Stormwater Calculations - Mathematics and Statistics for the Environment - page 772

25.6.1.1 Assumptions
The rational method is based on the following assumptions:

• Under steady rainfall intensity, the maximum discharge will occur at the watershed out-
let at the time when the entire area above the outlet is contributing runoff. This time is
commonly known as the time of concentration, tc, and is defined as the time required for
runoff to travel from the most hydrologically distant point in the watershed to the outlet.

The assumption of steady rainfall dictates that even during longer events, when factors
such as increasing soil saturation are ignored, the maximum discharge occurs when
the entire watershed is contributing to the peak flow, at time t = t c . Furthermore, this
assumption limits the size of the drainage area that can be analyzed using the rational
method. In large watersheds, the time of concentration may be so long that constant
rainfall intensities may not occur for long periods. Also, shorter, more intense bursts
of rainfall that occur over portions of the watershed may produce large peak flows. The
time of concentration is equal to the minimum duration of peak rainfall. The time of
concentration reflects the minimum time required for the entire watershed to contrib-
ute to the peak discharge as stated above. The rational method assumes that all dis-
charge does not increase as a result of soil saturation, decreased conveyance time, etc.
Therefore, the time of concentration is not necessarily intended to be a measure of the
actual storm duration, but simply the critical time period used to determine the average
rainfall intensity from the IDF curves.

• The frequency or return period of the computed peak discharge is the same as the frequency
or return period of rainfall intensity (design storm) for the given time of concentration.

Frequencies of peak discharges depend not only on the frequency of rainfall intensity,
but also the response characteristics of the watershed. For small and mostly impervious
areas, rainfall frequency is the dominant factor since response characteristics are rela-
tively constant. However, for larger watersheds, the response characteristics will have
a much greater impact on the frequency of the peak discharge due to drainage struc-
tures, restrictions within the watershed, and initial rainfall losses from interception and
depression storage.

• The fraction of rainfall that becomes runoff is independent of rainfall intensity or volume.

This assumption is reasonable for impervious areas, such as streets, rooftops, and parking
lots. For pervious areas, the fraction of rainfall that becomes runoff varies with rainfall
intensity and the runoff will increase. This fraction is represented by the dimensionless
runoff coefficient, C . Therefore, the accuracy of the rational method is dependent on the
careful selection of a coefficient that is appropriate for the storm, soil, and land use condi-
tions. It is easy to see why the rational method becomes more accurate as the percentage of
impervious cover in the drainage area approaches 100%.

• The peak rate of runoff is sufficient information for the design of stormwater detention
and retention facilities.

25.6.1.2 Limitations
Because of the assumptions discussed above, the rational method should only be used when the
following criteria are met:

1. The given watershed has a time of concentration, t c , less than 20 minutes.

2. The drainage area is less than 20 acres.