State the Rational formula for estimating the peak rate of runoff from the small watersheds. List out the basic assumptions made under the Rational formula?


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 duration equal to the time of concentration. The rational formula is:


  • Q = maximum rate of runoff (cfs or m3/sec.)
  • C = runoff coefficient
  • I = average rainfall intensity (in./hr. or mm/hr.)
  • A = drainage area (ac or ha)
  • Z = conversion factor, 1 for English, 360 for metric

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.

Assumptions and Limitations

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

  • The method is applicable if tc for the drainage area is less than the duration of peak rainfall intensity.
  • The calculated runoff is directly proportional to the rainfall intensity.
  • Rainfall intensity is uniform throughout the duration of the storm.
  • The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing that event.
  • Rainfall is distributed uniformly over the drainage area.
  • 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.
  • 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.

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

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