Rational Method

The rational formula is one of the oldest and most commonly used methods to predict peak flows.  It was originally used to estimate peak flows only, but a triangular shaped hydrograph has also been used to define the hydrograph shape and runoff volume.  Precipitation is represented through an intensity (inches/hr) and it is assumed that the intensity is the same throughout the entire watershed.  All losses, including initial abstractions, are represented with a single runoff loss coefficient defined between 0.0 (no runoff) and 1.0 (no losses).  The only other input variable is the drainage area, in acres.

The rational hydrograph is defined as a triangle, with the peak flow occurring at the time of concentration and the total duration of the storm being two times the time of concentration.

This traditional rational hydrograph assumes that duration of the storm is equal to the time of concentration.  If the duration is longer, the hydrograph shape will change from a triangle to a trapezoid with the corresponding peak flow.

The rational method is simple and easy to use, but the difficulty in determining a runoff coefficient and the limitation of defining rainfall as a constant intensity make it applicable mostly for small, urban watersheds.