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The Rational Method

General

The rational method is used to predict peak flows for small drainage areas which can be either natural or developed. The rational method can be used for culvert design, pavement drainage design, storm drain design, and some stormwater facility design. The greatest accuracy is obtained for areas smaller than 40 hectares (100 acres) and for developed conditions with large areas of impervious surface (e.g., pavement, roof tops, etc.). Basins up to 400 hectares (1,000 acres) may be evaluated using the rational formula; however, results for large basins often do not properly account for effects of infiltration and thus are less accurate. Designers should never perform a rational method analysis on a basin that is larger than the lower limit specified for the USGS regression equations since the USGS regression equations will yield a more accurate flow prediction for that size of basin.
The formula for the rational method is:

eq1

Hydrologic information calculated by the rational method should be submitted on DOT Form 235-009 (see Figure 2-4.1). This format contains all the required input information as well as the resulting discharge. The description of each area should be identified by name or stationing so that the reviewer may easily locate each area.

[nextpage title=”Runoff Coefficients”]

The runoff coefficient “C” represents the percentage of rainfall that becomes runoff. The rational method implies that this ratio is fixed for a given drainage basin. In reality, the coefficient may vary with respect to prior wetting and seasonal conditions. The use of an average coefficient for various surface types is quite common and it is assumed to stay constant through the duration of the rain storm.

Frozen ground can cause a dramatic increase in the runoff coefficient. When this condition is coupled with heavy rainfall and, perhaps, melting snow, the runoff can be much greater than calculated values that did not account for these conditions. This condition is common for larger basins that are above 300 m (1000 ft.) in elevation and is automatically accounted for in the USGS regression equations. For small basins where the rational method is being used, the designer should increase the runoff coefficient to reflect the reduction in infiltration and resulting increased surface runoff.

In a high growth rate area, runoff factors should be projected that will be characteristic of developed conditions 20 years after construction of the project. Even though local storm water practices (where they exist) may reduce potential increases in runoff, prudent engineering should still make allowances for predictable growth patterns.

The coefficients in Figure 2-4.2 are applicable for peak storms of 10-year frequency. Less frequent, higher intensity storms will require the use of higher coefficients because infiltration and other losses have a proportionally smaller effect on runoff. Generally, when designing for a 25-year frequency, the coefficient should be increased by 10 percent; when designing for a 50-year frequency, the coefficient should be increased by 20 percent; and when designing for a 100-year frequency, the coefficient should be increased by 25 percent. The runoff coefficient should never be increased above 0.90.

Hydrologic information calculated by the rational method should be submitted on DOT Form 235-009 (see Figure 2-4.1). This format contains all the required input information as well as the resulting discharge. The description of each area should be identified by name or stationing so that the reviewer may easily locate each area.

[nextpage title=”Time of Concentration”]

If rainfall is applied at a constant rate over a drainage basin, it would eventually produce a constant peak rate of runoff. The amount of time that passes from the moment that the constant rainfall begins to the moment that the constant rate of runoff begins is called the time of concentration. This is the time required for the surface runoff to flow from the most hydraulically remote part of the drainage basin to the location of concern.

Actual precipitation does not fall at a constant rate. A precipitation event will begin with a small rainfall intensity then, sometimes very quickly, build to a peak intensity and eventually taper down to no rainfall. Because rainfall intensity is variable, the time of concentration is included in the rational method so that the designer can determine the proper rainfall intensity to apply across the basin. The intensity that should be used for design purposes is the highest intensity that will occur with the entire basin contributing flow to the location where the designer is interested in knowing the flow rate. It is important to note that this may be a much lower intensity than the absolute maximum intensity. The reason is that it often takes several minutes before the entire basin is contributing flow but the absolute maximum intensity lasts for a much shorter time so the rainfall intensity that creates the greatest runoff is less than the maximum by the time the entire basin is contributing flow.

Most drainage basins will consist of different types of ground covers and conveyance systems that flow must pass over or through. These are referred to as flow segments. It is common for a basin to have flow segments that are overland flow and flow segments that are open channel flow. Urban drainage basins often have flow segments that are flow through a storm drain pipe in addition to the other two types. A travel time (the amount of time required for flow to move through a flow segment) must be computed for each flow segment. The time of concentration is equal to the sum of all the flow segment travel times.

For a few drainage areas, a unique situation occurs where the time of concentration that produces the largest amount of runoff is less than the time of concentration for the entire basin. This can occur when two or more subbasins have dramatically different types of cover (i.e., different runoff coefficients). The most common case would be a large paved area together with a long narrow strip of natural area. In this case, the designer should check the runoff produced by the paved area alone to determine if this scenario would cause a greater peak runoff rate than the peak runoff rate produced when both land segments are contributing flow. The scenario that produces the greatest runoff should be used, even if the entire basin is not contributing flow to this runoff.

The procedure described below for determining the time of concentration for overland flow was developed by the United States Natural Resources Conservation Service (formerly known as the Soil Conservation Service). It is sensitive to slope, type of ground cover, and the size of channel. The designer should never use a time of concentration less than 5 minutes. The time of concentration can be calculated as follows:

Time of Concentration eq

[nextpage title=”Rainfall Intensity”]

After the appropriate storm frequency for the design has been determined (see Chapter 1) and the time of concentration has been calculated, the rainfall intensity can be calculated. Designers should never use a time of concentration that is less than 5 minutes for intensity calculations, even when the calculated time of concentration is less than 5 minutes. It should be noted that the rainfall intensity at any given time is the average of the most intense period enveloped by the time of concentration and is not the instantaneous rainfall. The equation for calculating rainfall intensity is:

Rainfall Intensity eq

The coefficients (m and n) have been determined for all major cities for the 2-, 5-, 10-, 25-, 50-, and 100-year mean recurrence intervals (MRI). The coefficients listed are accurate from 5-minute duration to 1,440-minute duration (24 hours). These equations were developed from the 1973 National Oceanic and Atmospheric Administration Atlas 2, Precipitation-Frequency Atlas of the Western United States, Volume IX-Washington. The designer should interpolate between the two or three nearest cities listed in the tables when working on a project that is in a location not listed on the table. If the designer must do an analysis with a storm duration greater than 1,440 minutes, the rational method should not be used.

[nextpage title=”Rational Formula Example”]

Compute the 25-year runoff for the Olympia watershed shown above. Three types of flow conditions exist from the highest point in the watershed to the outlet. The upper portion is 10.0 hectares of forest cover with an average slope of 0.15 m/m. The middle portion is 2.5 hectares of single family residential with a slope of 0.06 m/m and primarily lawns. The lower portion is a 2.0 hectares park with 450 mm storm sewers with a general slope of 0.01 m/m.

Rational Formula Example

[nextpage title=”Figures”]