Correction factor for rill flow velocity measured by the dye tracer method under varying rill morphologies and hydraulic characteristics

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.