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Section 12: Rational Method

The rational method is appropriate for estimating peak discharges for small drainage areas of up to about 200 acres (80 hectares) with no significant flood storage. The method provides the designer with a peak discharge value, but does not provide a time series of flow nor flow volume.

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Assumptions and Limitations

Use of the rational method includes the following assumptions and limitations:

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  • The method is applicable if tc for the drainage area is less than the duration of peak rainfall intensity.
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  • The calculated runoff is directly proportional to the rainfall intensity.
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  • Rainfall intensity is uniform throughout the duration of the storm.
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  • The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing that event.
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  • Rainfall is distributed uniformly over the drainage area.
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  • The minimum duration to be used for computation of rainfall intensity is 10 minutes. If the time of concentration computed for the drainage area is less than 10 minutes, then 10 minutes should be adopted for rainfall intensity computations.
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  • The rational method does not account for storage in the drainage area. Available storage is assumed to be filled.

The above assumptions and limitations are the reason the rational method is limited to watersheds 200 acres or smaller. If any one of these conditions is not true for the watershed of interest, the designer should use an alternative method.

The rational method represents a steady inflow-outflow condition of the watershed during the peak intensity of the design storm. Any storage features having sufficient volume that they do not completely fill and reach a steady inflow-outflow condition during the duration of the design storm cannot be properly represented with the rational method. Such features include detention ponds, channels with significant volume, and floodplain storage. When these features are present, an alternate rainfall-runoff method is required that accounts for the time-varying nature of the design storm and/or filling/emptying of floodplain storage. In these cases, the hydrograph method is recommended.

The steps in developing and applying the rational method are illustrated in Figure 4-8.

Steps in developing and applying the rational method (click in image to see full-size image) Anchor: #LKMKNJIFgrtop

Figure 4-8. Steps in developing and applying the rational method

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Procedure for using the Rational Method

The rational formula estimates the peak rate of runoff at a specific location in a watershed as a function of the drainage area, runoff coefficient, and mean rainfall intensity for a duration equal to the time of concentration. The rational formula is:

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Equation 4-20.

Where:

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Rainfall Intensity

With the drainage area A and design AEP known, the designer will determine appropriate values of I and C for use in Equation 4-20. I is given by:

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Equation 4-21.

Where:

Values of Pd for use in Equation 4-19 are found in the Atlas of Depth-Duration Frequency (DDF) of Precipitation Annual Maxima for Texas (TxDOT 5-1301-01-1). The atlas includes 96 maps depicting the spatial variation of the DDF of precipitation annual maxima for Texas. The AEPs represented are 50%, 20%, 10%, 4%, 2%, 1%, 0.4%, and 0.2% (2-, 5-, 10-, 25-, 50-, 100-, 250-, and 500-years). The storm durations represented are 15 and 30 minutes; 1, 2, 3, 6, and 12 hours; and 1, 2, 3, 5, and 7 days.

In most cases, the computed value of tc will not exactly match the durations provided in the atlas, i.e. tc = 4 hours. In these cases, the designer can obtain the depth for the desired duration by performing a log-log interpolation between depth-duration pairs provided in the atlas. This process is illustrated in Figure 4-16.

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Runoff Coefficients

Urban Watersheds

Table 4-10 suggests ranges of C values for urban watersheds for various combinations of land use and soil/surface type. This table is typical of design guides found in civil engineering texts dealing with hydrology.

Anchor: #i1081558Table 4-10: Runoff Coefficients for Urban Watersheds

Type of drainage area

Runoff coefficient

Business:

 

Downtown areas

0.70-0.95

Neighborhood areas

0.30-0.70

Residential:

 

Single-family areas

0.30-0.50

Multi-units, detached

0.40-0.60

Multi-units, attached

0.60-0.75

Suburban

0.35-0.40

Apartment dwelling areas

0.30-0.70

Industrial:

 

Light areas

0.30-0.80

Heavy areas

0.60-0.90

Parks, cemeteries

0.10-0.25

Playgrounds

0.30-0.40

Railroad yards

0.30-0.40

Unimproved areas:

 

Sand or sandy loam soil, 0-3%

0.15-0.20

Sand or sandy loam soil, 3-5%

0.20-0.25

Black or loessial soil, 0-3%

0.18-0.25

Black or loessial soil, 3-5%

0.25-0.30

Black or loessial soil, > 5%

0.70-0.80

Deep sand area

0.05-0.15

Steep grassed slopes

0.70

Lawns:

 

Sandy soil, flat 2%

0.05-0.10

Sandy soil, average 2-7%

0.10-0.15

Sandy soil, steep 7%

0.15-0.20

Heavy soil, flat 2%

0.13-0.17

Heavy soil, average 2-7%

0.18-0.22

Heavy soil, steep 7%

0.25-0.35

Streets:

 

Asphaltic

0.85-0.95

Concrete

0.90-0.95

Brick

0.70-0.85

Drives and walks

0.75-0.95

Roofs

0.75-0.95


Rural and Mixed-Use Watershed

Table 4-11 shows an alternate, systematic approach for developing the runoff coefficient. This table applies to rural watersheds only, addressing the watershed as a series of aspects. For each of four aspects, the designer makes a systematic assignment of a runoff coefficient “component.” Using Equation 4-22, the four assigned components are added to form an overall runoff coefficient for the specific watershed segment.

The runoff coefficient for rural watersheds is given by:

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Equation 4-22.

Where:

The designer selects the most appropriate values for Cr, Ci, Cv, and Cs from Table 4-11.

Anchor: #i1081675Table 4-11: Runoff Coefficients for Rural Watersheds

Watershed characteristic

Extreme

High

Normal

Low

Relief - Cr

0.28-0.35

Steep, rugged terrain with average slopes above 30%

0.20-0.28

Hilly, with average slopes of 10-30%

0.14-0.20

Rolling, with average slopes of 5-10%

0.08-0.14

Relatively flat land, with average slopes of 0-5%

Soil infiltration - Ci

0.12-0.16

No effective soil cover; either rock or thin soil mantle of negligible infiltration capacity

0.08-0.12

Slow to take up water, clay or shallow loam soils of low infiltration capacity or poorly drained

0.06-0.08

Normal; well drained light or medium textured soils, sandy loams

0.04-0.06

Deep sand or other soil that takes up water readily; very light, well-drained soils

Vegetal cover - Cv

0.12-0.16

No effective plant cover, bare or very sparse cover

0.08-0.12

Poor to fair; clean cultivation, crops or poor natural cover, less than 20% of drainage area has good cover

0.06-0.08

Fair to good; about 50% of area in good grassland or woodland, not more than 50% of area in cultivated crops

0.04-0.06

Good to excellent; about 90% of drainage area in good grassland, woodland, or equivalent cover

Surface Storage - Cs

0.10-0.12

Negligible; surface depressions few and shallow, drainageways steep and small, no marshes

0.08-0.10

Well-defined system of small drainageways, no ponds or marshes

0.06-0.08

Normal; considerable surface depression, e.g., storage lakes and ponds and marshes

0.04-0.06

Much surface storage, drainage system not sharply defined; large floodplain storage, large number of ponds or marshes

Table 4-11 note: The total runoff coefficient based on the 4 runoff components is C = Cr + Ci + Cv + Cs


While this approach was developed for application to rural watersheds, it can be used as a check against mixed-use runoff coefficients computed using other methods. In so doing, the designer would use judgment, primarily in specifying Cs, to account for partially developed conditions within the watershed.

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Mixed Land Use

For areas with a mixture of land uses, a composite runoff coefficient should be used. The composite runoff coefficient is weighted based on the area of each respective land use and can be calculated as:

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Equation 4-23.

Where:

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