Question

Calculate the time of concentrations (or overland flow) for the two sub-areas of a watershed given below by multiple applicable methods (at least 3). Compare your answers for each method and watershed and discuss which may be the most accurate and why.

Sub Area	Area (acres)	Impervious Acres	Avg. Surface Slope (%)	Runoff Coefficient	Distance to Inlet
Residential & small residences	52.6	10.5	3.0	0.42	1800
Small Business	14.0	6.3	4.5	0.66	850

Answer 1

Ans) Method 1 - FAA( Federal Aviation Administration ) method :

Residential & small residences

According to FAA ,

t_c = 1.8 (1.1 - C) L^0.5 / (100S)^0.333

where, C = runoff coefficient

L = distance to inlet

S = slope

Putting values,

t_c = 1.8(1.1 - 0.42) (1800)^0.5 /[100(0.03)]^0.333

= 36 minutes

For small business area,

C =0.66 , L = 850 ft

Putting values,

t_c = 1.8(1.1 - 0.66) (850)^0.5 / [100(0.045)]^0.333

= 14 minutes

Method 2 - Kirpich Method

According to this method,

T_c = 0.0078K (L/S^0.5)^0.77

where K =Kirpich adjustment factor

L = distance to inlet

S = slope

For residential area , K = 1

Hence,

t_c = 0.0078[1800/(0.03)^0.5]^0.77

= 9 min 40 sec

For business area ,

t_c = 0.0078 [ 850/(0.045)^0.5]^0.77

= 4 min 38 sec

Method 3) Kerby Method

According to Kerby,

t_c = 0.8268 ( L r /S^0.5 )^0.467

where r = Kerby roughness coefficient

S = slope

L = distance to inlet

For residential area , r = 0.02

Hence, tc = 0.8268 (1800(0.02) / ( 0.03)^0.5]^0.467

= 10 minutes

For business area,

t_c = 0.8268[850(0.02) / (0.045)^0.5]^0.467

= 6 minutes 24 sec

Therefore, results calculated are as follows,

Sub Area	tc (FAA method)	tc (Kirpich Method)	tc (Kerby method)
Resedential	36 min	9 min 40 sec	10 min
Business	14 min	4 min 38 sec	6 min 24 sec

Out of the above three results we can see that results from Kirpich and Kerby methods are close to each other but FAA method is different from the other two methods. The Kirpich and Kerby methods are older methods and not commonly used now.Also, the FAA method is most commonly used nowadays and is most accurate then others because it uses runoff coefficient to describe watershead ground cover which is widely recognized.