Time of Concentration (TR-55 Velocity Method)
Time of concentration by the NRCS TR-55 velocity method, summing the travel time through sheet flow.
Example
You enter
- Sheet n 0.24
- Sheet length (ft) 100
- P2 (in) 3.6
- Sheet slope 0.01
- Shallow concentrated: surface unpaved
- Shallow length (ft) 1400
- Shallow slope 0.01
- Channel n 0.05
- Channel hyd radius (ft) 0.75
- Channel length (ft) 3000
- Channel slope 0.005
You get
- Tt sheet (min) 17.7528
- Tt shallow (min) 14.4618
- Tt channel (min) 28.7449
- Time of concentration 60.9595
- V shallow (fps) 1.6135
- V channel (fps) 1.7394
Details, formula, and sources
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.
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.
TR-55 is a free USDA NRCS publication; the sheet/shallow/channel travel-time equations and their constants are published in it and in every hydrology text.
Estimate. AHJ and licensed professional govern.
Field names used by the API: sheet_n, sheet_length_ft, p2_in, sheet_slope, shallow_surface, shallow_length_ft, shallow_slope, channel_n, channel_hyd_radius_ft, channel_length_ft, channel_slope, tt_sheet_min, tt_shallow_min, tt_channel_min, tc_min, v_shallow_fps, v_channel_fps
- Sheet flow Tt = 0.007 (n L)^0.8 / (P2^0.5 s^0.4), L capped at 100 ftTR-55 Eq 3-3
- Shallow concentrated V = 16.1345 sqrt(s) unpaved / 20.3282 sqrt(s) pavedTR-55 Figure 3-1
- Channel Manning V = (1.49/n) R^(2/3) sqrt(s), Tt = L / (3600 V)TR-55 Chapter 3
- Use Tc sets the design storm duration read off the local IDF curve, not a routed hydrographNRCS drainage practice