Time of Concentration

Time of concentration, abbreviated as Tc, is the time it takes for water to flow from the most distant point in the watershed to the outlet or point of interest.  It represents the longest time it takes for water to travel through the watershed, following the path of flow.  It is crucial for understanding how fast runoff will reach the outlet after a rainfall event.

Tc is used to compute the peak discharge for a watershed.  Peak discharge is the maximum rate of runoff (flow rate) at the outlet of a watershed during a rainfall event.  Peak discharge is used in flood management and stormwater design, as it helps estimate the highest potential flood flows.

Key Points about Time of Concentration

Slope  -  Steeper slopes reduce Tc, as water moves faster.
Land Use  -  Urbanization, impervious surfaces (like concrete), and vegetation cover affect the flow speed.
Length of Flow Path  -  The distance water travels.
Surface Roughness  -  Dense vegetation or rough terrains slow water down, increasing Tc.

 

Time of Concentration Formula
\( Tc  \;=\;  G \; (\;1.1 - c\;) \; L^{0.5} \;/\; (100 \; S)^{1/3} \)     (FFA Equation) \( Tc  \;=\;  G \;  k  \; (\;L \;/\;  S^{0.5}\;)^{0.77}  \)     (Kirpidh Equation) \( Tc  \;=\;  G \; (\;L \; r \;/\;  S^{0.5}\;)^{0.467}  \)     (Kerby Equation)
Symbol	English	Metric
\( Tc \) = Time of Concentration	\(cfm\)	-
\( G \) = Constant. FAA: G = 1.8, Kirpich: G = 0.0078, Kerby: G = 0.8268	\(dimensionless\)	-
\( k \) = Kirpich Adjustment Factor	\(dimensionless\)	-
\( c \) = Rational Method Runoff Coefficient	\(dimensionless\)	-
\( L \) = Longest Watercourse Length in the Watershed	\(acre\)	-
\( S \) = Average Slope of the Watercourse	\(ft\;/\;ft\)	-
\( r \) = Kerby Retardance Roughness Coefficient	\(dimensionless\)	-

 

Table of Coefficients
Ground Cover	Runoff Coefficient
Asphault Streets	0.7 - 0.95
Brick Streets	0.7 - 0.85
Buisness Areas	0.5 - 0.95
Concrete Streets	0.7 - 0.95
Cultivated Lands	0.08 - 0.41
Forests	0.05 - 0.25
Industrial Areas	0.5 - 0.9
Lawns	0.05 - 0.35
Meadows	0.1 - 0.5
Parks, Cemeteries	0.1 - 0.25
Pasture	0.12 - 0.62
Residential Areas	0.3 - 0.75
Roofs	0.75 - 0.95
Unimproved Areas	0.1 - 0.3
Ground Cover	Kirpich Adjustment Factor
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
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