Estimating the correction factor of surface velocity in rill flows

• Correction factor α v of surface rill flow velocity is studied by laboratory runs. • Three dimensionless groups affecting α v were deduced by dimensional analysis • Reynolds number, slope, and roughness height affect α v . • An α v predictive equation is obtained by dimensional analysis and rill measurements. • Literature data are used to test the predictive equation of α v . The dye-tracer technique is widely applied for measuring the surface velocity of shallow flows, which is jointly used with a correction factor α v to obtain the mean flow velocity. The primary purpose of this paper is to evaluate the effect of the soil roughness height on the correction factor in rill flows. For this aim, experimental runs were performed with clear water flowing in two flumes covered by glued soil particles resulting in different roughness heights ( k s = 0.135 mm and 1.317 mm). Ten slopes s , ranging from 0.1 % to 15 %, and five flow discharges Q varying from 0.20 to 0.87 L s −1 were utilized. Previous measurements, collected in the same flumes for k s = 0 and 0.119 mm, were also used. Using dimensional analysis, Reynolds number, flume slope, and a dimensionless group embedding the roughness height were identified as influential factors of α v . The proposed predictive equation of α v established that the correction factor (i) decreases as the Reynolds number increases, (ii) generally increases with increasing roughness height, and (iii) depends on slope following a non-monotonic trend. The proposed equation can reliably estimate the correction factor, with a mean absolute error of 5.4 % for smooth bed rills and 5.8 % for rough bed rills. Further experiments need to investigate the effect of rill width on the correction factor and test the proposed equation with different roughness heights.