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close this bookStormwater Drainage and Land Reclamation for Urban Development (HABITAT, 1991, 94 p.)
close this folderD. FLOOD ESTIMATION
View the documentD.1 General
View the documentD.2 Modified rational method
View the documentD.3 Design hydrograph
View the documentD.4 Partial areas effect

D.2 Modified rational method

The formula for peak runoff estimation is:

Q = FCCSIA, (D.1)


Q = the peak discharge in cubic metres per second of return period T years

I = the average intensity of rainfall in mm per hour for a duration equal to the time of concentration (tc) and return period T year

A = the catchment area in hectares

C = coefficient of runoff

CS = storage coefficient

F = factor of proportionality (= 0.00278 when A in hectares)

(a) Time of concentration

The time of concentration is the time required for water to flow from the most remote point of the catchment to the point being investigated. For urban stormwater drains, the time of concentration (tc) consists of the time required for runoff to flow over the ground surface to the nearest drain (to) and the time of flow in the drain to the point under consideration (td):

tc = to + td, (D.2)

Overland flow time

The time for overland flow (to) should be estimated from figure D.1 using appropriate values of length, slope and runoff coefficient C (see table D.2 and figures D.2 and D.3 for values of C.)

Drain flow time

The time of flow in drains (td) is estimated from the hydraulic properties of the drain. In the case of natural streams where the hydraulic properties are difficult to determine the time of flow shall be estimated using the velocities shown in table D.1.

Table D.1. Approximate steam velocity

Average slope of Stream (percentage)

Average velocity (metres/second)

Less than 1


1 - 2


2 - 4


4 - 6


6 - 10


10 - 15


(b) Rainfall intensity

For a given storm recurrence interval, the rainfall intensity (I) is the average rate in millimetres per hour of precipitation from a storm having a duration equal to the time of concentration (tc). Rainfall intensity - duration - frequency relationships must be derived for the locality.

(c) Runoff coefficient

The runoff coefficient C is difficult to determine precisely and can be interpreted in different ways. Engineering judgement is necessary in selecting the appropriate procedure. Coefficients for the modified rational method described above should be based on ultimate catchment development and weighted where more than one land use is likely.

A weighted coefficient (Cw) should be calculated where land uses vary or surface characteristics exist in the catchment:

Figure D.1. Surface flow times (time of concentration) for areas with sheet flow



t = time of travel over surface in minutes

n = roughness coefficients for the surface

Lf = length of flow in metres

s = Slope of surface in %


Length of overland flow 100 m
Average slope of surface 2%
Poorly grassed surface
Time of travel = 15 minutes.

Cw = (A1C1 + A2C2 +..... + AnCn) ÷ A, (D.3)


A1, A2, An = n areas of relatively uniform land use or surface character comprising the total area A

C1, C2, Cn = corresponding runoff coefficients obtained from table D.2 (or from figures D.2 and D.3)

Table D.2: Rational method runoff coefficient

Land use

Runoff coefficient (c)


Central commercial Industrial

0.90 - 0.95


0.80 - 0.90

- Low-density: 20 houses/ha

0.25 - 0.40

- Medium-density: 20-60 houses/ha

0.40 - 0.70

- High-density: 60-160 houses/ha

0.70 - 0.80

Parks and recreation areas

0.20 - 0.30


Steep slopes > 20 percent

0.50 - 0.60

Undulating slopes > 20 percent

0.40 - 0.50

Terraced slopes

0.25 - 0.35

Irrigated ricefields and pasture

0.45 - 0.55

(d) Storage coefficient

As the catchment areas gets larger the effect of channel storage on the attenuation of the flood wave becomes more pronounced. To allow for channel storage effect the peak discharge calculated by the basic Rational Method formula Q = CIA/360 should be multiplied by a storage coefficient (Cs) to modify the basic formula:

Cs = 2tc/(2tc+td) (D.4)