Lesson 8:
Estimating Runoff


Rational Method



The rest of this lesson will be concerned with the Rational Method.  This is the most commonly used method of determining peak discharge from small drainage areas.  The Rational Method is most effective in urban areas with drainage areas of less than 200 acres.

The Rational Method is typically used to determine the size of storm sewers, channels, and other drainage structures.  This method is not recommended for routing stormwater through a basin or for developing a runoff hydrograph.  



Limitations that Affect Accuracy

When used correctly, the Rational Method can be a very effective tool at estimating runoff.  However, several limitations should be considered before using this method.

The Rational Method assumes that the drainage basin characteristics are fairly homogeneous.  If the drainage basin includes a variety of surfaces, such as paved areas, wooded areas, and agricultural fields, then another method should be selected.

The type of surface in the drainage basin is also important.  The Rational Method becomes more accurate as the amount of impervious surface, such as pavement and rooftops, increases.  

The Rational Method is less accurate for larger areas and is not recommended for drainage areas larger than 200 acres.

For this method, it is assumed that a rainfall duration equal to the time of concentration results in the greatest peak discharge.  The time of concentration is the time required for runoff to travel from the most distant point of the watershed to the outlet.  Intuitively, the amount of water flowing out of the watershed will increase until the entire watershed is contributing water, at the time of concentration.  If this assumption is not valid for a watershed, then the rational method's estimate of peak runoff will not be accurate.



The Formula

The rational formula is:

                         Q  =  C i A



Q  = 
Peak rate of runoff in cubic feet per second
C  = 
Runoff coefficient, an empirical coefficient representing a relationship between rainfall and runoff 
i  = 
Average intensity of rainfall for the time of concentration (Tc) for a selected design storm 
A  = 
Drainage area in acres



How the Rational Method Works

The Rational Method is based on empirical data (data collected from the site being studied) and hypothetical rainfall-runoff events.  The hypothetical portion of the Rational Method is assumed to model what would happen during natural storm events.  

During an actual storm event, the peak discharge is dependent upon many factors, including:

Antecedent moisture conditions.  (If the ground is already saturated from a previous rain, then more runoff will result than would be expected if the ground was drier.)

Rainfall magnitude.  (The total amount of rainfall, in inches.)

Rainfall intensity.  (The amount of rainfall over a certain period of time, in inches per hour.)

Rainfall duration.  (Length of time over which rainfall occurs, in hours.)

Rainfall distribution.  (The rain may fall over only a certain portion of the drainage area or over the entire drainage area.)

The effects of infiltration, detention, and flow routing throughout the watershed.

The Rational Model is very simple and depends on the user to compensate for most of the variables listed above.  Thus the accuracy of the Rational Method is highly dependent upon the judgment and experience of the user.  The user must choose the appropriate runoff coefficient(s) and determine the time of concentration based on plan information (which will include proposed hydrologic changes expected to result from construction.)  



Using the Rational Method


General Procedure

The general procedure for determining peak discharge using the Rational Method is as follows:

Step 1: Determine the drainage area (in acres.)  This step has been discussed previously.

Step 2: Determine the runoff coefficient (C).

Step 3:  Determine the hydraulic length or flow path that will be used to determine the time of concentration.  Also, determine the types of flow (or flow regimes) that occur along the flow path.

Step 4:  Determine the time of concentration (Tc) for the drainage area.

Step 5: Determine the intensity using the time of concentration.

Step 6: Input the drainage area, C value, and intensity into the formula to determine the peak rate of runoff.

We will consider steps 2 through 6 in more detail in the rest of this lesson.



Runoff Coefficients 

The runoff coefficient is used to fit the Rational Method to the particular drainage area being considered.  The engineer must use judgment in selecting the appropriate runoff coefficient.  In general, areas with permeable soils, flat slopes, and dense vegetation should have the lowest values.  Areas with dense soils, moderate to steep slopes, and sparse vegetation should be assigned the highest values.  

If the types of land use and the soil cover are homogeneous for the entire drainage area, then a runoff coefficient can be determined directly from Table 2.  For example, a woodland on a relatively steep slope would be given a C value of 0.20, a single family residential area with above average vegetation would be given a C value of 0.30, and an average downtown would be given a C value of 0.83.

If the drainage area contains multiple land uses or soil conditions, deciding on a C value becomes slightly more complicated.  The drainage area should be divided into sections, with an area calculated for each section and a C value assigned to each area.  For example, let's consider a drainage area which is 50 acres in size and contains 11 acres of asphalt roads (C = 0.85), 1 acre of playground (C = 0.25), 4 acres of parks (C = 0.20), and 34 acres of suburban residential areas (C = 0.30).

A weighted average C is calculated as follows:


In this case, the calculations would be as follows.  First the CA would be calculated for each area:


Then the Weighted Average "C" would be calculated:


So the C value used for this area would be 0.412.



Hydraulic Length

In order to determine the time of concentration of your property, you first must determine the hydraulic length, or flow path.  The hydraulic length is the distance between the most distant point in the watershed and the watershed outlet.  


The first step is to draw the drainage patterns onto your watershed map.  I have drawn the drainage patterns in blue on the map below.


The hydraulic path for this watershed has been outlined in yellow below.  



Flow Regimes

Before using the hydraulic path to determine the time of concentration, we must characterize the flow regimes throughout the hydraulic path.  The flow regime is the type of flow.  The three flow regimes are presented below.  

Overland flow, also known as sheet flow, is a shallow flow of water, usually less than one inch deep, over plane surfaces.  Overland flow is usually found at the upper reaches of the hydraulic flow path.  In this case, the existing overland flow along the hydraulic path is extensive, and is shown below in orange.


The overland flow on the map above is about 1,000 feet long  The recommended maximum length for this type of flow is 300 feet; however, many engineers agree that the overland flow should be limited to 200 feet or less.  As a result, our stormwater plan will include channels which limit the overland flow to 200 feet.

Although the length of overland flow can be estimated based on drainage diagrams such as the one shown above, the actual length of overland flow varies considerably according to actual field conditions.  The length of overland flow should be verified by field investigation, if possible.

The second type of flow regime, shallow concentrated flow, usually begins where overland flow converges to form small rills or gullies and swales.  On the flow diagram above, the remaining yellow portion of the hydraulic path is shallow concentrated flow.  

Shallow concentrated flow can exist in small, man-made drainage ditches, paved or unpaved, and in curb and gutters.  The recommended maximum length for shallow concentrated flow is 1000 feet.

The third type of flow, channel flow, occurs where flow converges in gullies, ditches, and natural or man-made water conveyances (including pipes not running full.  Channel flow is assumed to exist in perennial streams or wherever there is a well-defined channel cross-section.  In my flow diagram, there is no existing channel flow within the watershed boundary, although the stream (pale blue line) just west of the watershed would be defined as channel flow.  



Changing Drainage and Estimating Flow Path

In my watershed, the overland flow exceeds the recommended maximum length.  So I will need to change the drainage pattern before calculating the length of each type of flow regime along the hydraulic path.  My stormwater plan will include manipulations to result in the flow regimes shown below:


Using the scale, I can now measure the length of each flow regime along the hydraulic path.  On the map shown above, these lengths are:

Overland Flow - 200 feet
Shallow Concentrated Flow - 600 feet
Channel Flow - 500 feet

Part 3: More Rational Method