On the variation of the correction factor of surface velocity with the measurement vertical for shallow flows over rough beds

Considering that water flow energy affects the detachment of soil particles, the transport and deposit of the detached particles, the flow velocity is a key variable governing the soil erosion processes at the hillslope scale. The simple dye-tracer technique for measuring mean flow velocity can be applied in non-controlled field applications for which some measurement difficulties (e.g. due to sediment transport, and shallow flows) can occur. The correction factor is usually obtained as the ratio between the mean velocity, deriving from measurements of flow discharge and water depth, and surface velocity. Alternatively, the possibility of using the velocity profile in a given vertical to determine a suitable correction factor has not yet been explored. In this article, the flow velocity measurements were carried out in five verticals having a different distance from the wall of a flume whose bed was covered by hemispheres with different concentrations (9%–64%) and organized in two arrangements (square, staggered). Fifteen runs, characterized by different Reynolds and Froude numbers, were performed and the correction factor αvv was calculated for each vertical. For the axial vertical αvv was independent of the arrangement, decreased with the hemisphere concentration, and increased with both the Froude and Reynolds numbers. Furthermore, αvv decreased from the bank to the flume axis as a result of the varying shape of the velocity profile. The analysis showed that the frequency distributions of the ratio between αvv and its mean value αm were overlaid and αm was used to represent the correction factor, accordingly. A relation of αm with the distance from the flume wall was detected. For the measured velocity profiles having a power shape, the analysis also demonstrated that the αvv values, obtained by fitting the power law to the measurements, were close to both those calculated as the ratio between the mean velocity along the vertical and the surface velocity and their averaged values across the hydraulic section. These three methods give comparable average values of the correction factor, in the range of 0.72–0.75, which are close to the commonly applied value of 0.8. Finally, this investigation demonstrated that a single survey of a power velocity profile allows for obtaining the correction factor accounting for different verticals across the entire hydraulic section.