Flow resistance continuity from overland to rill flows: evidence from experimental data and theoretical implications

• A continuity in flow resistance from overland to rill flows can be stated. • Transition from overland to rill can be represented in the flow resistance law by R/h. • Proposed flow resistance law is satisfactorily applicable for overland and rill flows. Knowledge of the friction factor of overland and channelized rill flows moving over rough hillslopes is required for modeling soil erosion and transport processes. The available literature flume investigations are characterized by different values of the ratio between the hydraulic radius R and the water depth h , and distinguish the two hydraulic cases corresponding to overland ( R quasi equal to h ) and rill flows ( R/h < 1). In this paper, literature flume measurements performed in smooth and rough channels, which are characterized by a fixed bed and a grain resistance condition, were firstly used to highlight the experimental evidence that a continuity in flow resistance from overland (hydraulic radius R quasi equal to water depth h ) to rill flows ( R/h < 1) can be stated. This analysis pointed out that the measured highest f values correspond to very wide rectangular cross-sections (VWR) and narrow rectangular cross-sections (NR), while for the intermediate geometric conditions, the lowest friction factor values were measured. This detected transition from VWR to NR cross-sections implies a transition in flow resistance that can be represented in the flow resistance equation by R/h . In particular, the proposed flow resistance law was theoretically deduced considering rectangular cross-sections characterized by different R/h values and calibrated by the available datasets. The agreement between the measured f values and those calculated by the theoretical flow resistance equation was characterized by errors, which were normally distributed, less than or equal to ± 10% for 96.8% of the cases and less than or equal to ± 5% for 82.0% of the cases. The proposed flow resistance equation is applicable for channels with a rectangular cross-section varying from VWR (overland flows) to NR (rill flows).