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Rational Method for Peak Flow

The rational method determines the max flow (Q) at a point after a storm event.

$$ Q = CiA $$

Q, peak flow

C, runoff coefficient

i, storm intensity ($$\frac{in}{hr} $$)

A, area (acres)

To use the rational method you need to divide the watershed (area contributing flow to the point) up into separate areas depending on the runoff coefficients (C). The runoff coefficient changes based on different land types such as concrete, bare earch, turf meadow, residential etc. If the entire area is under one runoff coefficient then lucky you. If not, determine the area of each subregion and it’s accompanying C value. Tables for C values are provided in both the AIO and CERM.

You should end up with (or be given) data similar to this:

Get the Average Runoff Coefficient

You can only enter one C value into the equation. It should be the weighted average of all of the C values.

$$ C_{avg} = \frac{ \sum{CA}}{ \sum{A} } $$

With the data above this would be:

$$ C_{avg} = \frac{25*0.2 + 15*0.3 + 2*0.4}{25+15+2} = 0.245$$

On a short question like on the breadth, I am thinking that the intensity MAY be provided to you, it is sort of a process to get it on your own. Either way, get the intensity. Once you have all three values, multiply for max Q!

Let’s just say I solved for intensity (using information that has not been provided in this example) and it is 1.25 $$\frac{in}{hr}$$ (on the less-intense end):

$$ Q = C_{avg} * i * A $$

$$ Q = 1.25 * 0.245 * 42 $$

$$ Q = 12.875 \frac{ft^3}{s}$$

There you have it! This seems like a high flow to me, but it’s a huge area. And it’s an example problem, I made all these values up.

Speed Tip

You may have noticed that to solve for the $$C_{avg}$$ value you have to divide by the total area. Why would you divide by the total area to get that and then turn around and multiply by the total area when you solve or Q?

To save some time, just multiply the sum of the region areas and coefficients by the intensity. It could be rewritten as $$Q=\left( \sum{ CA_{region}  }\right)*i$$.