Flow resistance of overland flow on a smooth bed under simulated rainfall

In this paper a recently theoretically deduced flow resistance equation, based on a power-velocity profile, was tested using laboratory measurements by Yoon and Wenzel for an overland flow on a smooth bed under rainfall. These measurements of the Darcy-Weisbach friction factor, corresponding to a wide range of the flow Reynolds number (191–5700), were carried out for an overland flow under a simulated rainfall characterized by different intensity values ranging from 13 to 381 mm h−1. At first, the available measured values of flow velocity, water depth, cross sectional area, wetted perimeter and bed slope were used to calibrate the relationship between the velocity profile parameter Γ, the slope steepness s and the flow Froude number F. Then the theoretical approach and the measurements in the investigated conditions allowed to state that the coefficients of the relationship (Eq. (8)) between Γ, s and F vary with rainfall intensity. Furthermore, the theoretical flow resistance equation (Eq. (9)) allowed an accurate estimate of the Darcy-Weisbach friction factor, which is characterized by errors less than or equal to ±10% for 91.3% of cases and less than or equal to ±5% for 84.8% of cases. Finally, the developed analysis stated that the effect of rainfall intensity on flow resistance is always negligible for turbulent conditions while for Re < 2000 the effect of rainfall impact becomes negligible for rainfall intensities greater than a critical value occurring in the range 31.75–95.25 mm h−1.