The Rational Formula

The hydraulic sizing of drainage and conveyance structures in urban settings always requires estimation of peak flow rates. Historically, the venerable Rational method has been the tool of choice for most practicing engineers around the world. Although the method definitely has its place in hydrologic design, it is routinely misapplied and overextended.

The roots of this methodology date as far back as 1851 (Mulvaney, 1851), and certainly as far back as 1889 (Kuichling, 1889). See discussion on chapter 1. The concept is attractive and easy to understand. If rainfall occurs over a basin at a constant intensity for a period of time that is sufficient to produce steady state runoff at the outlet or design point, then the peak outflow rate will be proportional to the product of rainfall intensity and basin area. In the United States, the method is commonly expressed by the equation known as the Rational formula :

(4.1)

where <i class="emphasis">Q</i>  = peak runoff rate (cfs)<i class="emphasis">          C</i>  = dimensionless runoff coefficient used to adjust for abstractions from rainfall<i class="emphasis">          I</i>   = rainfall intensity for a duration that equals time of concentration of the basin(in/hr)<i class="emphasis">          A</i>  = basin area (ac)

In English units, it turns out that the...