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Chapter: Environmental Engineering : Planning For Water Supply System

Population Forecasting Methods

1. Arithmetic growth method 2. Geometric growth method 3. Curvilinear method 4. Logistic method 5. Decline growth method 6. Ratio growth



Population is one of the most important factors for design of the water systems, so it should be estimated, so as to know the increasing demand and ensure continuous supply to them.


Population data is obtained by previous records and the rate of increase is found out and this used for further analysis, which may be by using the methods described below


1.     Arithmetic growth method

2.     Geometric growth method

3.     Curvilinear method

4.     Logistic method

5.     Decline growth method

6.     Ratio growth

Arithmetic growth method:

It is based on the assumption that the rate of growth of population is constant. It means that the each year population increase by the same increment.




dp / dt = Ka




dp / dt is the rate of change of population


Ka = the constant arithmetic increment


Ka can be determined by finding the slop of the graph of population against time. The population in the future is thus estimated.


Geometric method:

It is based on the hypothesis that rate of change of population is proportional to the population. According to this, method it is assumed that the rate of increase of population growth in a community is proportional to the present population.




dP /dt P => dp / dt = Kg where Kg = Geometric Growth constant.


If P0  is the population at any time t0  and Pf  is

the population at time tf then


?Pf P0 dp/p = Kg ? tf t0 dt = Ln (Pf/P0 = Kg (tf/t0)


=> Ln (Pf/P0 = Kg ?t


=> (Pf/P0 = (e) Kg ?t and Pf = P0 (e) Kg ?t


This method gives somewhat larger value as compared to arithmetic method and can be used for new cities with rapid growth. In normal practice, arithmetic and geometric growth average is taken.


Curvilinear method:

In this it is assumed that the population of a city will grow, in the same manner as in other cities in the past. This similarity between the cities includes geographical proximity, similarity of economic base, access to similar transportation system etc. In practice it is difficult to find similar cities.





Logistic method:

When the growth rate of population due to birth, death and migration are under normal situation and not subjected to extraordinary changes due to unusual situation like war, epidemics earth quakes and refugees etc. Then this method is used:


According to this method

P = P sat / (1+ ea+ b?t), where P sat is the saturation population, of the community and a, b are constants. P sat, a and b can be determined from three successive census populations and the equations are


Psat = 2 P0 P1P2 - P12 (P0 + P2) / (P0 P2 - P12)


Decline growth method:

This method like, logistic, assumes that the city has some limiting saturation population and that its rate of growth is a function of population deficit;


Ratio method:

Ratio method of fore casting is based on the assumption that the population of a certain area or a city will increase in the same manner to a larger entity like a province, or a country. It requires calculation of ratio of locals to required population in a series of census years.


Projection of the trend line using any of the technique and application of projected ratio to the estimated required population of projected ratio to the estimated required population in the year of interest. This method of forecasting does not take into account some special calculations in certain area but have the following advantages.

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Environmental Engineering : Planning For Water Supply System : Population Forecasting Methods |

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