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388 Chapter 11 Hydrology: Rainfall and Runoff
when the rainfall record is longer than the runoff record; and through statistical
generation of additional values.
3. Rational estimates of runoff from rainfall. This is a common procedure in the de-
sign of storm and combined sewers that are to drain existing built-up areas and sat-
isfy anticipated change in the course of time, or areas about to be added to existing
municipal drainage schemes.
4. Calculations based on empirical formulations not devised specifically from obser-
vations in the design area but reasonably applicable to existing watershed condi-
tions. Formulations are varied in structure and must be selected with full under-
standing of the limitations of their derivation. At best, they should be applied only
as checks of statistical or rational methods.
Where failure of important engineering structures is sure to entail loss of life or great
damage, every bit of hydrologic information should be adduced to arrive at economical but
safe design values. Hydraulic models may also be helpful.

11.17 ESTIMATES OF STORM RUNOFF
Among the various methods used to estimate storm runoff, two are of general interest: the
rational method and the unit-hydrograph method.

11.17.1 The Rational Method
This is the method commonly used as a basis for the design of storm drains and combined
sewers. Such facilities are expected to carry, without surcharge, the peak runoff expected to
be equaled or exceeded on the average once in a period (a recurrence interval) of T years.
The interval selected is short, T 2 to 5 years, when damage due to surcharge and street
flooding is small, and is long, T 20 to 100 years, when the damage is great as it some-
times can be when basements in residential and commercial districts are flooded.
The design peak flow is estimated using the equation
Q = cia (U.S. Customary Units) (11.24a)
3
where Q is the peak rate of runoff at a specified place, in ft /s; a is the tributary area, in
3
acres; and i the rainfall intensity, in in./h (1 in./h on 1 acre 1 ft /s), for the selected
values of T in years and t in min. The rainfall duration, t, is in fact a rainfall-intensity
averaging time.
The following are three equivalent Rational Method equations using the SI or metric units:
Q = cia (SI Units) (11.24b)
3
2
where the SI units are: Q (m /h); i (m/h); a (m ); c (dimensionless).
Q = 238 cia (SI Units) (11.24c)
3
where the SI units are: Q (m /d); i (mm/h); a (ha); c (dimensionless).
Q = 2.76 cia (SI Units) (11.24d)

where the SI units are: Q (L/s); i (mm/h); a (ha); c (dimensionless).
Of the three factors included in Eq. 11.24, the area a is found from a regional map or
survey, i is determined for a storm of duration equal to the time of concentration, and c is
estimated from the characteristics of the catchment area (see Table 11.11). The time of