Evaluating the Effects of the Rill Longitudinal Profile on Flow Resistance Law

Abstract

In this paper, for the first time, the effect of the longitudinal profile shape of the rill (uniform, concave, and convex) on flow resistance law was studied. The first part of the paper is based on a theoretical equation to estimate the Darcy–Weisbach friction factor f, deduced from the power velocity distribution and rill measurements performed on a plot. At first, the equation to estimate the Γ parameter of the velocity profile was calibrated using all available measurements. Then an analysis of the hydraulic characteristics at reach scale, for comparable values of discharge, was carried out, comparing the different profile shapes. To assess the influence of the rill profile shape on flow resistance law, this calibration was also carried out using the data categorized by profile. In the second part of the paper, an analysis of the scour depth and eroded rill volume was developed for four rills of each configuration. The results showed that an accurate estimate of f can be obtained by calibrating the flow resistance equation for each profile shape. The component of the Darcy–Weisbach friction factor that is due to the profile shape varied from 0.68 to 14.6% of the overall friction factor for the concave profile, and from 3.4 to 26.9% for the convex profile. The analysis also showed that, for the convex profile, the scour was concentrated downstream of the slope change, while for the uniform and concave profiles, it was uniformly distributed. Furthermore, the scour depth measured in correspondence of the rill thalweg had a generally increasing trend, with discharge for all the investigated profile shapes. Total eroded rill volume of the concave profile was lower than those detected for the uniform and convex profiles and was characterized by a reduction of 57.9%, as compared to the uniform profile.