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.
Anchor: #i1469973Assumptions and Limitations
Use of the rational method includes the following assumptions and limitations:
 Anchor: #REKEJIFK
 The method is applicable if t_{c} for the drainage area is less than the duration of peak rainfall intensity. Anchor: #IMJMNFHI
 The calculated runoff is directly proportional to the rainfall intensity. Anchor: #KMLFEMKG
 Rainfall intensity is uniform throughout the duration of the storm. Anchor: #LEKFFMKI
 The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing that event. Anchor: #KSJMMIMN
 Rainfall is distributed uniformly over the drainage area. Anchor: #JNKGHMFK
 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. Anchor: #PEKFMHFF
 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 inflowoutflow 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 inflowoutflow 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 rainfallrunoff method is required that accounts for the timevarying 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 48.
Figure 48. Steps in developing and applying the rational method
Anchor: #i1154472Procedure 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:
Equation 420.
Where:
 Anchor: #EMGLIHIL
 Q = maximum rate of runoff (cfs or m^{3}/sec.) Anchor: #JKHMKKEI
 C = runoff coefficient Anchor: #NJJFKKLN
 I = average rainfall intensity (in./hr. or mm/hr.) Anchor: #JHIKIKLJ
 A = drainage area (ac or ha) Anchor: #NVHLLKMG
 Z = conversion factor, 1 for English, 360 for metric
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 420. I is given by:
Equation 421.
Where:
 Anchor: #MEJMFHKG
 P_{d} = Depth of rainfall (in. or mm) for AEP design storm of duration t_{c} Anchor: #LIFHJMIH
 t_{c} = drainage area time of concentration (hr.)
Values of P_{d} for use in Equation 421 are found in the Atlas of DepthDuration Frequency (DDF) of Precipitation Annual Maxima for Texas (TxDOT 51301011). 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 500years). 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 t_{c} will not exactly match the durations provided in the atlas, i.e. t_{c} = 4 hours. In these cases, the designer can obtain the depth for the desired duration by performing a loglog interpolation between depthduration pairs provided in the atlas. This process is illustrated in Figure 416.
Anchor: #i1108889Runoff Coefficients
Urban Watersheds
Table 410 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.
Type of drainage area 
Runoff coefficient 

Business: 

Downtown areas 
0.700.95 
Neighborhood areas 
0.300.70 
Residential: 

Singlefamily areas 
0.300.50 
Multiunits, detached 
0.400.60 
Multiunits, attached 
0.600.75 
Suburban 
0.350.40 
Apartment dwelling areas 
0.300.70 
Industrial: 

Light areas 
0.300.80 
Heavy areas 
0.600.90 
Parks, cemeteries 
0.100.25 
Playgrounds 
0.300.40 
Railroad yards 
0.300.40 
Unimproved areas: 

Sand or sandy loam soil, 03% 
0.150.20 
Sand or sandy loam soil, 35% 
0.200.25 
Black or loessial soil, 03% 
0.180.25 
Black or loessial soil, 35% 
0.250.30 
Black or loessial soil, > 5% 
0.700.80 
Deep sand area 
0.050.15 
Steep grassed slopes 
0.70 
Lawns: 

Sandy soil, flat 2% 
0.050.10 
Sandy soil, average 27% 
0.100.15 
Sandy soil, steep 7% 
0.150.20 
Heavy soil, flat 2% 
0.130.17 
Heavy soil, average 27% 
0.180.22 
Heavy soil, steep 7% 
0.250.35 
Streets: 

Asphaltic 
0.850.95 
Concrete 
0.900.95 
Brick 
0.700.85 
Drives and walks 
0.750.95 
Roofs 
0.750.95 
Rural and MixedUse Watershed
Table 411 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 422, 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:
Equation 422.
Where:
 Anchor: #KLIKNNFE
 C = runoff coefficient for rural watershed Anchor: #FHIJKNEE
 C_{r} = component of coefficient accounting for watershed relief Anchor: #JNIIHMMN
 C_{i} = component of coefficient accounting for soil infiltration Anchor: #OLJNLNEF
 C_{v} = component of coefficient accounting for vegetal cover Anchor: #KLIKLLNK
 C_{s} = component of coefficient accounting for surface type
The designer selects the most appropriate values for C_{r}, C_{i}, C_{v}, and C_{s} from Table 411.
Watershed characteristic 
Extreme 
High 
Normal 
Low 

Relief  C_{r} 
0.280.35 Steep, rugged terrain with average slopes above 30% 
0.200.28 Hilly, with average slopes of 1030% 
0.140.20 Rolling, with average slopes of 510% 
0.080.14 Relatively flat land, with average slopes of 05% 
Soil infiltration  C_{i} 
0.120.16 No effective soil cover; either rock or thin soil mantle of negligible infiltration capacity 
0.080.12 Slow to take up water, clay or shallow loam soils of low infiltration capacity or poorly drained 
0.060.08 Normal; well drained light or medium textured soils, sandy loams 
0.040.06 Deep sand or other soil that takes up water readily; very light, welldrained soils 
Vegetal cover  C_{v} 
0.120.16 No effective plant cover, bare or very sparse cover 
0.080.12 Poor to fair; clean cultivation, crops or poor natural cover, less than 20% of drainage area has good cover 
0.060.08 Fair to good; about 50% of area in good grassland or woodland, not more than 50% of area in cultivated crops 
0.040.06 Good to excellent; about 90% of drainage area in good grassland, woodland, or equivalent cover 
Surface Storage  C_{s} 
0.100.12 Negligible; surface depressions few and shallow, drainageways steep and small, no marshes 
0.080.10 Welldefined system of small drainageways, no ponds or marshes 
0.060.08 Normal; considerable surface depression, e.g., storage lakes and ponds and marshes 
0.040.06 Much surface storage, drainage system not sharply defined; large floodplain storage, large number of ponds or marshes 
Table 411 note: The total runoff coefficient based on the 4 runoff components is C = C_{r} + C_{i }+ C_{v} + C_{s} 
While this approach was developed for application to rural watersheds, it can be used as a check against mixeduse runoff coefficients computed using other methods. In so doing, the designer would use judgment, primarily in specifying C_{s}, to account for partially developed conditions within the watershed.
Anchor: #IJGHMNLNMixed 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:
Equation 423.
Where:
 Anchor: #JNPIFEFK
 C_{W} = weighted runoff coefficient Anchor: #KITIGHFL
 C_{j} = runoff coefficient for area j Anchor: #KONIHKFM
 A_{j} = area for land cover j (ft^{2}) Anchor: #MOMGNHMK
 n = number of distinct land uses