Lesson 12:
More Runoff Calculations

Objective

In this lesson we will answer the following questions:

• How is peak runoff calculated for a watershed after development?
• How is peak runoff calculated for a watershed during a ten year storm?
• What other methods can be used to calculate runoff?
• How do you read a hydrograph?

There is no reading assignment associated with this lesson.

Lecture

Peak Runoff After Development

Introduction

In a later lesson, you will need to compare the peak runoff before development in your watershed to the peak runoff after development.  This comparison will give you an idea of what effect your construction project will have on the watershed under consideration.

In this section, we will cover the calculations you must use in order to come up with the peak runoff after development.  In general, you follow the same procedure outlined in the last lesson.  However, when calculating the peak runoff after development, you need to recalculate the time of concentration and intensity as well as the C value for the watershed.

Flow Regime Requirements

When you develop your stormwater management plan for the post-construction watershed, you will have to follow a few guidelines respecting flow regime.  Specifically, there are restrictions on the acceptable length of both overland flow and shallow concentrated flow.

The recommended maximum length for overland 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 the upper 200 feet of the drainage area.  Any excess overland flow length will have to be converted into shallow concentrated flow.

The recommended maximum length for shallow concentrated flow is 1,000 feet.  If your shallow concentrated flow (including the extra shallow concentrated flow converted from overland flow) is greater than this length, then you will need to convert the extra portion of the hydraulic path into channel flow.

To give you an idea of how these requirements will affect your watershed, let's look at the first example watershed we considered in the last lesson.

As you may recall, the hydraulic path for our watershed contained 1,000 feet of overland flow (shown as orange on the map above) and 600 feet of shallow concentrated flow (shown as yellow on the map above.)  There was no channel flow in our pre-construction watershed.

Since the length of overland flow exceeds the recommended maximum, our stormwater plan will need to include manipulations to shorten the overland flow to 200 feet.  This will increase the length of shallow concentrated flow to 1,400 feet, so the last 400 feet of shallow concentrated flow will have to become channel flow.  The post-construction flow regimes will be as follows:

The orange line represents 200 feet of overland flow, the yellow line represents 1,000 feet of shallow concentrated flow, and the green line represents 400 feet of channel flow.

Changing the Time of Concentration and Intensity

Since the length of each type of flow regime has changed in the post-development watershed, you will need to recalculate the time of concentration and intensity.  The calculations for these changes in our example watershed are summarized below:

1. Travel time for overland flow is calculated using the Seelye Chart, a length of 200 feet, the same coefficient of imperviousness (dense grass), and a slope of 10%.  A new slope was calculated from the map using the shorter length of overland flow, but in the case of our example the new slope calculation was the same as the old slope calculation.  The resulting travel time for overland flow is 15 minutes.

2. Travel time is calculated for shallow concentrated flow using Diagram 1, a length of 1,000 feet, a new slope of 0.5 ft./ft., and an unpaved channel.  We'll discuss channel improvements in a later lesson and may decide to pave the channel, but for now we will leave the channel unpaved.  The velocity from Diagram 1 is 11.5 ft./sec. and the resulting travel time for shallow concentrated flow is 1.4 minutes.

3. Travel time for channel flow is calculated from the Kirpitch chart using a height above outlet of 40 feet, a length of 400 feet, and a natural channel condition.  The resulting travel time for channel flow is 1.5 minutes.

4.  The total time of concentration is the sum of each travel time, which results in 17.9 minutes.

5. From the I-D-F curve showing 2 year storm data for Wise County, the intensity is 2.8.

Changing the C Value

The other aspect of our runoff calculation which is changed by development is the C value for the watershed.  In our example watershed, the C value before construction was 0.40.  However, we are going to be building a store and parking lot on the property which will cover the area shown as a red square on the maps in this lesson.  The addition of a rooftop and parking lot will increase the imperviousness of the watershed, which will change the C value of the watershed.

The first step in finding the new C value is to determine the surface area of the construction site.  Using the method outlined in Lesson 7, I determined that that area of the construction site in my example will be 0.8 acres.  The C value of this area will be 0.60 since our store will be an average neighborhood-type business.

Now we can calculate the new C value.  First, we calculate a weighted C value for each area.  The remaining 13.6 acres of woodland and pasture will have a weighted C value of 5.44.  The 0.8 acres of store will have a weighted C value of 0.48.  So the weighted average C value is 0.41.

Calculating Runoff After Development

Now you can input the new C value and intensity into the rational formula and calculate the peak runoff after development.  In the case of our example, the runoff will be 16.5 cfs. This is an increase of 6.25 cfs from our pre-development peak runoff of 10.25 cfs.

Peak Runoff During the Ten Year Storm

You will also be asked to calculate the peak runoff during a 10 year storm for a later lesson.  This calculation is just as simple as peak runoff during the 2 year storm.  The only difference is that, when finding the intensity on the I-D-F curve, you use the curve for the 10 year storm instead of the curve for the two year storm.

The illustration above shows the different curves on the I-D-F chart for Wise County.  Notice that each curve is labelled on the right side of the diagram --- the 10 year storm curve is the third from the bottom.

In order to calculate the intensity for the 10 year storm for our property after development, you still input a time of concentration of 17.9 minutes into the I-D-F chart, but this time you read the intensity from the curve for the 10 year storm.  So the intensity for the 10 year storm after development is 3.95.  As a result, the peak runoff during the 10 year storm for the property after development is 23.2 cfs.

Keep in mind that --- for any one watershed --- the peak runoff for the 10 year storm should always be greater than the peak runoff from the 2 year storm because the 10 year storm is a larger model storm than the 2 year storm.  By definition, a 10 year storm models an amount of rainfall which is likely to occur during a storm only once in a ten year period.

Other Methods of Calculating Runoff

Selecting a Calculation Method

Although we only present one method of calculating runoff in this course, you should be aware that four techniques are commonly used to estimate runoff --- the Rational Method, the Graphical Peak Discharge Method, the Tabular Method (TR-55), and the Unit Hydrograph Method.

The primary factors used to decide on a runoff calculation method are the size of the drainage area and the output information required.  The table below lists acceptable calculation methods for different drainage areas and output requirements.  The plan approving authority may require or accept other calculation methods deemed more appropriate for local conditions.

 Output Requirements Drainage Area Appropriate Calculation  Methods Peak Discharge only up to 200 acres up to 2000 acres up to 20 sq. mi. 1,2,3,4 2,3,4 3,4 Peak Discharge and  Total Runoff Volume up to 2000 acres up to 20 sq. mi. 2,3,4 3,4 Runoff Hydrograph up to 20 sq. mi. 3,4
1. Rational Method
2. Peak Discharge Method
3. Tabular Method (TR-55)
4. Unit Hydrograph Method

Output Requirements

In lesson 7, you learned how to calculate the surface area of the watershed affected by your construction site.  In most cases, the drainage area will be less than 200 acres, so the Rational Method may be used.  All four calculation methods can be used on small drainage areas while only the Tabular Method and the Unit Hydrograph Method may be used for very large drainage areas.

The other distinction between the different calculation methods is the output.  All four calculation methods provide an estimate of runoff.  But the form that this estimate takes varies from method to method.

The Rational Method only calculates the peak discharge for a watershed, but the other methods provide more information about the runoff.  The most descriptive type of output is a hydrograph, such as the one shown above.  A hydrograph is a graphic representation of the amount of runoff over time.  The area beneath the curve is the total runoff volume for the watershed.  The highest point in the curve is the peak discharge.  Only the Tabular Method and the Unit Hydrograph Method produce a hydrograph.  You will learn to read a hydrograph in the next section.

Understanding Hydrographs

Although you do not need to know how to perform the calculations used to produce a hydrograph, you should be able to draw and analyze a hydrograph based on a table of discharge values like the one shown below.

 Time (hours after storm begins) 12 12.2 12.4 12.8 13.2 13.6 14 14.6 15.5 16.5 Discharge (cfs) before development 15.3 159.6 253 191.2 179.1 132.9 94.6 64.6 46.9 37.1 Discharge (cfs) after development 16.6 192.4 337.5 221 193.9 144.1 103.9 71.9 53.1 42.1

The discharge summary table above tells how much rain is flowing out of the watershed at a variety of times in the pre-development watershed (row 2) and in the post-development watershed (row 3.)

The first thing to look for in a table like this is the peak discharge.  I have highlighted the peak discharge for each watershed condition in red.  Notice that the peak discharge is easy to find because it is the highest discharge value for the watershed.  For the pre-development watershed, the peak discharge is 253.0 cfs while the peak discharge for the post-development watershed is 337.5 cfs.  You can tell from the table that the peak discharge for both conditions occurs 12.4 hours after the storm begins.

Drawing a Hydrograph

The next step in analyzing the table of discharge values is to draw a hydrograph.  I will assume that you have a basic understanding of how to make a graph from a table of values.  If you need help with graphing, first you should read this tutorial webpage.  If you are still confused, please contact me for more help.

The hydrograph below is based on the discharge table from the last section for the watershed before development.  Notice that I have put time on the horizontal axis and the discharge value on the y-axis.

The hydrograph gives us an idea of how the runoff quantity will change during the course of the design storm.  You can see, in the hydrograph above, that the watershed takes about 12.4 hours to attain peak discharge.  After peaking, the runoff slowly dissipates over the next three or four hours.

Comparing Two Hydrographs

You can also plot the hydrographs for a watershed before and after development on the same graph, as shown below:

By comparing the hydrograph from the pre-development watershed to the hydrograph from the post-development watershed, we can determine how the pattern of runoff during the entire storm will change.  As you can see in the hydrograph above, the post-development storm mirrors the pre-development storm in all ways, except that it has a greater discharge of runoff.  In this case, the peak discharge occurs at the same time before and after development, but development can sometimes cause the time of peak discharge to shift.  Notice that the shape of the curves are the same and the peak and shoulder are in the same location for the pre- and post-development watershed.  The red area on the graph shows the extra volume of runoff which results from development.

Review

In order to calculate the peak discharge of a watershed after development, you must first ensure that the flow regimes are up to standards.  Overland flow cannot exceed 200 feet in length and shallow concentrated flow cannot exceed 1,000 feet in length.  Then you must calculate a new time of concentration, intensity, and C value for the watershed.  All other calculations are the same as for calculating the peak discharge of the watershed before development.

In order to calculate the peak discharge during a ten year storm, simply use the 10 year storm curve on the I-D-F chart rather than the 2 year storm curve.

There are four methods commonly used to estimate runoff - Rational Method, Peak Discharge Method, Tabular Method, and Unit Hydrograph Method.  The factors used to decide on a calculation method are the size of the drainage area and the output information required.

A hydrograph is used to graphically represent the amount of runoff over time.  A hydrograph can be plotted using a table of discharge values.  By plotting a hydrograph of the watershed before development on the same chart as a hydrograph of the watershed after development, you can compare the peak discharge values, the time of peak discharge, the course of the storm, and the change in runoff volume for the two watershed conditions.

Other Resources

Points on a Graph - a tutorial website for learning to graph points

Assignment

1. If the length of overland and/or shallow concentrated flow in your watershed is greater than the recommended maximum, change the flow regime lengths for your plan. Then calculate the peak discharge for your watershed during the 2 year storm after development. Hint: the subdivision which you are building will have a C value of about 0.4.

2.  Calculate the peak discharge for your watershed during the 10 year storm before development.

3. Calculate the peak discharge for your watershed during the 10 year storm after development.

4. Which methods of calculating peak discharge are appropriate for your watershed?  Why?

5. Using the discharge summary table below, draw a hydrograph for the watershed before development and after development.  What is the peak discharge for each watershed condition?  At what time does the peak discharge for each condition occur?  Label the peak discharge for each watershed condition on the hydrograph.  Label the extra volume resulting from runoff.
 Time (hours after storm begins) 5 5.2 5.4 5.8 6.2 6.6 7 7.6 8.5 9.5 Discharge (cfs) before development 1.9 46 118.2 41.8 20.8 15.8 13 10.3 8.6 6.9 Discharge (cfs) after development 3.2 78.8 202.7 71.6 35.6 27 22.3 17.6 14.8 11.9

Quiz

There is no quiz for this lesson.