Asymptotic model for velocity dip position in open channels

Abstract

An empirical model is proposed to predict the velocity dip position at the central section of open channels. The model is fitted based on asymptotic matching technique and validated by using a wide range of aspect ratios (channel width/flow depth) from 0.155 to 15. The matching approach, which relies on dividing the trend into smaller segments that can be combined into an overall relation, employs regression technique and thus warrants the best-fit accuracy results. The obtained model satisfies the upper and lower bounds of dip positions equal to 0.5 and 1, respectively. A comparison with other formulas widely reported in the literature is provided. The model is also applied to predict Reynolds shear stress and velocity distribution in open channels. This model will help extending our ability for analyzing velocity field in open channels under different flow and boundary conditions.