The Rational Method is an equilibrium-based approach to peak flow estimation that uses rainfall intensity data and watershed characteristics to predict peak flows for a rainfall event. The Rational Method is a popular choice for storm sewer design because this type of design usually considers only peak flows, and because of the simplicity of the calculations involved.
At the most fundamental level, the Rational Method assumes that a steady state is attained such that the rainfall inflow rate of water onto a drainage basin is equal to the outflow rate of water from the basin. If one expresses the volumetric inflow rate as the product of the basin area A and the effective rainfall intensity ie, the outflow rate Q is obtained as Q = ieA. Further, if one accounts for abstractions, the effective intensity is a product of the actual rainfall intensity and a runoff coefficient, resulting in
Q = CiA
where Q = runoff rate (ac-in/hr, ha-mm/hr) C = runoff (abstractions) coefficent i = rainfall intensity (in/hr, mm/hr) A = drainage area (ac, ha)
Because 1 ac-in/hr = 1.008 cfs ≈ 1 cfs, engineers performing calculations by hand typically ignore the conversion factor and simply assume that the discharge Q is in units of cfs. In SI units, a conversion factor of 0.278 will yield Q in units of m3/s.
The time of concentration is the smallest time for which the entire basin is contributing runoff to the basin outlet; therefore, the storm duration must be at least as long as the time of concentration if a steady-state condition is to be achieved. Also, steady-state
conditions dictate that the storm intensity be spatially and temporally uniform. It is not reasonable to expect that rainfall will be spatially uniform over a large drainage basin, or that it will be temporally uniform over a duration at least as long as the time of
concentration when tc (and hence A) is large. Therefore, these conditions limit the applicability of the Rational Method to small drainage basins. An upper limit of 200 acres has been suggested by some, but the limit should really depend on the storm
characteristics of the particular locale. These local characteristics may limit the applicability of the Rational Method to basins smaller than 10 acres in some cases.
When several drainage basins (or subbasins) discharge to a common facility such as a storm sewer or culvert, the time of concentration should be taken as the longest of all the individual times of concentration, and should include pipe travel times when appropriate.
Further, the total drainage area served (the sum of the individual basin areas) should be no larger than the 200-acre limit (or smaller where applicable) of the Rational Method.
The basic steps for applying the Rational Method are as follows:
Step 1: Apply I-D-F Data
Develop or obtain a set of intensity-duration-frequency (IDF) curves for the locale in which the drainage basin resides. Assume that the storm duration is equal to the time of concentration and determine the corresponding intensity for the recurrence interval of interest. Note that the assumption that the storm duration and time of concentration are equal is conservative in that it represents the highest intensity for which the entire drainage area can contribute.
Step 2: Compute Watershed Area
The basin area A can be estimated using topographic maps, computer tools such as CAD or GIS software, or by field reconnaissance. The time of concentration may be estimated using the procedures discussed in the preceding subsection.
Step 3: Choose C Coefficients
The runoff coefficient C may be estimated using Table 2-5 if the land use is
homogeneous in the basin, or a composite C value may be estimated if the land use is heterogeneous (see Example 2-6).
Step 4: Solve Peak Flow
Finally, the peak runoff rate from the basin can be computed using the equation Q = CiA.
The following example illustrates the use of the Rational Method for several subbasins draining into a common storm sewer system.
Example 2-9: Computing Flows for Multiple Subbasins with the Rational Method Figure 2-13 is a plan view of a storm sewer system draining three subbasins. Use the Rational Method to determine the peak discharge in each pipe and size each pipe assuming the pipes flow full. Assume also that the pipes will be concrete with n = 0.013.
Perform the calculations for a storm recurrence interval of 25 years. Subbasin and pipe characteristics and IDF data for the 25-year event are tabulated as follows:
Subbasin A (ac) C tc (min)
A 6.0 0.6 20
B 4.0 0.8 10
C 4.5 0.8 15
Pipe Length (ft) Slope (%)
1 500 1.0
2 400 1.2
3 500 0.9
Duration (min) Intensity (in/hr)
5 8.40
10 7.02
15 5.96
20 5.26
30 4.42
60 2.97
Figure 2-13: System for Example 2-9
Solution
Flow into Pipe 1 occurs from Subbasin A only. Using the time of concentration as the storm duration, the 25-year rainfall intensity is 5.26 in/hr. The peak discharge used in sizing Pipe 1 is therefore
Q = 0.6(5.26)(6.0) = 19 cfs
Assuming that Pipe 1 is flowing full, its required diameter D may be found using Manning’s equation as follows:
ft
Rounding up to the next commercially available size, Pipe 1 should have a diameter of 24 inches. Use FlowMaster to determine that the depth of flow is 1.40 ft and the area of flow is 2.36 ft2.
Because the cross-sectional area of Pipe 1 is 2.36 ft2, the average velocity in Pipe 1 is V = Q/A = 19/2.36 = 8.05 ft/s
The travel time in Pipe 1 is
t = L/V = 500/8.05 = 62 s = 1.04 minutes
Pipe 2 is treated the same way as Pipe 1, recognizing that runoff from Subbasin C only enters Pipe 2. The peak discharge from Subbasin C is Q = 22 cfs, and the required diameter of Pipe 2 is D = 24 in. The travel time in Pipe 2 is t = 45 s = 0.75 min.
Pipe 3 must be sized to handle the runoff from all three of the subbasins, which have a total area of A = 14.5 acres. The runoff coefficient for the combined areas is computed as a composite value and is
72
The time of concentration is computed as the longest of the travel times to the upstream end of Pipe 3. These travel times are (1) the time of concentration of Subbasin B (10 minutes), (2) the time of concentration of Subbasin A plus the travel time in pipe 1 (20 + 1.0 = 21 min), and (3) the time of concentration of Subbasin C plus the travel time in Pipe 2 (15 + 0.75 = 15.75min). Thus, the time of concentration for Pipe 3 is 21 minutes, and the corresponding rainfall intensity (by interpolation) is 5.17 in/hr.
The peak discharge for Pipe 3 is Q = 0.72(5.17)(14.5) = 54 cfs
The required diameter of Pipe 3 (rounded to the nearest standard size) is 36 inches.