Time of Concentration

The time of concentration (t_c) is the time needed for water to flow from the farthest point in a watershed to the outlet of the watershed. Definition aside (which is taken straight from Wikipedia) there are a lot of formula's that solve for time of concentration. So many that I doubt it's validity in all cases and wonder if it will be on the breadth test :). Without further ado, the formula's:

In all of these examples the following variables are used:
L     Length of flow path
S     Average Slopw
C     Overall rational coefficient (C_{avg})
i      intensity (in/hr)
n     manning's roughness coefficient


Kirpich (general, mostly rural)

 t_c = 0.0078L^{0.77}S^{-0.385}

Kirpich's equation should be used for a lot of areas in general.

FAA Formula (Urban Areas)

 t_c = \dfrac{1.8(1.1-C)\sqrt{L}}{S^{1/3}}

Manning's Kinematic Wave Formula (Paved Areas)

 t_c = \dfrac{0.938}{i^{0.4}} \left( \dfrac{nL_o}{\sqrt{S}} \right)^{0.6}

NCRS Lag Equation (Small urban areas, most cities)

 t_c = \dfrac{1.67 L_o^{0.8} \left(\dfrac{1000}{CN}-9 \right)^{0.7}}{1900S^{0.5}}

Kerby's Equation

 t_c = 0.67 \left( \dfrac{nL_o}{ \sqrt{S} } \right)^{0.467}

I am not a hydrologist, so which of these to use is a shot in the dark. I think part of being a hydrologist is picking your favorite of these methods and modifying it to fit your own needs for your region.

For those of us just tackling this stuff on the breadth test, well, I am definitely taking these formulas into the test with me... will I use them? I hope not, but if I have to  I will pick one of them based on what variables I am given.

About Conrad

I am a Civil Engineer. I work in San Diego and am preparing to take the PE Exam. I am interested in surfing, business, travelling, and spending time with my wife. Thanks!

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