Abstract
PurposeIn 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.MethodsThe 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).ResultsThis 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.ConclusionsThe 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.
Highlights
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 DarcyWeisbach friction factor due to sediment transport was deduced using the corresponding measurements carried out on mobile bed rills and the values estimated by flow resistance equation 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)
The component ft of the Darcy-Weisbach friction factor due to the sediment transport was calculated by the difference between the fmb value measured on a mobile bed rill, which takes into account both grain resistance and sediment transport (Table 1), and the f value, calculated for the fixed bed condition by Eqs. (5) and (10), which considers only grain resistance
The f value was calculated for the same hydraulic (Re, F) and slope (s) conditions as those corresponding to fmb
Summary
Mutchler and Young (1975) suggested that flows conveyed into rills can transport more than 80% of the soil loss originated from interrill areas and delivered to rills (Bagarello and Ferro 2004; Govers et al 2007; Bruno et al 2008; Bagarello and Ferro 2010; Di Stefano et al 2013, 2015; Bagarello et al 2015; Peng et al 2015; Zhang et al 2016). Flow resistance is affected by the interaction between flow and a mobile rill channel whose geometry varies with the flow shaping action and the joined sediment load. The result of the flow shaping action can be a flat bed, whose roughness is represented by a characteristic bed particle diameter, or bed forms constituted of deposited sediments (Di Stefano et al 2017a, b). Previous studies of bed-load transport resistance in rough open-channel flows Previous studies of bed-load transport resistance in rough open-channel flows (Chow 1959; Vanoni and Nomicos 1960; Baiamonte and Ferro 1997; Song et al 1998; Gao and Abrahams 2004; Campbell et al 2005; Recking et al 2008b; Wang et al. Vol.:(0123456789)
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