Curved-streamline transitional flow from mild to steep slopes

Abstract

Flows from mild to steep slopes are relevant in hydraulic engineering relating to chute spillways and slope changes in irrigation networks. These flows are associated with transitional flow from sub- to super-critical conditions, smooth curvilinear-streamline feature involving a continuous free surface profile, and a rapid variation of the bottom pressure profile. Herein, the transition from a horizontal to a steeply sloping rectangular channel reach is investigated to analyze the application range of the Boussinesq-type equation. Slope breaks with a rounded transition from the brink section to the tailwater channel are considered and compared with the potential flow solution based on the Laplace equation. The Boussinesq-type equation is further compared with test data for a steep downstream slope to investigate the strong curvilinear gravity effect. A singular point analysis is also compared with the Boussinesq approach. The generalized momentum equation for curvilinear flows is developed and compared with the results pertaining to the energy concept.