# WMS:Kirpich Tc Equation

Kirpich’s equation (1940) was developed for small, agricultural watersheds. It was derived by examining the required time for the stream to rise from low to maximum stage during a storm. The time of concentration was then assumed equal to that time.

${\displaystyle t_{c}={\frac {0.00013L^{0.77}}{S^{0.385}}}}$

where:

tc = time of concentration in hours.
L = length of the overland flow in feet.
S = average overland slope in ft/ft.

This equation given below was developed for overland flow on bare earth. For overland flow on grassy earth, tc should be multiplied by 2.0. On concrete and asphalt surface it should be multiplied by 0.4. An adjustment is made for watersheds with a CN number less than 80 using the following equation:

${\displaystyle t_{c}=t_{c}\ast (1+(80-CN)\ast 0.04)}$

The CN value must be defined for the given model (HEC-1, TR-20, etc.), otherwise a default CN of 50 is used.