Revisiting the concept of hydraulic radius

Abstract

Hydraulic radius has long been customarily used as a characteristic length to assess the cross-sectional geometry and efficiency of channels and conduits. This review paper revisits the concept of the hydraulic radius in light of its extensive applications in recent studies, with the aim of piecing together a state-of-the-art understanding of its physical underpinnings. The original definition of the hydraulic radius is presented as the ratio of cross-sectional flow area to wetted parameter, which inherently integrates the properties of the flow domain and the contacting surface. The use of hydraulic radius as a versatile characteristic length in classical Manning’s formula and the Reynolds number underscores its significance in relation to flow resistance. Through a thorough review of its diverse applications, this paper provides a unified understanding of the physical meaning of hydraulic radius, highlighting its interpretation as a measure of large-scale eddies within a given flow domain. This new insight can be justified beyond uniform flows, as evidenced by its use in addressing sediment transport issues in complex vegetated flows, based on turbulence phenomenological theory. Furthermore, the original formulation of the hydraulic radius provides insights into how large-scale flow structure can be quantified with geometrical boundary characteristics, leading to a promising framework for scour prediction based on large-scale vortex size. This paper highlights the versatility and utility of hydraulic radius across various fields of fluid mechanics and sediment transport research, and proposes its potential for future studies as a proxy for large-scale flow structures.