Study on the Characteristic Point Location of Depth Average Velocity in Smooth Open Channels: Applied to Channels with Flat or Concave Boundaries

Abstract

Based on the flow partition theory, we derive a mathematical expression by using the log-law for the characteristic point location (CPL) of depth average velocity in channels with flat or concave boundaries. It can manifest the position of the characteristic points in the vertical direction relative to the channel side wall or bed. Taking rectangular and semi-circular channels as research objects, we put forward a method to calculate the discharge of channels with CPL. Additionally, we carried out some experiments on rectangular and semi-circular channel sections. CPL’s analytic expression is validated against experimental results through comparison of velocity and discharge. The proposed formulation of characteristic point location could be extensively employed in flow measurements of flat and concave boundary channels, which has practical application value in simplifying the flow measurement steps of open channels.

Physical and Mathematical Fluid Mechanics

“…[17] consider an extension of future experimental studies of flow in open channels with regard to wall roughness to be very useful, especially with respect to the transition from smooth channels to vegetation-covered channels. Based on a detailed analysis and discourse, the two different potential approaches considered by [18] can be explained in the light of their different origins. Despite the very positive stage of development of both methods, some open questions remain, for instance, whether a general and all-encompassing potential approach exists, reducing to both the Clebsch and the tensor potential approach as special cases.…”

“…In their review article, [18] retrace alternative formulations of the Navier-Stokes equation based on potential fields, ranging from the classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches which are diametrically opposed in their origin: (i) the Clebsch transformation originally applies to inviscid flow (Re → ∞), while (ii) the classical complex variable method utilising Airy's stress function applies to Stokes' flow (Re → 0).…”