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Use of resistance coefficients derived from single planes to estimate time of concentration of two-plane systems

By coupling the Darcy-Weisbach friction formula with the kinematic wave time of concentration formula, a kinematic-Darcy-Weisbach time of concentration formula for 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 rainfall intensities, to planes subject to different rainfall intensities, and to planes with a combination of all these variables. By applying the observed times of concentration to the formula for single planes, the Darcy-Weisbach resistance coefficient for a concrete surface and for an artificial grass surface are derived. Based on the derived resistance coefficients, they indicate that the flow regime on concrete was transitional and the flow regime on artificial grass was laminar. Further, by applying the derived resistance coefficients to two-plane systems (i.e. planes with combinations of concrete surface and artificial grass surface in series), the comparisons of the estimated times of concentration from the formula with the observed values show very good agreement. In one particular two-plane system, even with the occurrence of kinematic shocks, the agreement is still good. This study shows that the resistance coefficients that are derived from uniform planes can be applied to two-plane systems.