Time of Concentration (Kirpich Method)
Time of Concentration (Kirpich Method)
Time of concentration is the time it takes runoff to travel from the hydraulically most distant point of a watershed to its outlet, and it is a key input to rational-method peak flow calculations and IDF-curve lookups. The Kirpich formula estimates it directly from the flow path length and average slope, without needing a full hydrograph model.Because tc sets the design storm duration used elsewhere, an error here propagates directly into the peak flow estimate used to size culverts, storm drains and detention ponds — an underestimated tc leads to an overestimated (too intense) design storm and an oversized, costly drainage structure.
The Kirpich time of concentration is t_c = 0.0195·L^0.77·S^(-0.385) minutes, an empirical fit with L in meters and S dimensionless. where L is the length of the longest flow path (in meters, used here as a plain number) and S is the average watershed slope (dimensionless).
Inputs
L_len := 500=500
S_kirp := 0.02=0.02
The Kirpich formula is an empirical fit whose numeric constant already carries hidden units, so the flow path length is used as a plain number of meters rather than a dimensioned length.
tc_num := 0.0195·L_len^0.77·S_kirp^-0.385=10.53
Kirpich’s formula returns the result in minutes, so that unit is attached to the numeric result to make it a proper time quantity.
tc := tc_num·(1 min)=631.68 s
Results
A time of concentration around 10–11 minutes is typical for a small, fairly steep urban watershed with a 500 m flow path. Longer flow paths or flatter slopes stretch tc out considerably since the formula is much more sensitive to length than to slope; this tc should then be used as the storm duration when reading the site’s IDF curve for the design intensity.
Assumptions & limitations
- Empirical formula developed for small, well-defined watersheds.
- Flow path treated as a single dominant channel/overland path.
- Not valid for very large or very flat watersheds outside the original calibration range.