Using dimensional analysis to estimate flow resistance for sheet flow subjected to raindrop impact

Abstract

The impact of raindrops on sheet flow (SF) is a common phenomenon, which plays a vital role in many important nature and engineering fields. The flow resistance of SF is critical for describing flow characteristics and calculating the sediment transport capacity. However, information regarding the theoretical resistance equations of the total resistance of SF subjected to raindrop impact (fr) and the resistance induced by raindrop impact (Δf) is limited. In this study, combination of the π-theorem of dimensional analysis and multiple experimentally simulated rainfalls and inflows was conducted to obtain and verify the deduced predictive flow resistance equations. The results indicated that using dimensionless variables deduced by the π-theorem to calculate the flow resistance equation was appropriate. The main control of fr of SF under rainfall is the ratio of surface roughness to water depth deduced by π-theorem. A newly developed equation [Eq. (24)] can be used to predict fr, with a Nash-Sutcliffe efficiency index (NSE) of 0.91 and a normalized root mean square error (NRMSE) of 0.166. Δf is a very important component to overall SF resistance, accounting for 0.34%–47.79% of fr. The deduced dimensionless variable of the ratio of rainfall intensity to flow velocity is the main controlling factor of Δf. Finally, a new equation [Eq. (26)] was developed to predict Δf, with NSE = 0.673 and NRMSE = 0.445. This study is helpful for understanding the flow resistance subjected to raindrop impact and provides new and scientific equations for flow resistance coefficient prediction.