Section 6: The Rational Method
Anchor: #i1026352Introduction
The Rational Method was first introduced in 1889. Although it is often considered simplistic, it still is appropriate for estimating peak discharges for small drainage areas of up to about 200 acres (80 hectares) in which no significant flood storage appears.
Anchor: #i1026362Assumptions of the Rational Method
The rate of runoff resulting from any constant rainfall intensity is maximum when the duration of rainfall equals the time of concentration. That is, if the rainfall intensity is constant, the entire drainage area contributes to the peak discharge when the time of concentration has elapsed. This assumption becomes less valid as the drainage area increases. For large drainage areas, the time of concentration can be so large that the assumption of constant rainfall intensities for such long periods is not valid, and shorter more intense rainfalls can produce larger peak flows. Additionally, rainfall intensities usually vary during a storm. In semi-arid and arid regions, storm cells are relatively small with extreme intensity variations.
The frequency of peak discharge is the same as the frequency of the rainfall intensity for the given time of concentration. Frequencies of peak discharges depend on the following:
- rainfall frequencies
- antecedent moisture conditions in the watershed
- the response characteristics of the drainage system.
For small, mostly impervious areas, rainfall frequency is the dominant factor. For larger drainage basins, the response characteristics are the primary influence on frequency. For drainage areas with few impervious surfaces (less urban development), antecedent moisture conditions usually govern, especially for rainfall events with a return period of 10 years or less.
The rainfall intensity is uniformly distributed over the entire drainage area. In reality, rainfall intensity varies spatially and temporally during a storm. For small areas, the assumption of uniform distribution is reasonable. However, as the drainage area increases, it becomes more likely that the rainfall intensity will vary significantly both in space and time.
The fraction (C) of rainfall that becomes runoff is independent of rainfall intensity or volume. The assumption is reasonable for impervious areas, such as streets, rooftops, and parking lots.
For pervious areas, the fraction of runoff varies with rainfall intensity, accumulated volume of rainfall, and antecedent moisture conditions. Thus, the art necessary for application of the Rational Method involves the selection of a coefficient that is appropriate for storm, soil, and land use. By limiting the application of the Rational Method to 200 acres (80 hectares), these assumptions are more likely to be reasonable.
Anchor: #i1026412Applicability
Modern drainage practice often includes detention of urban storm runoff to reduce the peak rate of runoff downstream and to provide storm water quality improvement. The Rational Method severely limits the evaluation of design alternatives available in urban and, in some instances, rural drainage design because of its inability to accommodate the presence of storage in the drainage area. When accommodation of any appreciable storage features in the drainage area is required, employ runoff hydrograph methods such as the NRCS Dimensionless Unit Hydrograph method.
Anchor: #i1026424The Rational Method Equation
The Rational formula estimates the peak rate of runoff at any location in a watershed as a function of the drainage area, runoff