Kirpich Time of Concentration

Every peak-flow method needs to know how long water takes to travel from the far corner of the catchment to the outlet, and Kirpich's 1940 fit is the shortest route to an answer. He measured six small agricultural watersheds in Tennessee, none larger than 45 hectares, and produced $t_c = 0.0078 L^{0.77} S^{-0.385}$ with the flow length in feet and the answer in minutes. A thousand feet of flow path on a five percent grade concentrates in 5.05 minutes. In metres the same equation reads $t_c = 0.0195 L^{0.77} S^{-0.385}$, and this solver converts whatever you type before applying the published constant.

The exponents are worth reading. Length matters slightly less than proportionally, slope rather less than the square root, and the practical consequence is that halving the grade on a channel lengthens the travel time by only about thirty percent. That is why regrading rarely fixes a timing problem and why lengthening the flow path with a swale often does more than anything you can do to the slope.

Kirpich was fitted to bare or sparsely vegetated agricultural channels, and applying it unchanged to anything else is the standard error. The published guidance is to multiply by 0.4 for overland flow on concrete or asphalt, by 0.2 for a concrete-lined channel, and by 2.0 for overland flow on grass, and those multipliers span an order of magnitude. There is a floor as well: most agencies refuse a time of concentration below 5 or 10 minutes regardless of what any equation says, because IDF curves are not defined at shorter durations and the rational method becomes nonsense. If Kirpich hands you 2.3 minutes, the honest answer is the agency minimum, not 2.3.