How to Determine Storm Water Flow? | Waste Management

For determining storm water (or rain water) flow or runoff by rational formula three factors viz., catchment area or drainage area, runoff coefficient and intensity of rainfall are required to be determined.

These factors may be determined as indicated below:

Factor # 1. Catchment Area or Drainage Area:

The catchment area or drainage area to be served by a sewer can be determined from the map of the town or city. Since the coefficient of runoff depends on the type of surface, the portions of the catchment area or drainage area having different types of surfaces should be determined separately.

Factor # 2. Runoff Coefficient:

The runoff coefficient represents the fraction of the total rainfall that is available in the form of storm water (or rain water) flow or runoff reaching a sewer. Its value depends on the imperviousness and the shape of the catchment area or drainage area, and the duration of storm. The runoff coefficient increases with the increase in the imperviousness of the catchment area or drainage area, because greater is the imperviousness of the area lesser will be infiltration and hence greater will be runoff.

The percent imperviousness of the catchment area or drainage area can be obtained from the records of the area. However, in the absence of such data the following values of the percentage imperviousness may be adopted –

A catchment area or drainage area usually consists of areas with different imperviousness.

As such it is necessary to determine the weighted average imperviousness of the total catchment area or drainage area which may be obtained by the following expression:

Where

A₁, A₂,…, are areas with different imperviousness;

i₁, i₂,…, are imperviousness of the respective areas;

A is total catchment area or drainage area; and

i is weighted average imperviousness of the total catchment area or drainage area.

The runoff coefficient is also affected by the duration of storm. A continuously long light rain saturates the soil and produces higher runoff coefficient than that due to heavy but intermittent rain in the same area because of the lesser saturation in the later case.

Further runoff from an area is significantly influenced by the saturation of the surface nearest to the point of concentration, rather than the flow from the distant area. The runoff coefficient of a large area has to be adjusted by dividing the area into zones of concentration and by suitably decreasing the coefficient with the distance of the zones.

The weighted average runoff coefficients for rectangular areas of length four times the width as well as for sector shaped area with varying percentages of impervious surface for different duration of storm have been computed by Horner and the same are given in Table 3.6.

Although these values of runoff coefficient are applicable to particular shapes of areas, they can be applied to areas of other shapes also which are usually encountered in practice. Errors due to difference in shape of catchment area or drainage area are within the limits of accuracy of the rational method and of the assumptions on which it is based.

For various types of surfaces Kuichling has also recommended different values of runoff coefficient which are given in Table 3.7. Further Fruhling has recommended different values of runoff coefficient for various types of localities which are given in Table 3.8. The runoff coefficient has been designated as impermeability factor by Kuichling and Fruhling.

A catchment area or drainage area usually consists of various types of surfaces for which different values of runoff coefficient or impermeability factor are applicable.

As such it is necessary to determine an average runoff coefficient or impermeability factor applicable to the entire catchment area or drainage area, which may be obtained by the following expression:

Where

A₁, A₂,…, are areas of different types of surfaces;

C₁, C₂,…, are runoff coefficients or impermeability factors of the respective areas; and

A is total catchment area or drainage area; and

C is average runoff coefficient or impermeability factor.

It may, however, be noted that the effect of duration of storm is not taken into account on the values of runoff coefficient or impermeability factor recommended by Kuichling and Fruhling. As such the values of runoff coefficient or impermeability factor given by Horner appear to be more rational.

Factor # 3. Intensity of Rainfall:

The intensity of rainfall can be worked out from the rainfall records of the area under consideration. The longer the rainfall record available the more dependable is the forecast. The intensity of rainfall, however, depends on frequency and duration of storms.

(A) Frequency of Storm:

The frequency of storm means the number of times a rainfall of given magnitude will be equaled or exceeded in any one year. It is usually expressed in terms of return period or recurrence interval T, which is the number of years during which a rainfall of given magnitude will be equaled or exceeded once.

The return period for a rainfall of given magnitude may be determined from the record of rainfall for a number of years. The rainfalls are arranged in the descending order of magnitude and assigned serial numbers. Thus the highest rainfall is placed at the top and given serial number 1, next highest is given serial number 2, and so on. Thus if rainfall record of n number of years is considered, the lowest rainfall will be at the bottom with serial number n.

If a particular rainfall has a serial number m then its return period can be found by any of the following methods:

Where C is known as Gumbel’s correction the value of which depends on (m/n) and it can be found from Table 3.9.

It may be mentioned that sewers are usually not designed for the peak storm water (or rain water) flow of rare occurrence such as the one resulting from a storm having a return period of 10 years or more, because this would require sewers of very large size. However, it is necessary to provide sewers of sufficient capacity to avoid too frequent Hooding of the catchment area or drainage area.

There may be some flooding when the rainfall exceeds the design value, which has to be permitted. The frequency of such permissible flooding may vary from place to place depending on the importance of the area. Though such flooding causes inconvenience, it may be accepted once in a while considering the economy that would be achieved due to sewers of small size being required to be provided which would involve less cost.

The frequency of storm for which the sewers are to be designed depends on the importance of the area to be drained. Commercial, industrial and high priced areas should be subjected to less frequent flooding.

The Manual on Sewerage and Sewage Treatment prepared by Central Public Health and Environmental Engineering Organisation suggests the following values of frequency of flooding permissible in different areas-

(a) Residential Areas:

(i) Peripheral areas: Twice a year

(ii) Central and comparatively high priced areas: Once a year

(b) Commercial and high priced areas: Once in 2 years

(B) Duration of Storm:

The duration of storm is the time during which rainfall takes place. However, for the design of sewers the duration of storm is taken equal to the time of concentration. It is the time required for the rain water to flow over the ground surface from the extreme point of the catchment area or drainage area and reach the point under consideration.

When the duration of storm is equal to the time of concentration then, since the entire catchment area or drainage area will be simultaneously contributing the runoff, maximum runoff will occur at the point under consideration.

On the other hand when the duration of storm is shorter than the time of concentration then, as indicated below although the intensity of rainfall will be more, since the entire catchment area or drainage area will not be simultaneously contributing the runoff, lesser runoff will occur at the point under consideration.

Further when the duration of storm is longer than the time of concentration then as indicated below the rainfall intensity will be less which will result in a lesser runoff at the point under consideration.

The time of concentration t_c is equal to inlet time t_o plus the time of flow in the sewer t_f, that is –

t_c = t_o+t_f …(3.12)

The inlet time is the time taken by the rain water to flow from the farthest point in the catchment area or drainage area to the inlet end of the sewer. The inlet time depends on the distance of the farthest point in the catchment area or drainage area to the inlet end of the sewer; the shape, characteristics and topography of the catchment area or drainage area; and it may generally vary from 5 to 30 minutes. In highly developed areas the inlet time may be as low as 3 minutes.

Since for different types of surfaces the inlet times will be different, if a particular catchment or drainage area comprises different types of surfaces, the inlet time for the entire area may be found by taking the weighted average of the different areas.

For example if in a particular catchment area or drainage area A₁ is built up area with inlet time t_ob, and A₂ is the area of lawns with inlet time t_ol, then the inlet time t_o for the entire area is given by the following expression:

The time of flow is the time taken by the rain water to flow in the sewer from the inlet end of the sewer to the point under consideration. The time of flow is determined by the length of the sewer and the velocity of flow in the sewer. Thus for computing the time of flow the length of sewer from its inlet end to the point under consideration is measured and the velocity of flow in the sewer is suitably assumed.

The time of flow is then given by the following expression:

The time of flow is to be computed for each length of sewer to be designed.

The intensity of rainfall decreases as the duration of storm increases. Further a storm of any given duration will have a larger intensity of rainfall if its return period is large. Fig. 3.2 shows typical rainfall intensity—duration of storm curves for different return periods.

These curves may be prepared from the rainfall data. From these curves the value of intensity of rainfall I can be determined for a known value of time of concentration t_c, since duration of storm is taken equal to the time of concentration.

The intensity of rainfall may also be determined from the various empirical formulae which express relationship between intensity of rainfall and duration of storm.

These empirical formulae are available in the following two general forms:

Some of the empirical formulae are as given below:

Introducing the above expression for the intensity of rainfall in the rational formula, equation 3.4, it becomes

Where

Q is storm water (or rain water) flow or runoff in cumec (or m³/s);

C is runoff coefficient;

A is catchment area or drainage area in hectare: and

r and t_c are same as indicated above.

Lloyd Davis formula is based on the following assumptions:

(i) The storm water discharge from any district is directly proportional to the percentage of impermeable area contained in it.

(ii) The discharge of storm water is proportional to the aggregate rainfall during the time of concentration.

(iii) The maximum rate of flow is reached when the duration of storm is equal to the time of concentration.

(iv) The total volume of storm water is proportional to the maximum rate of flow.