OpenSpecEngineering

Estimates the time of concentration of a drainage area: the time water takes to travel from the hydraulically most distant point to the outlet. Drainage engineers use it to pick the storm duration, and so the rainfall intensity, for the Rational Method, and as an input to NRCS hydrographs. Three empirical methods are offered.

Equations

Kirpich: t_c = 0.0078·L^0.77·S^−0.385

FAA: t_c = 1.8·(1.1 − C)·L^0.5/S_%^1/3

NRCS lag: L_lag = L^0.8·(S_r + 1)^0.7/(1900·S_%^0.5)

t_c = L_lag/0.6

t_c is in minutes for Kirpich and FAA [1], [2], and L_lag is the watershed lag in hours [3], [4]. L is the flow path length in feet. S is the average slope along it in ft/ft, and S_% the same slope in percent. C is the rational runoff coefficient. S_r = 1000/CN − 10 is the potential maximum retention in inches, from the NRCS curve number CN.

Inputs

• The formulas use feet, so the page converts any length unit to feet first and shows the converted length.
• For FAA, choosing a Surface / Land Use fills in the midpoint of its C range from HEC-22 Table 3-1 [5].
• For NRCS, choosing a Land Cover and Hydrologic Soil Group looks up CN in TR-55 Tables 2-2a and 2-2c [3]. Group A soils drain fastest and give the lowest CN.

Limits and common mistakes

• Pick the method that matches the flow. Kirpich came from small rural watersheds with defined channels [1]. FAA is for overland sheet flow on airfields and similar paved or grassed surfaces [2]. The NRCS lag equation is for whole watersheds with mixed flow [3].
• The methods can differ by a factor of two or more for the same site. For overland flow, Chow et al. multiply the Kirpich time by 2 on grass and by 0.4 on concrete or asphalt [4].
• S is the slope along the flow path, not the steepest slope on the site.
• HEC-22 suggests a minimum t_c of 5 minutes [5], and many local drainage manuals set their own minimum.

Worked example

A subdivision of quarter-acre lots on group C soil drains to a culvert. The longest flow path is 2,400 ft at an average slope of 2 %. What is the time of concentration?

1. Choose Method NRCS (SCS) lag equation.
2. Enter Flow Path Length 2400 ft and Slope 0.02.
3. Choose Land Cover Residential, 1/4 acre (38 % impervious) and Hydrologic Soil Group C — sandy clay loam, and press Solve. The Solution shows: Formula: t_c = L_lag/0.6
   Flow path length: 2,400 ft
   Curve number CN (TR-55, group C): 83
   Time of concentration: 41.0894 min
   Time of concentration: 0.684824 hr

Check by hand: S_r = 1000/83 − 10 = 2.048 in. L_lag = 2400^0.8 × 3.048^0.7/(1900 × √2) = 506.0 × 2.182/2687 = 0.411 hr, and 0.411/0.6 = 0.685 hr, or 41.1 min. Kirpich gives 14.1 min for the same path, which shows how much the choice of method matters.