Abstract Flow velocity is an important parameter for rill erosion process studies. The dye tracer method is the most widely used method for measuring rill flow velocity, but the influential factors and reasonable values of the correction factor α remain uncertain. Therefore, the experimental datasets from different studies were used to evaluate the α values from the previous studies could be applied to calculate the mean velocity of rill flow, and a detailed laboratory study was conducted to investigate the effects of rill morphology and hydraulic characteristics on the α of rill flow. The slope gradients varied from 5 to 25°, flow discharges from 2 to 8 L min−1, and Reynolds numbers from 172 to 1040. The surface velocity was measured by the dye tracer method, and the mean velocity was derived indirectly from the flow depth measurements. The results showed that a single α value was not suitable for rill flow velocity measurement. The α values of rill-free flow and rill flow ranged from 0.295 to 0.729 and from 0.330 to 0.990, respectively. The effect of the slope gradient on the α of rill-free flow was noticeably different from that of rill flow, and the α of this study increased with increasing Reynolds number. For the rill-free flow, α could be estimated with a logarithmic function of the slope gradient and Reynolds number (R2 = 0.930, NSE = 0.930). For rill flow, α increased linearly with increasing rill width, depth and cross-sectional area. The value of α could be estimated with an equation of the rill depth and Reynolds number (R2 = 0.811, NSE = 0.811). The results of this study provide a reference for rill flow velocity measurement using the dye tracer method.

中文翻译：

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不同细沟形态和水力特性下染料示踪法测得的细沟流速修正系数

摘要 流速是细沟侵蚀过程研究的重要参数。染料示踪法是测量细沟流速应用最广泛的方法，但影响因素和修正系数α的合理取值尚不确定。因此，使用不同研究的实验数据集来评估先前研究的 α 值可用于计算细沟流的平均速度，并进行了详细的实验室研究，以研究细沟形态和水力特性对细沟流的影响。细流的α。坡度梯度从 5 到 25°不等，流量从 2 到 8 L min-1，雷诺数从 172 到 1040。表面速度由染料示踪法测量，平均速度由流量间接得出深度测量。结果表明，单一的α值不适用于细沟流速的测量。无细沟流和细沟流的 α 值分别为 0.295 至 0.729 和 0.330 至 0.990。坡度梯度对无细沟流α的影响与细沟流的影响明显不同，本研究的α随着雷诺数的增加而增加。对于无细沟流，可以用斜率和雷诺数的对数函数（R2 = 0.930，NSE = 0.930）估计 α。对于细沟流，α随着细沟宽度、深度和横截面积的增加而线性增加。α 的值可以用细沟深度和雷诺数的方程来估计（R2 = 0.811，NSE = 0.811）。研究结果为染料示踪法测量细沟流速提供了参考。