RESEARCH ARTICLE Comparing flow resistance law for fixed and mobile bed rills Costanza Di Stefano 1 | Alessio Nicosia 1 | Vincenzo Palmeri 2 | Vincenzo Pampalone 1 | Vito Ferro 2 1 Department of Agricultural, Food and Forestry Sciences, University of Palermo, Palermo, Italy 2 Department of Earth and Marine Sciences, University of Palermo, Palermo, Italy Correspondence Vito Ferro, Department of Earth and Marine Sciences, University of Palermo, Via Archirafi 20, Palermo 90123, Italy. Email: vito.ferro@unipa.it Abstract Rills caused by run-off concentration on erodible hillslopes have very irregular pro- files and cross-section shapes. Rill erosion directly depends on the hydraulics of flow in the rills, which may differ greatly from hydraulics of flow in larger and regular chan- nels. In this paper, a recently theoretically deduced rill flow resistance equation, based on a power–velocity profile, was tested experimentally on plots of varying slopes (ranging from 9% to 26%) in which mobile and fixed bed rills were incised. Ini- tially, measurements of flow velocity, water depth, cross-section area, wetted perim- eter, and bed slope, carried out in 320 reaches of mobile bed rills and in 165 reaches of fixed rills, were used for calibrating the theoretical flow resistance equation. Then the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number was separately calibrated for the mobile bed rills and for the fixed ones. The measurements carried out in both conditions (fixed and mobile bed rills) confirmed that the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach. For mobile bed rills, the data were support- ive of the slope independence hypothesis of velocity, due to the feedback mecha- nism, stated by Govers. The feedback mechanism was able to produce quasicritical flow conditions. For fixed bed rills, obtained by fixing the rill channel, by a glue, at the end of the experimental run with a mobile bed rill, the slope independence of the flow velocity measurements was also detected. Therefore, an experimental run car- ried out by a rill bed fixed after modelling flow action is useful to detect the feedback mechanism. Finally, the analysis showed that, for the investigated conditions, the effect of sediment transport on the flow resistance law can be considered negligible respect to the grain roughness effect. KEYWORDS fixed bed, flow resistance, mobile bed, plot measurements, rill flows, rill hydraulics, soil erosion 1 | INTRODUCTION Interrill and rill erosion are two processes controlling soil erosion in upland areas and are characterized by different mechanisms of soil particle detachment, transport, and deposition. The detachment in interrill areas is controlled by soil intrinsic characteristics (Le Bissonnais et al., 2005; Wirtz, Seeger, & Ries, 2012) and is caused by raindrop impact (Beuselinck, Govers, Hairsine, Sander, & Breynaert, 2002). Rill erosion is controlled by the detachment of soil particles and sediment transport by channelized flows, whereas the impact of raindrops on soil particle detachment can be neglected (Govers, Gimenez, & Van Oost, 2007). Hydrological Processes. 2019;1–19. wileyonlinelibrary.com/journal/hyp © 2019 John Wiley & Sons, Ltd. 1 Received: 15 January 2019 Accepted: 1 August 2019 DOI: 10.1002/hyp.13561