Zonal discharges and boundary shear in prismatic channels

Abstract

This paper illustrates a new approach to obtaining analytical stage–discharge formulae for both zonal and total discharges in straight prismatic channels of any shape, based on the concepts of a zero–shear force interface and an analytical solution for the lateral variation of depth-averaged velocity. The analytical solution for velocity is derived from the depth-integrated form of the Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence, and secondary flows/planform vorticity. The analytical formulae for stage discharge are given for both simple and compound trapezoidal channels, together with formulae that permit the boundary shear force to be determined for every linear element on the wetted perimeter. These stage–discharge and shear force formulae depend on the channel geometry and on three hydraulic parameters related to the bed friction factor f, lateral eddy viscosity λ and depth-averaged secondary flow Γ, as required in the original Shiono and Knight method. The analytical results show good agreement with experimental data. Ways of extending this approach to more complex shaped channels are outlined.