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Time of Concentration

Time of concentration is a term that describes the time required for water to travel from the hydraulically most distant point in a drainage area to a specific outlet, such as a storm drain, culvert, channel, or watershed outlet.  It represents the point at which runoff from the entire drainage area is contributing flow at the outlet.  Before the time of concentration is reached, only part of the watershed contributes runoff to the discharge at that location.  After it is reached, the whole watershed is effectively contributing flow simultaneously under the assumed rainfall conditions.

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 \(dimensionless\) -

 The concept is used in stormwater engineering, flood analysis, watershed modeling, and the design of drainage systems.  A shorter time of concentration generally produces a higher peak flow because runoff arrives at the outlet more quickly and with less attenuation.  Conversely, a longer time of concentration spreads runoff over a greater period, usually reducing peak discharge.  Factors that influence time of concentration include watershed slope, surface roughness, land cover, soil characteristics, flow path length, rainfall intensity, channel geometry, and the degree of urbanization.  Impervious surfaces such as pavement and roofs typically reduce the time of concentration because they allow water to move more rapidly than natural ground surfaces.

There is no single universal equation for determining time of concentration because different hydrologic conditions require different empirical or analytical methods.  Engineers select the appropriate method based on watershed size, terrain, land use, and applicable engineering standards or regulatory guidance.

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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