Time of Concentration Calculator Compute watershed time of concentration using FAA equation (rational method), Kirpich equation, or Kerby equation

Fig. 1. Sample Watershed.
Heavy black line indicates watershed boundary
Heavy blue line indicates longest watercourse.
Length of longest watercourse = 4500 ft. (curvy length)
Slope of longest watercourse = (980-760) ft / 4500 ft = 0.0489 ft/ft = 0.0489 m/m

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Introduction
Time of concentration is a fundamental watershed parameter. It is used to compute the peak discharge for a watershed. The peak discharge is a function of the rainfall intensity, which is based on the time of concentration. Time of concentration is the longest time required for a particle to travel from the watershed divide to the watershed outlet. Each of the three equations used in our time of concentration calculation require inputs for the longest watercourse length in the watershed (L), the average slope of that watercourse (S), and a coefficient representing the type of groundcover. Usually L and S can be obtained from topographic maps as in Fig. 1 above. The coefficient is determined from photographs of the watershed or field reconnaissance. Our calculation computes the time of concentration and average velocity in the longest watercourse. A variety of units may be selected.

Our calculation uses the FAA, Kirpich, and Kerby equations. The FAA (U.S. Federal Aviation Administration) equation is the most commonly used of the three because it uses the widely recognized Rational Coefficient to describe watershed ground cover. The ASCE (American Society of Civil Engineers) recommends its use. The Kirpich equation, developed in 1940, is the oldest of the three equations and is probably the most widely recognized, but no longer the most commonly used. The Kerby equation is the least common of the three equations and has the most limitations. Please see the section below for applicability of the equations. There are other equations for time of concentration, but most of them require rainfall intensity as an input. Thus, using those other equations to determine the rainfall intensity for computing peak discharge results in an iterative process because the rainfall intensity itself is a function of the time of concentration.

Equations
The following equations are used for the calculation. All of the equations shown below use the English units indicated in the Variables section. Of course, our calculation uses a variety of units with all of the unit conversions handled internally by the program. The equations can be found in Chin (2000), Chow et al. (1988), Corbitt (1999), and Singh (1992).

FAA equation:   t = G (1.1 - c) L0.5 / (100 S)1/3

Kirpich equation:   t = G k (L / S0.5) 0.77

Kerby equation:  t = G (L r / S0.5) 0.467

Recommendations
The FAA method was developed from data obtained from airport runoff but has been successfully applied to overland flow in urban areas.
The Kirpich equation was developed from data obtained in seven rural watersheds in Tennessee (USA). The watersheds had well-defined channels and steep slopes of 0.03 to 0.1 ft/ft (3 to 10%) and areas of 1 to 112 acres. It is used widely in urban areas for both overland flow and channel flow; and it is used for agricultural watersheds up to 200 acres (80 hectares).
The Kerby equation was developed from data obtained in watersheds having watercourses less than 1200 ft. (365 m), slopes less than 0.01 ft/ft (1%), and areas less than 10 acres (4 hectares).

Variables

The units refer to the units that must be used in the equations shown above.  However, a variety of units may be used in our calculation.

c = Rational method runoff coefficient. See table below.

k = Kirpich adjustment factor.  See table below.
L = Longest watercourse length in the watershed, ft.
r = Kerby retardance roughness coefficient. See table below.
S = Average slope of the watercourse, ft/ft or m/m.
t = Time of concentration, minutes.
V = Average velocity in watercourse, ft/min. V=L/t.

Table of Coefficients

 Ground Cover Rational Runoff Coefficient for FAA Method, c (Corbitt, 1999; Singh, 1992) Lawns 0.05 - 0.35 Forest 0.05 - 0.25 Cultivated land 0.08-0.41 Meadow 0.1 - 0.5 Parks, cemeteries 0.1 - 0.25 Unimproved areas 0.1 - 0.3 Pasture 0.12 - 0.62 Residential areas 0.3 - 0.75 Business areas 0.5 - 0.95 Industrial areas 0.5 - 0.9 Asphalt streets 0.7 - 0.95 Brick streets 0.7 - 0.85 Roofs 0.75 - 0.95 Concrete streets 0.7 - 0.95 Ground Cover Kirpich Adjustment Factor, k (Chow et al., 1988; Chin, 2000) General overland flow and natural grass channels 2.0 Overland flow on bare soil or roadside ditches 1.0 Overland flow on concrete or asphalt surfaces 0.4 Flow in concrete channels 0.2 Ground Cover Kerby Retardance Coefficient, r (Chin, 2000) Conifer timberland, dense grass 0.80 Deciduous timberland 0.60 Average grass 0.40 Poor grass, bare sod 0.30 Smooth bare packed soil, free of stones 0.10 Smooth pavements 0.02

Error Messages given by calculation
"Need S>0", "Need L>0".  Initial input checks. Slope and Length must be positive numbers.

"Need 0<c<1.1 for FAA". c must be in this range for the FAA equation. c cannot physically be greater than 1.0, but you will only get an error message if it is greater than 1.1 since that will cause t to be negative.

"Need k>0 for Kirpich", "Need r>0 for Kerby". Input checks.

References
Chin, David A. 2000. Water-Resources Engineering. Prentice-Hall.

Chow, Ven Te, David R. Maidment, and Larry W. Mays. 1988. Applied Hydrology. McGraw-Hill.

Corbitt, Robert A. 1999. Standard Handbook of Environmental Engineering. McGraw-Hill. 2ed.

Singh, Vijay P. 1992. Elementary Hydrology. Prentice-Hall.