Engineering
Kirpich Watershed Time of Concentration (tc) & NRCS Basin Lag Time
Calculate stormwater watershed Time of Concentration t_c = 0.01947 * L^0.77 * S^(-0.385) (minutes, SI flow length L in meters and slope S in m/m) and NRCS Unit Hydrograph Lag Time t_lag = 0.60 * t_c.
Select the right design storm duration for Rational Method and hydrograph routing!
Every Rational Method peak-discharge (Q = C * i * A) and SCS/NRCS unit hydrograph study begins with Time of Concentration (t_c): the travel time in minutes required for runoff from the hydraulically most distant ridge of a catchment to reach the outlet culvert! Setting IDF storm duration equal to t_c produces peak basin outflow because 100% of watershed area contributes simultaneously!
Using SI hydraulic flow-path length L (in meters) and average main-channel slope S = Delta_H / L (in m/m), Z.P. Kirpich's (1940) empirical formula gives: t_c = 0.01947 * (L ^ 0.77) * (S ^ -0.385) (in minutes; for paved concrete channels multiply t_c by 0.4, for overland grass multiply by 2.0), and NRCS Unit Hydrograph Basin Lag Time follows directly as t_lag = 0.60 * t_c!
| Catchment Geometry (Flow Path L = 1,200 m) | Channel Slope S (m/m) | Kirpich Time t_c (Minutes) | NRCS Lag Time t_lag = 0.6 * t_c |
|---|---|---|---|
| Moderate Agricultural Swale | 0.025 (2.5% grade) | 18.93 min | 11.36 min |
| Steep Foothill Ravine | 0.080 (8.0% grade) | 12.10 min (Faster peak!) | 7.26 min |
| Concrete-Lined Channel (x0.4) | 0.025 (2.5% grade) | 7.57 min | 4.54 min |
SI Kirpich Watershed Time of Concentration t_c (Minutes)
Evaluates 0.01947 * (L^0.77) * (S^-0.385) from main channel length B2 (meters) and dimensionless slope B3 (m/m).
=IF(OR(B2 <= 0, B3 <= 0), "Length and Slope Must Be > 0", ROUND(0.01947 * (B2 ^ 0.77) * (B3 ^ -0.385), 2))NRCS Unit Hydrograph Basin Lag Time t_lag = 0.60 * t_c (Minutes)
Computes centroid-of-excess-rainfall to hydrograph-peak lag time as 60% of t_c.
=ROUND(0.6 * (0.01947 * (B2 ^ 0.77) * (B3 ^ -0.385)), 2)Try the example
Use the original values or change them to test your understanding.