Shape Effects and Definition of Hydraulic Radius in Manning 's Equation in Open Channel Flow

Abstract

In the Manning equation the hydraulic radius can be defined as the cross-section dimension of the shape. In pipe flow the bed shear stress is assumed to be uniformly distributed along the wetted perimeter which cannot be true in open channel flow. Hence, three approximation of the true boundary shear-stress distribution are examined and more practical conveyance depth or resistance radius formulae are developed in three case to substitute for the hydraulic radius. In this study, special emphasis is placed on a particular channel cross-section including rectangular and triangular sections. Based on the logarithmic velocity profile a formula for a normal depth of this particular channel section is also developed it is shown that the shear stress distribution may be calculated with sufficient accuracy by simpler approximation methods. Finally, a presentation is made of a numerical e ample comparing the proposed formulae to the classic hydraulic radius concept.