*Source of lead image: http://www.geograph.org.uk/photo/2255129*

*Source of activity: http://www.lmnoeng.com/Hydrology/rational.php*

# About this activity:

The rational equation method can be used to "determine peak discharge from drainage basin runoff." According to lmnoeng.com, this method "is the most common method used for sizing sewer systems." The method uses an equation to help you understand how much runoff would come from an area under different conditions.

# Why you might do this activity:

This activity can be useful if you're trying to determine:

- How much water a site would absorbed in a rain events of different intensities. For example:
- How much water would this site absorb with 3 inches of rain over an hour, verse 1 inch of rain over an hour.

- How much runoff would result from different ground covers. For example:
- If we change the ground cover of this area from impervious pavement to a rain garden, how much water would be absorbed?
- How much added stormwater would result from building a house on this plot of land?

# What you will need:

To do this method of determining discharge you need:

- the drainage area (acres),
- to know the ground cover that is in your drainage area,
- the rainfall intensity in your location,
- internet connection to get to the site to plug in your equation.

The steps below will walk you through determining these.

# Step by step instructions:

### Step 1: Determining the drainage area:

To determine the drainage area of your site, you need to know how big it is. Figuring out the square feet of your site can be done by multiplying the length (ft) of the site by the width (ft) of the site.

**Large areas:**

*Tool:* If your site is big enough to show up on google maps, you can figure out the approximate size of your site with their are tool. Check out this link to get the area of your site, you can search your location then use your curser to click around the outside of your site. Your total area will show up below.

*Tip:* If your site is too big to measure in feet you can change your units to square acres. Because 1 acre = 43560 square feet (4840 square yards). You can take your total squire feet and divide it by 43560 to get the total acres.

**Irregular shapes:**

*Tool:* You can use google to help you figure out these areas for example an equation will show up if you google "the area of a triangle"

*Tip:* To find the exact area of smaller irregular shapes, you can divide the irregular shape into regular shapes such as triangles, rectangles, circles, squares, then add them all up.

### Step 2: Determine the ground cover of your drainage area

Because we know how fast water absorbs into different types of ground cover, we can assign different ground covers different "Runoff Coefficients." There are some standard Runoff Coefficients below:

| **Ground Cover**| **Runoff Coefficient, c**|
| Lawns| 0.05 - 0.35|
| Forest| 0.05 - 0.25|
| Cultivated land| 0.08-0.41|
| Meadow| 0.1 - 0.5|
| Parks, cemeteries| 0.1 - 0.25|
| Unimproved areas| 0.1 - 0.3|
| Pasture| 0.12 - 0.62|
| Residential areas| 0.3 - 0.75|
| Business areas| 0.5 - 0.95|
| Industrial areas| 0.5 - 0.9|
| Asphalt streets| 0.7 - 0.95|
| Brick streets| 0.7 - 0.85|
| Roofs| 0.75 - 0.95|
| Concrete streets| 0.7 - 0.95|

*Tip:* If you have an area that has more than one ground cover type, you should calculate the equation for each area.

### Step 3: Determine the rainfall intensity

The last piece of data you will need to run your equation is the rainfall intensity. You can get this number from a specific event you are exploring, say for example, you want to know how three inches of rain/hour affects your site next to a rain event that was just one inch of rain/hour.

*Tip:* You can look at historic data or average data for rain events your location. A good place to find this information is the historic data from the weather underground.

### Step 4: Plug in your data

The data you've now gathered gives you everything you need to figure out peek discharge from your site in a rain event. Take your numbers from above, and plug them into the equation on this site: *http://www.lmnoeng.com/Hydrology/rational.php*

Key:

A = Drainage area, acre (your answer from step 1)

c = Rational method runoff coefficient (your answer from step 2)

i = Rainfall intensity, inch/hour (your answer from step 3)

These together give you: "Q," your Peak discharge. The entire equation looks like this: Q=ciA

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