How is the time of concentration defined?

Time of concentration has several definitions including:

• The minimum time required after runoff begins for the entire basin to contribute flow to the outlet.
• The time required for a particle of water to travel from the most hydraulically distant point in the basin to the outlet.
• The time required for a flood wave to travel from the most hydraulically distant point to the outlet.

How do I calculate the travel time (T_t ) for sheet flow?

Sheet flow is flow over plane surfaces. It usually occurs in the headwater of streams. With sheet flow, the friction value (Manning’s n) is an effective roughness coefficient that includes the effect of raindrop impact; drag over the plane surface; obstacles such as litter, crop ridges, and rocks; and erosion and transportation of sediment. These n values are for very shallow flow depths of about 0.1 foot or so. The table below gives Manning’s n values for sheet flow for various surface conditions.

For sheet flow of less than 300 feet, use Manning’s kinematic solution to compute T_t :

where:
	Tt n L P2 s	= = = = =	travel time (hr) Manning’s roughness coefficient flow length (ft) 2-year, 24 hour rainfall (in) slope of hydraulic grade line (land slope, ft/ft)

This simplified form of the Manning’s kinematic solution is based on the following: shallow steady uniform flow, constant intensity of rainfall excess (that part of a rain available for runoff), rainfall duration of 24 hours and minor effect of infiltration on travel time. Rainfall depth (P2) can be obtained from appendix B in TR-55.

How do I calculate the travel time (T_t ) for shallow concentrated flow?

After a maximum of 300 feet, sheet flow usually becomes shallow concentrated flow. The average velocity for this flow is a function of watercourse slope and type of channel. Tillage can affect the direction of shallow concentrated flow. Flow may not always be directly down the watershed slope if tillage runs across the slope.

First, use one of the following equations to calculate the velocity:

V = 16.1345(s)^0.5    (unpaved)

V = 20.3282(s)^0.5    (paved)

where:

V    =    average velocity (ft/s)
s     =    slope of the hydraulic grade line (watercourse slope, ft/ft)

These two equations shown above 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.

Finally, the travel time for shallow concentrated flow is determined using:

where:
	Tt L V 3600	= = = =	travel time (hr) flow length (ft) average velocity (ft/s) conversion factor from seconds to hours

How do I calculate the travel time (T_t ) for an open channel?

Open channels are assumed to begin where surveyed cross section information has been obtained, where channels are visible on aerial photographs or where blue lines (indicating streams) appear on United States Geological Survey (USGS) quadrangle sheets. Manning’s equation or water surface profile information can be used to estimate average flow velocity. Average flow velocity is usually determined for bankfull elevation.

Manning’s equation is:

where:
	V r A Pw s n	= = = = = =	average velocity (ft/s) hydraulic radius (ft) and is equal to A/Pw cross sectional flow area (ft2) wetted perimeter (ft) slope of the hydraulic grade line (channel slope, ft/ft) Manning’s roughness coefficient for open channel flow.

After computing the average velocity using the above equation, the travel time (T_t ) for the channel segment can be estimated using:

where:
	Tt L V 3600	= = = =	travel time (hr) flow length (ft) average velocity (ft/s) conversion factor from seconds to hours

Where do I find roughness (n) values for Manning’s equation?

Table of Manning roughness (n) values for open channels can be found here, and a guide for the selection of roughness (n) values is also available.

How do I estimate the travel time (T_t ) through a reservoir or lake?

Sometimes it is necessary to estimate the velocity of flow through a reservoir or lake at the outlet of a watershed. This travel time is normally very small and can be assumed as zero.

What are some other time of concentration methods?

In addition to the TR-55 method, the following are common methods for determining the time of concentration:

• Carter
• Eagleson
• FAA
• Kirpich

Why is the time of concentration important?

The time of concentration is an important variable since it influences the shape and peak of the runoff hydrograph. Urbanization usually decreases the time of concentration, thereby increasing the peak discharge. However, the time of concentration can be increased as a result of ponding behind small or inadequate drainage systems, including storm drain inlets and road culverts, or as a result of land slope reduction from grading.

How does urbanization impact the time of concentration?

The following physical characteristics can be modified through urbanization and consequently impact the time of concentration:

• Surface roughness
• Channel shape and flow patterns
• Slope

How does urbanization impact surface roughness and the time of concentration?

One of the most significant effects of urban development on flow velocity is less resistance to flow. That is, undeveloped areas with very slow and shallow overland flow through vegetation become modified by urban development: the flow is then delivered to streets, gutters, and storm sewers that transport runoff downstream more rapidly. Travel time through the watershed is generally decreased.

How does urbanization impact the surface shape and flow patterns and the time of concentration?

In small non-urban watersheds, much of the travel time results from overland flow in upstream areas. Typically, urbanization reduces overland flow lengths by conveying storm runoff into a channel as soon as possible. Since channel designs have efficient hydraulic characteristics, runoff flow velocity increases and travel time decreases.

How does urbanization impact the slope and the time of concentration (T_c)?

Slope, both land and channel, controls the flow velocity of water. Accordingly, higher land slopes result in a lower time of concentration while lower land slopes yield a higher time of concentration.

Slopes may be increased or decreased by urbanization, depending on the extent of site grading or the extent to which storm sewers and street ditches are used in the design of the water management system. Slope will tend to increase when channels are straightened and decrease when overland flow is directed through storm sewers, street gutters, and diversions.

What are the limitations of the TR-55 time of concentration method?

The limitations of the TR-55 time of concentration method are:

• Manning’s kinematic solution is not applicable for sheet flow longer than 300 ft.
• The travel time form of Manning’s equation for sheet flow was developed for use with the four standard rainfall intensity-duration relationships listed in TR-55.
• In watersheds with storm sewers, carefully identify the appropriate hydraulic flow path to estimate T_c. Storm sewers generally handle only a small portion of a large event. The rest of the peak flow travels by streets, lawns, and so on, to the outlet. Consult a standard hydraulics textbook to determine average velocity in pipes for either pressure or nonpressure flow.
• The minimum T_c used in TR-55 is 0.1 hour.
• A culvert or bridge can act as a reservoir outlet if there is significant storage behind it. The procedures in TR-55 can be used to determine the peak flow upstream of the culvert. Detailed storage routing procedures should be used to determine the outflow through the culvert

A short paper discussing some of the technical concerns with respect to the TR-55 sheet flow implementation can be found here.

Which time of concentration methods are support by StormNET?

StormNET supports the following time of concentration methods:

• Carter
• Eagleson
• FAA
• Kirpich
• SCS (NRCS) TR-55
• User-defined

What is TR-55?

Technical Release 55 (TR-55) is one of the most commonly used design methods in the United States for the management of storm water runoff in urban settings. Originally published in 1975 by the Soil Conservation Service (SCS), TR-55 presents procedures for the calculation of storm runoff volume, peak rate of discharge, hydrographs and detention pond storage volumes for small watersheds. The Natural Resources Conservation Service (NRCS), formally known as the SCS, published a revised version of TR-55 in 1986. The methods in TR-55 are also described in the hydrology section of the National Engineering Handbook which was also compiled by the SCS (NRCS).

Where can I get TR-55?

The original TR-55 documentation and the MS-DOS version can be found on the NRCS TR-55 webpage. The WinTR-55 program, documentation and tutorials can be downloaded from the NRCS WinTR-55 webpage. Links to all NRCS hydraulics and hydrologic software can be found here.