Contents preface (VII) introduction 1—37

2.8.1.1. Rational Method
The runoff rate during and after a precipitation of uniform intensity and long duration typically varies as shown in Fig. 2.28. The runoff increases from zero to a constant peak value when the water from the remotest area of the catchment basin reaches the basin outlet. If t_c is the time taken for water from the remotest part of the catchment to reach the outlet and the rainfall continues beyond t_c, the runoff will have attained constant peak value. When the rain stops the runoff starts decreasing. The peak value of runoff, Q_p (m³/s) is given as

Q =	1	C i A	(2.26)
3.6
	p

where, C = coefficient of runoff (Table 2.3) depending upon the nature of the catchment surface and the rainfall intensity, i.
i = the mean intensity of rainfall (mm/hr) for a duration equal to or exceeding t_c and an exceedence probability P, and
A = catchment area in km².

Runoffandrainfallrates

End of rainfall

Recession i

Peak

value

Qp
Runoff

t_c

Time

(Volume of the two hatched portions are equal)

Fig. 2.28 Runoff hydrograph due to uniform rainfall

86	IRRIGATION AND WATER RESOURCES ENGINEERING
	Table 2.3 : Coefficient of runoff C for different surfaces
	Type of surface	Value of C
	Wooded areas	0.01 – 0.20
	Parks, open spaces lawns, meadows	0.05 – 0.30
	Unpaved streets, Vacant lands	0.10 – 0.30
	Gravel roads and walks	0.15 – 0.30
	Macadamized roads	0.25 – 0.60
	Inferior block pavements with open joints	0.40 – 0.50
	Stone, brick and wood-block pavements with open or uncemented joints	0.40 – 0.70
	Stone, brick and wood-block pavements with tightly cemented joints	0.75 – 0.85
	Asphalt pavements in good order	0.85 – 0.90
	Watertight roof surfaces	0.70 – 0.95

The time t_c (known as time of concentration) can be obtained from Kirpich equation

t = 0.01947 L^0.77	S–0.386	(2.27)
c

where, t_c is in minutes, L is the maximum length (in metres) of travel of water from the upstream end of the catchment basin to the basin outlet, and S is the slope of the catchment which is equal to ∆H/L in which ∆H is the difference of elevations of the upstream end of the catchment and the outlet.
The method is suitable for catchments of small size less than about 50 km² i.e., 5000 hectares and is often used for peak flow estimation required for deisgn of storm drains, culverts, highway drains etc.
2.8.1.2. Empirical Methods
The empirical relations are based on statistical correlation between the observed peak flow, Q_p (m³/s) and the area of catchment, A (km²) in a given region and are, therefore, region-specific. The following empirical relations are often used in India:
(a) Dicken’s formula, used in the central and northern parts of India, is as follows:

	Q = C A^3/4			(2.28)
	p	D
where, CD (known as Dicken’s constant) is selected from the following Table (8):
	Region				Value of CD
	North Indian plains			6
	North Indian hilly regions			11 – 14
	Central India				14 – 28
	Coastal Andhra and Orissa		22 – 28
(b) Ryves formula, used in Tamil Nadu and parts of Karnataka and Andhra Pradesh, is
as follows :	Q = C A^2/3	(2.29)
			p	R

The recommended values of C_R are as follows:

C_R = 6.8 for areas within 80 km from the east cost

• 
  8.5 for areas which are 80 – 160 km from the east coast
  

• 
  10.2 for limited areas near hills.
  

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(c) Inglis formula, used in regions of Western Ghats in Maharashtra, is as follows:

124 A
^Qp ^= A + 10.4	(2.30)

( d) Envelope curve technique is used to develop peak flow-area relationship for areas having meager peak flood data. The data of peak flow from large number of catchments (having meteorological characteristics similar to the region for which peak flow-area relationship is sought to be prepared) are plotted against catchment area on a log-log graph paper. The enveloping curve, encompassing all the data points, gives peak flow–area relation for any catchment that has meteorological characteristics similar to the ones of catchments whose data were used to obtain the envolope curve. Equation of the envelope curve would yield empirical formula of the type Q_p = f(A). Two such curves, based on data from large catchments of areas in the range of 10³ to 10⁶ km², are shown in Fig. 2.29 (8).

	5
	10
	5
			Northern and central
	3		indian rivers
3(m/s)	2
flooddischarge	4
	10					Southern indian rivers
5
Peak
	3
	2
	3
	10	3		4				5		6
	10	2	5	10	2	5	10	2	5	10
							2

Drainage area (km )
Fig. 2.29 Envelope curves for Indian rivers (8)
Based on data of peak flood in various catchments throughout the world, Baird and

McILL wraith have given the following formula for Q_p (8) :

Qp =	3025 A	(2.31)
(278 + A)^0.78

Similarly, CWC (11, 12, and 13) recommended the following relation for the estimation of peak flood flow for small to medium catchments (A < 250 sq. km) :

Q	= A [a(t )^b]	...(2.32)
p	p

in which, t_p is the time (in hours) to peak and is expressed as

t	p	= c [L /	S ]^d	...(2.33)
		c

88 IRRIGATION AND WATER RESOURCES ENGINEERING

in which, L _c is the length of the longest stream from the point, opposite to the centroid of the catchment, up to the gauging site in km, S is the slope of the catchment in m/km, and the values of the constants a, b, c, and d in Eqs. (2.32) and (2.33) are region-dependent (Table 2.4).