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This article explains the use of the TR-55 Shallow Concentrated Flow method for calculating the time of concentration (Tc) for different types of surfaces based on the USDA equation developed.
There are many ways to compute the time of concentration for a catchment. When selecting the Modified Rational or the Unit Hydrograph method to determine runoff from a catchment, the User can define time of concentration by a single user defined value or a composite value based on different methods available to calculate time of concentration (Tc).
The method of computation can be defined in the Tc Data Collection field. When the ellipsis next to the Tc Data Collection field is clicked it will open a dialog box where the appropriate method for computation of Tc can be specified from a drop-down menu.
This article specifically addresses the TR-55 Shallow Concentrated Flow method.
The TR-55 (Technical Release – 55) is a standard document released by USDA (United States Department of Agriculture) which provides the equation to be followed for computation of time of concentration based on different surface types.
The equations developed by USDA for Paved and Unpaved (Grassed Waterway) surfaces are as follows;
V=16.1345×Sf^(0.5) – For Unpaved (Grassed Waterway) Surfaces
V=20.3282×Sf^(0.5) – For Paved Surfaces
Here V is in ft/sec and slope (Sf) in ft/ft.
Note: The calculations are done by default in US units since the equation is developed for US units. However, the user can input the data required (slope, length) is any other unit system but it would be converted to US units for calculation.
The time of concentration (Tc) is calculated by the following formula;
The paved and grassy waterway options are available by default in the TR-55 Shallow Concentrated Flow method from the Land Cover drop down field.
Along with the two predefined options a third option named “Other” is available which allows the user to define the K coefficient depending on the Land Cover available.
As per the equations developed for shallow concentrated flow, the relationship between velocity and slope can be generalized into the following standard equation;
Where, K is a constant which changes as per the land cover / surface properties. Thus, for the above equations for paved and grassy waterway the K coefficients would be 20.3282 and 16.1345 respectively.
When choosing the “Other” option under Land Cover, the User can define the K coefficient for surfaces other than paved and grassy waterway (which are available by default).
The USDA has developed a graph of slope vs. velocity for different types of surfaces along with some standard equations.
More information can be obtained in the following document;
Part 630 Hydrology National Engineering Handbook
To define a surface other than paved or grassy waterway you must select the “Other” option under the drop-down menu of Land Cover.
Once selected the K coefficient field becomes active. It should be noted that the K coefficient field would remain inactive for paved or grassy waterway surfaces as these are the default surfaces available and their K coefficients are known.
The other fields which are important are the length (ft) and the slope (ft/ft). The slope entered would be used in the equation for shallow concentrated flow which would give the velocity of flow. The length input would be used to calculate the time of concentration as per the equation defined in the above section.
An example is worked out below for the following data;
Length = 510 ft.; Slope = 0.034 ft/ft and K coefficient of 6.962 for Short Grass Pasture surface type.
When the window is closed, the time of concentration is computed and reflected in the field of Time of Concentration (Composite). The result is obtained as 0.11 hours.