Time of Concentration (TR-55 Velocity Method)
The three-segment time of concentration the Kirpich tile approximates in one equation: the NRCS TR-55 velocity method sums the travel time through sheet flow, shallow concentrated flow, and open channel. Sheet Tt = 0.007 (n L)^0.8 / (P2^0.5 s^0.4) (n the overland roughness, P2 the 2-yr 24-hr rainfall, L capped at 100 ft); shallow V = 16.13 sqrt(s) unpaved or 20.33 sqrt(s) paved; channel V = (1.49/n) R^(2/3) sqrt(s). The TR-55 Chapter 3 example -- 100 ft dense-grass sheet, 1,400 ft unpaved swale, 3,000 ft channel -- gives 17.8 + 14.5 + 28.7 = 61.0 min. Enter a length of 0 to skip a segment. This is the method modern US stormwater design actually uses; Kirpich is the older rural single-channel shortcut. A design aid; the local drainage manual and the engineer of record govern.
Formula and source
Tc = Tt_sheet + Tt_shallow + Tt_channel. Sheet (TR-55 Eq 3-3): Tt = 0.007 (n L)^0.8 / (P2^0.5 s^0.4) hr. Shallow concentrated: V = 16.1345 sqrt(s) unpaved / 20.3282 sqrt(s) paved, Tt = L/(3600 V) hr. Channel (Manning): V = (1.49/n) R^(2/3) sqrt(s), Tt = L/(3600 V) hr.
The NRCS TR-55 (Urban Hydrology for Small Watersheds, 1986) Chapter 3 velocity method for time of concentration, by name; constants verified against the TR-55 Chapter 3 worked example.
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