 2 ×
(2+1)
2
y
̅]……………………………………………..(23)
Similarly,
P3 = P2+(x
̅ + 3y
̅)…………………………………………………..(24)
P3 = Po + 2x
̅ + 3y
̅ + (x
̅ + 3y
̅) = Po + 3x
̅ + 6y
̅…………………..(25)

P3 = Po + 3x
̅ + 3(
3+1
2
) y
̅………………………………………….(26)
Similarly,
P4 = P3 + (x
̅ + 4y
̅) = Po + 3x
̅ + 6y
̅ + (x
̅ + 4y
̅)
P4 = Po + 4x
̅ + 10y
̅
P4 = [Po + 4x
̅ + 4 (
4+1
2
) y
̅]……………………………….(27)
Pn = Po + nx
̅ +
n(n+1)
2
× y
̅………………………………………….(28)
Pn= population after n decades from present (i.e; last known census)
x
̅ = average increase of populations of known decades
y
̅ = average of incremental increases of the known decades
This method will give end results, somewhere between the results given by
arithmetic increase method and geometric increase method and is thus
considered to be giving quite satisfactory results.
III. DECREASING RATE OF GROWTH METHOD
Since the rate of increase in population goes on reducing, as the cities reach
towards saturation, a method which makes use of the decrease in the percentage
increase, is many a times used and gives quite rational results. In this method,
the average decrease in the percentage increase is worked out and is then
subtracted from the latest percentage increase for each successive decade. This
method is however applicable only in cases, where the rate of growth shows a
downward trend.
IV. SIMPLE GRAPHICAL METHOD
In this method a graph is plotted from the available data, between time in X axis
and population in Y axis. The curve is then smoothly extended up to the desired
year. The method however gives very approximate results as the extension of the
curve is done by the intelligence of the designer.
All the five methods described up to now are based on the assumption that
factors and conditions which were responsible for population increase n the past
will continue in the future also, with the same intensity. This is a vague
assumption and may or may not be satisfied. For example, a city or a community
may suddenly impose immigration restrictions, or may impose compulsory

family planning methods for eligible couples, or may develop enhanced medical
facilities thereby reducing death rates etc. Due to such reasons, the results
obtained from these methods may or may not be precise. However, they are less
time consuming and are used by engineers. They are also useful for providing a
check on the results obtained by some other advanced and time consuming
methods of population forecasting.
V. COMPARATIVE GRAPHICAL METHOD
In this method, the cities having conditions and characteristics similar to the city
whose future population is to be estimated are, first of all selected. It is then
assumed that the city under consideration will develop, as the selected similar
cities have developed in the past. This method has a logical background, and if
statistics of development of similar cities are available, quite precise and reliable
results can be obtained. However it is rather difficult to find identical cities with
respect to population growth. The use of this method is explained below:
Consider figure. Let the population of a city X be given for 4 decades (say
1940, 1950, 1960 and 1970). The population-time curve is then plotted.
Now suppose it is required to estimate the population of the city X at the
end of the year 2020. The available data show that this city X has reached the
present population of 50000 in the year 1970. Then the available data of similar
cities ( say city A,B,C,D) is analysed. Let it be found that city A has reached
50000 in the year 1900, then its curve is plotted beyond the year 1900 onward.

However, this curve for city A should start from point P which represents the
present population of city X. Similarly the populations of cities B, C and D are
plotted from the year they have reached 50000 onwards. Now the curve for city
X is carefully extended between the curves of cities A, B, C and D allowing it to
be influenced more by the rates of growth of cities, which are more similar to the
city in consideration.
VI. MASTER PLAN METHOD OR ZONING METHOD
Big and metro-politan cities are generally not allowed to develop in haphazard
and natural ways, but are allowed to develop only in planned ways. The
expansion of such cities are regulated by various by-laws of corporations and
other local bodies. Only those expansions are allowed, which are permitted or
proposed in the master plan of that city.
The master plan prepared for a city is generally such as to divide the city
in various zones, and thus to separate the residence, commerce and industry from
each other. The population densities are also fixed. Say for example, there may

be 5 persons living in a residential plot and there may be 10000 plots in a zone.
Then, the total population of this zone when fully developed can be easily
worked out as 5× 10000 = 50000. Hence, when the development is regulated
by such a scheme, it is very easy to access precisely the design population,
because the master plan will give us as to when and where the given number of
houses, industries and commercial establishments would be developed.
The common figures for population densities which may be taken in master plan
preparations or in population estimates are shown in table.
VII. RATIO METHOD OR APPORTIONMENT METHOD
In this method of forecasting future population of a city or a town, the city’s
census population record is expressed as the percentage of the population of the
whole country. In order to do so, the local population and the country’s
population for the last four to five decades is obtained from the census records.
The ratios of the local population to national population are worked out for these
decades. A graph is then plotted between time and these ratios, and extended up
to the design period, so as to extrapolate the ratio corresponding to the future
design year. Sometimes, the last census ratio or the average of the past few years
may be used. This ratio is then multiplied by the expected national population at
the end of the design period, so as to obtain the required city’s future population.
The expected national population in different future years are generally available,
as they are worked out precisely by the by Census department by some rational
recommended method. This method is therefore very suitable for areas whose
growths are parallel to the national growth. However, this method does not take
into consideration, the abnormal conditions that may prevail in certain local
areas.
VIII. LOGISTIC CURVE METHOD

Under normal conditions, the population of a city shall grow as per the logistic
curve as shown in figure 2.3. P.F.Verhulst has put forward a mathematical
solution for this logistic curve. According to him, the entire curve AD can be
represented by an autocatalytic first order equation given by
loge (
Ps−P
P
) − loge (
Ps−Po
Po
) = −K × Ps × t………………………………(29)
K =constant
Po = Population at the start point of the curve A
Ps =saturation population
P =population at any time t from the origin A
From equation (29) loge [(
Ps−P
P
) × (
Po
Ps−Po
)] = −K × Ps × t
(
Ps−P
P
)(
Po
Ps−Po
) = loge
−1
(−KPst)
(
Ps − P
P
) = [
Ps − Po
Po
]loge
−1
(−KPst)
Ps
P
− 1 = [
Ps−Po
Po
]loge
−1
(−KPst)
Ps
P
= 1 + [
Ps−Po
Po
]loge
−1
(−KPst)
P =
Ps
1+
Ps−Po
Po
loge
−1(−KPst)
……………………………………..(30)
substituting
Ps−Po
Po
= m ( constant) in equation (30)
−KPs = n (another constant) in equation (30)
P =
Ps
1+m × loge
−1(nt)
…………………………………………(31)
This is the required equation of the logistic curve. Mc Lean further suggested
that if only three pairs of characteristic values Po,P1, P2 at times t = to = 0,t1 and
t2 = 2t1 extending over the useful range of the census populations, are chosen, the
saturation value Ps and the constants m and n can be evaluated from three
simultaneous equations as follows:
Ps = −
2PoP1P2 −P1
2(Po+P2 )
PoP2 −P1
2 ……………………………………………………(32)
m =
Ps−Po
Po
…………………………………………………………………….(33)
n = (
1
t1
) loge [
Po(Ps−P1)
P1(Ps−Po)
]………………………………………………………..(34)
n =
2.3
t1
log10 [
Po(Ps−P1)
P1(Ps−Po)
]………………………………………………………..(35)

Knowing Po,P1 and P2 from census data and using them in these equations, the values
of Ps, m and n are known and the equation of the logistic curve (equation (31)) is
thus known. From that, the population P at any time t can then be obtained.

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