Maximum Shear-Stress Method for Stable Channel Design

Abstract

Stable channel design is important for conveying water among stakeholders in a safe and cost-effective manner. The current design methods include the regime theory, the permissible velocity method, and the tractive force method. Nevertheless, they are not yet conclusive, despite decades of study, because of difficulties in finding the maximum bed and sidewall shear stresses from the Navier-Stokes equation. To advance stable channel design, we assume a constant eddy viscosity and apply Leighly’s conformal mapping idea to the Navier-Stokes equations in rectangular open channel flow, which results in analytic solutions for the bed and sidewall shear stress distributions, including the maximum bed and sidewall shear stresses. We then modify the maximum bed and sidewall shear stress equations with data and apply the resulting equations for stable channel design. We demonstrate that in terms of the regime theory or the tractive force method, the channel geometry parameters (slope, width, and depth) can be theoretically solved by combining the two maximum shear stress equations and Manning’s equation for uniform flow.