Viscous Channel Flows

Abstract

The computation of non-hydrostatic viscous flows is considered here. Steady, partially developed flows in a vertical plane are treated by using Prandtl’s boundary layer theory. Scale effects on flows over round-crested weirs, originating from surface tension and viscosity, are considered in a general weir-flow equation. An analytical solution for the boundary layer development over round-crested weirs is produced and compared with detailed one- and two-dimensional numerical solutions. Surface tension effects, which depend on the modeling of the free surface curvature, are accounted for in high-head flows over small-scale weirs. The ensuing discharge equation is found to produce reliable results, and the theory is used to set limits to avoid scale effects in hydraulic experiments. Developing non-hydrostatic flows on a steep slope are characterized by analytical solutions of the energy equation in the irrotational flow outside the boundary layer and the momentum equation for the turbulent flow within it. For turbulent flows in undular hydraulic jumps, a depth-averaged integration of the RANS equations is presented, and various degrees of approximations to this system of equations are discussed, with Serre’s (1953) theory as a particular case. Serre’s (1953) theory for turbulent flows is then expanded for various applications, including undular weir flows, gate flows, submerged jets, spatially varied flows, sediment bed erosion during dike breaches, solitary sand waves, and compound channel flows.