§ 2.4.2. Time of Concentration

The time of concentration is the time for surface runoff to flow from the most remote point in the watershed to the point of interest. This applies to the most remote point in time, not necessarily the most remote point in distance. Runoff from a drainage area usually reaches a peak at the time when the entire area is contributing. However, runoff may reach a peak prior to the time the entire drainage area is contributing if the area is irregularly shaped or if land use characteristics differ significantly within the area. Sound engineering judgment should be used to determine a flow path representative of the drainage area and in the subsequent calculation of the time of concentration. The time of concentration to any point in a storm drainage system is a combination of the sheet flow (overland), the shallow concentrated flow and the channel flow, which may include storm drains. The minimum time of concentration for any drainage area shall be 5 minutes. Additionally, the minimum slope used for calculation of sheet and shallow flow travel time components should be 0.005 feet per foot (0.5%). The preferred procedure for estimating time of concentration is the NRCS method as described in NRCS's Technical Release 55 (TR-55). This method is outlined below. The overall time of concentration is calculated as the sum of the sheet, shallow concentrated and channel flow travel times. Note that there may be multiple shallow concentrated and channel segments depending on the nature of the flow path.

T _C = T _t(sheet) + T _{t(shallow concentrated)} + T _t(channel)       (Eq. 2-2)

A.

Sheet Flow. Sheet flow is shallow flow over land surfaces, which usually occurs in the headwaters of streams. The engineer should realize that sheet flow occurs for only very short distances, especially in urbanized conditions. Sheet flow for both natural (undeveloped) and developed conditions should be limited to a maximum of 100 feet. Sheet flow for developed conditions should be based on the actual pavement or grass conditions for areas that are already developed and should be representative of the anticipated land use within the headwater area in the case of currently undeveloped areas. In a typical residential subdivision, sheet flow may be the distance from one end of the lot to the other or from the house to the edge of the lot. In some heavily urbanized drainage areas, sheet flow may not exist in the headwater area. The NRCS method employs equation 2-3, which is a modified form kinematic wave equation, for the calculation of the sheet flow travel time.

T _t = 0.42(nL) ^0.8 /((P ₂ ) ^0.5 s ^0.4 )       (Eq. 2-3)

Where,

T _t = Sheet flow travel time in minutes

L = Length of the reach in ft.

n = Manning's n (see Table 2-2)

P ₂ = 2-year, 24-hour rainfall in inches (see Table 2-3)

s = Slope of the ground in ft/ft

B.

Shallow Concentrated Flow. After a maximum of approximately 100 feet, sheet flow usually becomes shallow concentrated flow collecting in swales, small rills, and gullies. Shallow concentrated flow is assumed not to have a well-defined channel and has flow depths of 0.1 to 0.5 feet. The travel time for shallow concentrated flows can be computed by equations 2-4 and 2-5. These two equations are based on the solution of Manning's equation with different assumptions for n (Manning's roughness coefficient) and r (hydraulic radius, ft). For unpaved areas, n is 0.05 and r is 0.4; for paved areas, n is 0.025 and r is 0.2.

Unpaved T _t = L/(60(16.1345)(s) ^0.5 ) (Eq. 2-4)

Paved T _t = L/(60(20.3282)(s) ^0.5 ) (Eq. 2-5)

Where,

T _t = Travel time for shallow concentrated flows in minutes

L = Length of the reach in ft.

s = Slope of the ground in ft/ft

C.

Channel or Storm Drain Flow. The velocity in an open channel or a storm drain not flowing full can be determined by using Manning's Equation. Channel velocities can also be determined by using backwater profiles. For open channel flow, average flow velocity is usually determined by assuming a bank-full condition. Note that the channel flow component of the time of concentration may need to be divided into multiple segments in order to represent significant changes in channel characteristics. The details of using Manning's equation and selecting Manning's "n" values for channels can be obtained from Section 6.

For storm drain flow under pressure conditions (hydraulic grade line is higher than the lowest crown of a storm drain) the following equation should be applied:

V = Q/A (Eq. 2-6)

Where:

V = Average velocity, ft/s

Q = Design discharge, cfs

A = Cross-sectional area, ft2

Flow travel time through a channel can be calculated by equation (2-7):

T _t = Σ(L _i /60 V _i ) (Eq. 2-7)

Where:

L _i = The i-th channel segment length, ft

V _i = The average flow velocity within the ith channel segment, ft/s

T _t = Total Flow travel time through the channel, min

TABLE 2-1 RATIONAL METHOD RUNOFF COEFFICIENTS FOR COMPOSITE ANALYSIS Runoff Coefficient (C)
Character of Surface	Return Period
	2 Years	5 Years	10 Years	25 Years	50 Years	100 Years	500 Years
DEVELOPED
Asphaltic	0.73	0.77	0.81	0.86	0.90	0.95	1.00
Concrete	0.75	0.80	0.83	0.88	0.92	0.97	1.00
Grass Areas (Lawns, Parks, etc.)
Poor Condition*
Flat, 0-2%	0.32	0.34	0.37	0.40	0.44	0.47	0.58
Average, 2-7%	0.37	0.40	0.43	0.46	0.49	0.53	0.61
Steep, over 7%	0.40	0.43	0.45	0.49	0.52	0.55	0.62
Fair Condition**	0.25	0.28	0.30	0.34	0.37	0.41	0.53
Flat, 0-2%	0.25	0.28	0.30	0.34	0.37	0.41	0.53
Average, 2-7%	0.33	0.36	0.38	0.42	0.45	0.49	0.58
Steep, over 7%	0.37	0.40	0.42	0.46	0.49	0.53	0.60
Good Condition***
Flat, 0-2%	0.21	0.23	0.25	0.29	0.32	0.36	0.49
Average, 2-7%	0.29	0.32	0.35	0.39	0.42	0.46	0.56
Steep, over 7%	0.34	0.37	0.40	0.44	0.47	0.51	0.58
UNDEVELOPED
Cultivated
Flat, 0-2%	0.31	0.34	0.36	0.40	0.43	0.47	0.57
Average, 2-7%	0.35	0.38	0.41	0.44	0.48	0.51	0.60
Steep, over 7%	0.39	.042	0.44	0.48	0.51	0.54	0.61
Pasture/Range
Flat, 0-2%	0.25	0.28	0.30	0.34	0.37	0.41	0.53
Average, 2-7%	0.33	0.36	0.38	0.42	0.45	0.49	0.58
Steep, over 7%	0.37	0.40	0.42	0.46	0.49	0.53	0.60
Forest/Woodlands
Flat, 0-7%	0.22	0.25	0.28	0.31	0.35	0.39	0.48
Average, 2-7%	0.31	0.34	0.36	0.40	0.43	0.47	0.56
Steep, over 7%	0.35	0.39	0.41	0.45	0.48	0.52	0.58
Assumptions:
1. Composite "C" value for developed conditions (C DEV ) is : C DEV = IC 1 + (1-I)C 2
	Where: I = Impervious cover, percent C 1 = "C" value for impervious cover C 2 = "C" value for pervious area (grass, lawns, parks, etc.)
2. For maximum allowable impervious coverage values for various land use types, refer to the City of Austin Zoning Ordinance.
* Grass cover less than 50 percent of the area.
** Grass cover on 50 to 75 percent of the area.
*** Grass cover larger than 75 percent of the area.
Source: 1. Rossmiller, R.L. "The Rational Formula Revisited." 2. City of Austin, Watershed Engineering Division

 

TABLE 2-2 Manning's "n" for overland flow
Manning's "n"	Surface Description
0.015	Concrete (rough or smoothed finish)
0.016	Asphalt
0.05	Fallow (no residue)
	Cultivated Soils:
0.06	Residue Cover ≤ 20%
0.17	Residue cover > 20%
	Grass:
0.15	Short-grass prairie
0.24	Dense grasses
0.13	Range (natural)
	Woods:
0.40	Light underbrush
0.80	Dense underbrush
1 The Manning's n values are a composite of information compiled by Engman (1986).
2 Includes species such as weeping lovegrass, bluegrass, buffalo grass, blue grama grass, and native grass mixtures.
3 When selecting n, consider cover to a height of about 0.1 ft. This is the only part of the plant cover that will obstruct sheet flow.

 

( Rule No. 161-14.24, 9-2-2014 )