Saturday, December 26, 2009

The Rational Method

Okay, let’s say that my method for calculating average monthly rainfall in my previous post just isn’t good enough for you. You are too detail-oriented for that little amount of information to be satisfying. You want to know how to calculate how much rain you are getting in a particular storm. Well, this post is for you. For the rest of you who came here looking for some interesting gardening information: may I show you to another lovely post? Just keep it in mind as a reference. At any rate, I’ll have another post up shortly. It is gonna get pretty math-y pretty quickly here.

The Rational Method is an old method that civil engineers use to determine how much water a particular storm even is going to deliver. So, if you are designing a culvert to carry the water from a 100 year storm, this one will do it. As technology and science have improved our accuracy for calculating runoff, the Rational Method hasn’t really gotten left behind. It is still considered pretty accurate up to about 600 acres or so and is often used as a check when more complex methods are used.

The beauty of the Rational Method is its simplicity. Here it is:


Q is the runoff in cubic feet per second (cfs)
C is the runoff coefficient
i is the rainfall intensity in inches/hour, and
A is the drainage basin area in acres

Starting with the easier ones, A is pretty easy to calculate. The only tricky part is measuring it. If you have a small area, you might be able to get it with a measuring tape or similar measuring device. If you have a larger drainage area, you might need to go to the USGS and find yourself a topo map of your area. Remember: water always flows perpendicular to the contour lines, so trace perpendicular to the contour lines until you can find the ridgeline. Then measure off and calculate your area. It is easiest for this sort of thing, unless you happen to have a planimeter, to just break it up into simple geometric shapes and calculate the areas individually. Then convert by the scale factor of the drawing and then convert to acres.

Your value for C is going to be based on observation. Take a look at the area that you are draining from. C gives you the percentage of water that is actually draining off. So impervious surfaces will give you a higher C value than a soft, fluffy forest floor. Here are some sample C values:

Paved areas, roof areas, impermeable areas: 0.95
Bare ground: 0.25
Lawn area: 0.20
Suburban areas: 0.35
Steep terrain: 0.70

The value for i is the tricky one. Basically, shorter storms tend to be more intense. However, when a drop of rain falls on the farthest reaches of your drainage basin, it takes a certain amount of time to reach your concentration point. If it takes 30 minutes for your raindrop to reach your concentration point and you calculate for the 10 minute storm, the storm will be over before the entire area is contributing to the runoff at the same time. However, for most areas that a homeowner would be dealing with, i.e. under a few acres, 10 minutes is a reasonable assumption, so use the 10 minute storm. To actually get the values for your area (in the United States), go to the NOAA site and get an intensity-duration-frequency chart for your area and use the column for a 10 minute storm. Just make sure that the final number you plug into the Rational Method is in inches/hour. If not, be sure to convert it beforehand.

Then you just plug the numbers in and calculate your flow. You can use that to tell you how quickly your basin will fill up in a particular storm, or multiply by the length of your storm to figure how much rain you will get.

I will offer one caution, though. A lot of what is involved in accurately determining the numbers to plug into the formula relies on expertise. If you don’t have the expertise, it is called guessing. If you really need this calculated accurately, which you will if you have flooding issues, or you are building it near your or anyone else’s building, or if you have a large drainage area near your house, to name a few, you should really have this calculation done professionally by a civil engineer.

To say it another way: The calculation above is for entertainment purposes only and should not be attempted by non-professionals for any purpose other than idle curiosity.

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