Time of Concentration and Peak Discharge Formulas for Planes in Series

Abstract

Based on the kinematic-wave equations, a time of concentration formula for overland flow over a series of planes is derived. The formula is applicable to a cascade of planes, to planes of different roughnesses, to planes of different flow regimes, to planes of different soil types and infiltration rates resulting in different net intensities, to planes subject to different rainfall intensities, and to planes with a combination of all these variables. For practical applications, the formula is developed in terms of the Manning resistance coefficient that is applicable to turbulent or near turbulent flow only. For the series of planes subject to uniform rainfall excess, under the full-area contribution, the corresponding peak discharge formula in terms of the Manning resistance coefficient is derived. This formula can also be used to estimate the peak discharge under the partial-area contribution. The derived formulas are all consistent with the published formulas for a single plane.