A method for determining steady velocity of shallow water flow on hill-slope and the distance when water flow reaches stability

Abstract

Understanding the velocity distribution of shallow water flow along hill-slope is of great significance in soil erosion studies. This study proposes a method to estimate the steady flow velocity and the distance when water flow reaches stability, using hill-slope flow velocity distribution data along a simulated rill measured by the electrolyte tracer pulse method. Laboratory experiments were performed using a flume of 12 m long, 0.1 m wide and 0.3 m height under five slope gradients (5°, 10°, 15°, 20° and 25°) and four flow discharges (2, 4, 8 and 16 L min−1). The electrolyte tracer pulse method was employed to measure the flow velocities at locations of 1, 2, 3, 4, 6, 8, 10 and 12 m from the inlet of the flowing water. The flow velocities measured by the dye tracer method served as a control. The results showed that the flow velocities measured by the electrolyte tracer pulse method initially accelerated and then reached a steady value. An equation for estimating flow velocity on the basis of the measurement distance was established. The flow velocities calculated by the equation agreed well with those measured by the electrolyte tracer pulse method. The determination (R2) and the Nash-Sutcliffe model efficiency (NSE) were greater than 0.800, except for a few cases. In addition, the equation established in this study was shown to successfully predict flow velocities measured in other studies. The steady flow velocities and the distances when water flow reached stability under different slope gradients and flow discharges were determined by this equation. When the differences between the measured flow velocity and the steady flow velocity were very small, that is, 5% and 10%, the steady distances ranged from 2.239 m to 4.772 m and from 2.843 m to 6.059 m, respectively. By comparing the steady flow velocities with the flow velocities measured by the dye tracer method, the results indicated that the steady flow velocities were 0.702–0.735 times that of the flow velocities measured by the dye tracer method at various slope gradients and flow discharges. A linear function existed between the two, and the regressed parameter k (i.e., 0.718) could be used as the correction factor between the two. In general, the equation established in this study can facilitate the prediction of the steady flow velocity.