Flumes for indirect discharge measurements are widespread and are characterized by a particular shape of the cross section area with various degrees of convergence and subsequent divergence. The flume named Samani, Magallanez, Baiamonte, Ferro (SMBF) is a simple and inexpensive instrument and its channel contraction is obtained by applying two semicylinders to the walls of a rectangular cross section. At first, in this paper a new stage-discharge equation for the SMBF flume is theoretically deduced. Then, this equation is experimentally calibrated using the laboratory measurements from the literature for different values of the contraction ratio. Finally the field measurements carried out at Sparacia experimental area (Sicily, South Italy) by a SMBF flume inserted into a horizontal flume and characterized by a contraction ratio equal to 0.5, are used for testing both the new stage-discharge relationship and the one originally proposed in the literature.

In this paper, the outflow process of a weir with an irregular shape is studied using dimensional analysis and the incomplete self-similarity theory. The new unique stage–discharge relationship, which is deduced theoretically, represents a novel and comprehensive equation to describe the weir outflow process for a full range of flow and different geometric variables of weirs, including finite-crested weirs, broad-crested weirs with positive or negative crest slope, broad-crested weirs with an upstream, downstream, or both upstream and downstream crest ramps, and, triangular weirs with an upstream or downstream ramp. Finally the proposed stage–discharge relationship is calibrated using measurements available in literature.

Purpose: In this paper, a deduced flow resistance equation for open-channel flow was tested using measurements carried out in mobile bed rills with sediment-laden flows and fixed bed rills. The main aims were to (i) assess the effect of sediment transport on rill flow resistance, and (ii) test the slope-flow velocity relationship in fixed bed rills. Methods: The following analysis was developed: (i) a relationship between the Γ function of the velocity profile, the rill slope and the Froude number was calibrated using measurements carried out on fixed bed rills; (ii) the component of Darcy-Weisbach friction factor due to sediment transport was deduced using the corresponding measurements carried out on mobile bed rills (grain resistance and sediment transport) and the values estimated by flow resistance equation (grain resistance) for fixed bed rills in the same slope and hydraulic conditions; (iii) the Γ function relationship was calibrated using measurements carried out on mobile bed rills and the data of Jiang et al. (2018). Results: This analysis demonstrated that the effect of sediment transport on rill flow resistance law is appreciable only for 7.7% of the examined cases and that the theoretical approach allows for an accurate estimate of the Darcy-Weisbach friction factor. Furthermore, for both fixed and mobile beds, the mean flow velocity was independent of channel slope, as suggested by Govers (1992) for mobile bed rills. Conclusions: The investigation highlighted that the effect of sediment transport on rill flow resistance is almost negligible for most of the cases and that the experimental procedure for fixing rills caused the unexpected slope independence of flow velocity.