Time of Concentration

The time of concentration equals the summation of the travel times for each flow regime.  There are numerous methods used to calculate the travel time for each of the flow regimes.  Here, we will discuss a few of the most prevalent methods. 

Overland Flow - Lo
    The travel time for overland flow may be determined by using the following methods as appropriate.  If the ground cover conditions are not homogeneous for the entire overland flow path, determine the travel time for each ground cover condition separately and add the travel times to get overland flow travel time.  Do not use an average ground cover condition. 
a. Seelye Method:  Travel time for overland flow can be determined by using the Seelye chart.  This method is perhaps the simplest and is most commonly used for small developments where a greater margin of error is acceptable.

    First, determine the length of overland flow and enter the nomograph on the left axis, "Length in Feet".  Intersect the "Coefficient of Imperviousness" to determine the turn point on the "Pivot" line.  Intersect the "Percentage Slope" and read the travel time for overland flow.

b. Kinematic Wave Method:  This method allows for the input of rainfall intensity values, thus allowing you to adjust the model to a selected design storm, such as the region's 2-year, 10-year, or 100-year storms.  

    The equation is:

Kinematic Wave Method.

Where:  
            Tt = travel time
               L  =  length of overland flow in feet
               n  =  Manning's roughness coefficient
               i   =  rainfall intensity
               S  =  slope in feet/foot

The first step is to decide on values for "L", "n", and "S".  This leaves two unknown values (travel time and rainfall intensity.) 

In order to solve the equation, find your region's I-D-F curve and choose a model storm.  A trial and error process is then used to determine the overland flow time.  First, assume a rainfall intensity value and solve the equation for travel time.  Then compare the assumed rainfall intensity value with the rainfall intensity value that corresponds with the travel time on the I-D-F curve.  The correct travel time will come from an assumed intensity which is equal to the intensity determined using the I-D-F curve. 


c. Manning's Kinematic Equation: This is the method used in TR-55.

The equation is:



Where: 

Tt  =  travel time (hr.)
n  =  Manning's roughness coefficient (Table 3)
L  =  flow length (ft.)
P2  =  2-year, 24-hour rainfall (in.) (Diagram 5)
s  =  slope of hydraulic grade line (feet/foot)

All of the values are inputted into the formula to find the travel time. 

 

    Shallow Concentrated Flow - Lsc

    To calculate the travel time of shallow concentrated flow, first determine the velocity of the flow using Diagram 1.  You will need to know the slope of the shallow concentrated flow and whether the flow path is paved or unpaved. 

    Next, calculate the travel time using the following equation:

Equation for shallow concentrated flow.

        Where: 
                       Tt  = travel time (minutes)
                       L  =  length of shallow concentrated flow (feet)
                      V  =  velocity (feet per second)  
         


    Channel Flow - Lc

    The last flow regime we need to consider is channel flow. 

      a. Kirpitch Chart: A simple method using a nomograph.

      To calculate channel flow, you need to know:

      Then we simply use this data with the Kirpitch Chart to determine the travel time.  (Be sure to multiply the result by 0.2 if the channel is paved.) 


      b. Manning's equation: Manning's equation is used to determine the velocity of channel flow.  You can either solve Manning's equation mathematically or you can use the nomograph in Diagram 7 to solve Manning's equation.

Manning's equation is:

Manning's equation for channel flow.


Where: 

V  =  average velocity (ft./sec.)
r   =  hydraulic radius (ft.) and is equal to a/Pw
a  =  cross sectional flow area (ft.2)
Pw =  wetted perimeter (ft.)
s  =  slope of the hydraulic grade line (ft./ft.)
n  =  Manning's roughness coefficient for open channel flow.


Once the velocity is found, the travel time is determined using the same method used for shallow concentrated flow.  


Total Time of Concentration

The time of concentration along the hydraulic path is simply the sum of the travel times for the overland flow, shallow concentrated flow, and channel flow.

Tc = Lo + Lsc + Lc