Rational Coefficients for Steeply Sloped Watersheds

When computing peak discharges for the design of drainage systems using the rational method, it is important to have an accurate value for the rational coefficient $\left(C\right)$ . For steeply sloped watersheds the origin of values of the rational coefficient are unknown and lack even modeling verification. A model that shows the relationship between the rational coefficient and watershed slope was developed for steeply sloped watersheds. Using Horton’s infiltration equation, Manning’s equation, the velocity method for computing times of concentration, and generalized intensity-duration-frequency curves, a model was developed to test the effect of variation of several watershed characteristics on the relationship between slope and the rational coefficient. Analyses with the model showed that both Manning’s coefficient and land use had the greatest effect on the relationship between $C$ and slope. A mathematical function was then developed from data generated from the Horton–Manning model. This model allows $C$ to be estimated for a given slope and a value of Manning’s coefficient for the land cover. A rational coefficient at a 6% slope is also required input. The model was tested using several watersheds with moderate to steep slopes. This relationship should be used to better estimate values of $C$ on steep slopes, and thereby, lead to more accurately hydrologic designs.