Hydraulics of developing chute flow

A turbulent boundary layer develops if water flows down a chute. This region is referred to as the developing zone, where a turbulent boundary layer coexists with a irrotational flow above it. No computational approach is currently available for the developing zone based on the simultaneous solution of the momentum equation inside the boundary layer and the energy equation for the irrotational flow zone. An analytical solution of the energy, and the von Karman momentum equations using a power law velocity profile inside the boundary layer yield explicit equations for the free surface and the turbulent boundary layer profiles. The model developed is applicable to an uncontrolled spillway crest followed by a steep chute of constant slope. The analytical results obtained herein proved to be a close fit to both experimental data and detailed solutions of the Reynolds equations for chute flow. Itwas demonstrated herein that the Colebrook–White equation generally underestimates the friction factor in developing chute flow.