Time of Concentration (Kirpich)
The storm duration stormwater-rational needs but never computes: the Kirpich estimate tc = 0.0078 L^0.77 S^(-0.385) (tc min, L ft, S ft/ft) - the time for runoff to reach the outlet, the duration at which a designer reads the design rainfall intensity off the local IDF curve. A 1,000 ft flow path at 2% slope gives 7.2 min; flatten it to 0.5% and the water takes 12.3 min, a lower intensity and a smaller peak - the flood-control value of grading a site flat. Single-segment estimate, not the TR-55 three-segment sum. A design aid; the engineer of record governs.
Formula and source
tc_min = 0.0078 L^0.77 S^(-0.385) (tc minutes, L feet, S ft/ft); tc_hr = tc_min / 60.
The Kirpich (1940) time-of-concentration equation tc = 0.0078 L^0.77 S^(-0.385), as compiled in the USDA TR-55 and NRCS drainage references, by name.
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