Sewerage projects may be design period normally to meet the requirements over a thirty year period after their completion. The period between design and completion should also be taken into account which should be between three to six years depending on the type and size of the project.

The thirty year period may however be modified in regard to certain components of the project depending on their useful life or the facility for carrying out extensions when required and rate of interest so that expenditure far ahead of its utilization is avoided. Necessary land for future expansion /duplication of components should be acquired in the beginning itself. Where expensive tunnels and large aqueducts are involved entailing large capital outlay for duplication, they may be designed for ultimate project requirements.

The project components may be designed to meet the periods mentioned below

design period

**POPULATION FORECAST**

The design population will have to be estimated with due regard to all the factors governing the future growth and development of the project area in the industrial, commercial, educational, social and administrative spheres. Special factors causing sudden immigration or influx of population should also be foreseen to the extent possible.

A judgement based on these factors would help in selecting the most suitable method of deriving the probable trend of the population growth in the area or areas of the project from out of the following mathematical methods, graphically interpolated where necessary. The following are some of the methods prescribed by the CPHEEO for working out the projected population.

**1) Arithmetical increase Method:**

This method is based upon the assumption that the population increases at the constant rate, i.e. the rate of change of population with time is constant.

Mathematically,

dp/dt=constant=k

From the census data of past 3or 4 decades, the increase in population for each decade is found, and from that an average increment is found .For each successive future decade, this average increment is added. The future population Pn after n decade is thus given by

Pn=P+nI

Where,Pn=future population at the end of n decades

P=present population

I= average increment for decade

This method is used for large city, which have reached their saturation population.

**2) Geometrical increase Method**

In this method, the per decade percentage increase or percentage growth rate is assumed to be constant, and the increase is compounded over the existing population every decade. This method is, there for also known as uniform increase method.

In arithmetic method, no compounding is done where as in geometrical method compound is done every decade.

Hence, the assume constant value of percentage growth rate per decade(r) is analogous to the rate of interest per annum.

Pn=Po (1+r/100)n

Where, Pn=future population at the end of n decades

P0=initial population

r=assumed growth rate (%)

**3) Incremental increase Method**

This method combines both the arithmetic average method and geometrical method .From the census data for the past several decades, the actual increase in each decade is first found .then the increment in increase for each decade is found. For these an average increment of the increase is found.

The population in the next decade is found by adding to the present population the average increase plus the average incremental increase per decade. The process is repeated for the second future decade, and so on.

Pn =P+nI +n (n+1)/2*r

Where, Pn=future population at the end of n decades

r =assumed growth rate (%)

I = average increment for decade

n = no of decade

**4) Decrease rate of Growth Method.**

**5) Graphical extension method.**

**6) Graphical comparison method**

**7) Zooning method**

**8) Ratio correlation method**

**9) Growth composition analysis**

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design period