Recent research on rill flows recognised that an 18% slope can be used to distinguish between ‘gentle’ and ‘steep’ slope cases for the detected differences in hydraulic (flow depth and velocity) and sediment transport variables (flow transport capacity, actual sediment load). The effects of slope on flow velocity, friction factor and transport capacity and their interactions affect process-based erosion modelling. The main aim of this paper is to investigate, for the first time, how slope affects the overland flow resistance on sandy soils, which are characterised by loose particles readily available to be transported and deposited. Using literature measurements carried out in sandy soils for both gentle and steep slopes, a theoretical overland flow resistance equation, based on the integration of the power velocity distribution, is tested. The relationship between the velocity profile parameter Γ, the channel slope, the Reynolds and Froude number is calibrated using measurements characterized by a wide range of hydraulic conditions and distinguishing between gentle (5.2%–13.2%) and steep (17.4%–42.3%) slope conditions. The analysis demonstrated that: (1) the parameter Γ can be accurately estimated by Equation (15) in which the exponents are independent of slope condition; (2) the coefficient a of Equation (15) is equal to 0.8750 and 0.8984 for the gentle and steep slope condition, respectively; (3) the estimations of the Darcy–Weisbach friction factor f (Equation 19) are accurate and characterised by errors less than or equal to ±5% for 97.2% of cases; and (4) in the range of steep slopes, the flow resistance law calibrated for the gentle slope condition (Equation (19) with a = 0.8750) systematically overestimates the f value. In conclusion, this study allowed the recognition, for an unlimited soil detachment condition and an overland flow, of how the energy dissipation processes and the estimate of the friction factor are affected by slope.

中文翻译：

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沙土上地表流阻力的坡度阈值

最近对小溪流的研究认识到，18% 的坡度可用于区分“缓坡”和“陡坡”情况，因为检测到的水力（水流深度和速度）和泥沙输送变量（流量输送能力、实际泥沙负荷）的差异）。坡度对流速、摩擦系数和输送能力的影响及其相互作用会影响基于过程的侵蚀建模。本文的主要目的是首次研究坡度如何影响沙质土壤的地表流阻力，沙质土壤的特点是易于运输和沉积的松散颗粒。使用在沙质土壤中对缓坡和陡坡进行的文献测量，测试了基于功率速度分布积分的理论地表流阻力方程。速度剖面参数 Γ、河道坡度、雷诺数和弗劳德数之间的关系使用以各种水力条件为特征的测量值进行校准，并区分平缓 (5.2%–13.2%) 和陡峭 (17.4%–42.3%)坡度条件。分析表明： (1) 式(15)可以准确估计参数Γ，其中指数与坡度条件无关；(2)系数 (1) 参数Γ可以通过式(15)准确估计，其中指数与斜率条件无关；(2)系数 (1) 参数Γ可以通过式(15)准确估计，其中指数与斜率条件无关；(2)系数对于缓坡和陡坡条件，式（15）的a分别等于 0.8750 和 0.8984；(3) Darcy-Weisbach 摩擦系数f （方程 19）的估计是准确的，并且在 97.2% 的情况下误差小于或等于 ±5%；(4) 在陡坡范围内，针对缓坡条件校准的流阻定律（方程（19），a  = 0.8750）系统地高估了f值。总之，这项研究允许认识到，对于无限的土壤剥离条件和地表溢流，能量耗散过程和摩擦系数的估计如何受坡度影响。