Author(s): N. S. Cheng; M. Wei; Y. Lu
Linked Author(s): Wei Miao, Yao Lu
Keywords: Hydraulic radius; Scour depth; Densimetric Froude number; Turbulent eddies; Open channel flow
Abstract: The hydraulic radius has been widely used to evaluate resistance and average velocity for pipe and open channel flows in hydraulic engineering. It is defined as the ratio of the area to wetted perimeter for a cross section in an open or closed channel. It has a dimension of length, being equivalent to the flow depth for wide channels and half the width for narrow channels. In spite of the fact that the hydraulic radius is a geometric parameter for a cross section, it also serves as a measure of the size of dominant eddies in turbulent flow. With this understanding, Gioia & Bombardelli (2001) showed that the hydraulic radius is helpful in theoretically explaining the Manning equation in terms of turbulent energy cascade. By applying the concept of hydraulic radius to a three-dimensional domain, the resistance induced by vegetation in open channel flows can be conveniently estimated in terms of drag coefficient and Reynolds number, of which both are defined based on vegetation-related hydraulic radius (Cheng & Nguyen, 2011). Furthermore, the concept of hydraulic radius can be used to compare equilibrium scour depths at bridge piers, abutments and culverts. In these scour cases, the hydraulic radius measures the eddy size that dominates the incoming turbulent flow, and potentially the scour hole (Cheng & Wei, 2019; Cheng et al., 2011). By analyzing experimental data collected under the clear-water scour conditions, we show that the scour depth, when normalized with the redefined hydraulic radius, depends solely on the densimetric Froude number. The functional relation holds for all scour cases involving piers, abutments, culvert and wall jets.
Year: 2023