Generally there are two methods by which the quantity of storm-water is calculated: 1. The Rational Method 2. Empirical Formulae Method.
In both the above methods, the quantity of storm water is a function of the area (in hectares): the intensity of rainfall and the coefficient of runoff. The coefficient of runoff or the maximum rate of runoff mainly depends on the surface slope and the estimated condition of the drainage area with reference to the proportion of the rainfall that will run.
1. The Rational Method:
This method is mostly used in determining the quantity of storm water.
The storm water quantity is determined by the rational formula.
Where Q = quantity of storm-water in m3/sc.
C = coefficient of runoff
i = intensity of rainfall in mm/hour.
A = drainage area in hectares.
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From the above formula, it is clear that for the application of rational method, the selection of coefficient C and the rainfall intensity i, are required, which can be obtained by correct judgement.
The area A can be more accurately determined by the following three steps:
In first step, the plan of the city is prepared and tentative arrangement of sewer lines is shown on it. The whole area is also divided into zones and the concentration points along the proposed sewer lines are marked.
In the second step, the selection of rainfall frequency and the rainfall intensity for this frequency is determined. The time of concentration of storm water includes inlet time and the time of travel.
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The inlet time is the time required for the rain in falling on the most remote point of the tributary area to flow across the ground surface along drains or gutters up to the inlet of sewer. The time of travel is the time required by the storm water in travelling from the uppermost inlet up to the point of concentration.
In the third step, the proportion of rainfall which enters the sewer directly as runoff, is determined.
Runoff Coefficient:
In Rational Method, the value of runoff coefficient ‘C’ is required. The whole quantity of rain water that falls over ground does not reach the sewer lines or drains. A portion of it percolates in the ground, a portion evaporates, a portion is stored in ponds and ditches, and only the remaining portion of rain water reaches the drains and sewers. The runoff coefficient is a fraction which is multiplied with the quantity of total rainfall, to determine the quantity of rain water which will reach the sewers.
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After continuous rainfall for some time, the ponds and ditches are filled up and the atmosphere becomes nearly saturated, therefore the runoff coefficient mainly depends on the characteristics of ground surface as porosity, wetness, ground cover etc.
Table 4.1 gives the common values of runoff coefficient, which are commonly used in determining the quantity of storm water reaching the sewer lines.
As every locality consists of different types of surface areas, therefore, for calculating the over-all runoff coefficient the following formula is used.
Where A1, A2, A3 …………. Are the different types of area and C1, C2, C3 are their runoff coefficients respectively.
From the above expression, it is clear that for calculating runoff coefficient, area of each type of surface is to be measured and then substituted in the formula. The calculation of area of each type of surface is very tedious and impracticable. Therefore runoff coefficients are chosen by inspection of the localities, which directly depends on the density of population. Table 4.2 gives overall runoff coefficient for different types of localities.
2. Empirical Formulae Method:
For determining runoff from very large areas, generally empirical formulae are used. All the empirical formulae are applicable only under certain specific conditions such as slope of land, imperviousness, rate of rainfall etc. These have been developed suiting a particular region after long practical experience and collection of field data. Following original F.P.S. unit formulae have been converted into M.K.S. units.
Where Q = runoff in cu. m/sec.
c = runoff coefficient
z = intensity of rainfall in cm/hour.
S = slope of the area in metre per thousand metre.
A = drainage area in hectare.
M = drainage area in square km.
Empirical Formulae for Rainfall Intensities:
The intensity of rainfall can be worked out from the rainfall records of the area under consideration. The rainfall intensity may be taken from rainfall records of that area for which storm sewers are to be designed.
In case, where rainfall records are not available, the intensity of rainfall is obtained by applying suitable empirical formula.
Following are some of the empirical formulas which are used for this purpose:
(a) General Formula:
where i = intensity of rainfall in mm/hr
t = duration of storm in minutes a and b are constants
According to Ministry of health, U.S.A., the values of constant a and b are as follows:
(i) a = 30 and b = 10 when duration of storm is 5 to 20 minutes.
(ii) a = 40 and b = 20 when duration of storm is 20 to 100 minutes.
(b) For localities where rainfall is frequent:
This formula is adopted for area having heavy and frequent rainfall. It gives intensity of rainfall which will occur once in 5 yrs. or so.
(c) For storms occurring once in 10 yrs.:
(d) For storms occurring once in a year:
(e) Kuichling’s formula:
Example 1:
The catchment area of a city is 200 hectares.
Assuming that the surface on which the rain falls is classified as follows:
Calculate the impervious factor. If the maximum intensity of rainfall is 40 mm/hour, calculate the quantity of storm water which will reach sewer lines.
Solution:
Impervious factor or overall runoff coefficient ‘c’
Example 2:
In the above example if the density of population is 300persons/hectare and the rate of water supply is 250 litres/capita/day, calculate the quantity of sanitary sewage for (a) separate system and (b) for partially separate system.
Solution:
(a) Quantity of sanitary sewage for separate system:
(b) Quantity of sanitary sewage for partially separate system:
