Vorticity equation for the streamline and the velocity profile

Abstract

Water flow over short hydraulic transitions is usually modelled by the irrotational flow theory, for which the energy head remains constant over the entire flow domain. Velocity and pressure distributions are then obtained based on the stream and potential functions of the flow net. However, experimental evidence may dictate non-uniform energy profiles resulting either from vorticity, viscous effects, or both. For rapidly-varied flows, Hunter Rouse (1906–1996) proposed in the early 1930s the inviscid Euler flow equations. Most of the current curvilinear flow models, however, resort to irrotational flow. In this work, a generalized curvilinear method for real fluid flow is proposed. Based on the streamline vorticity equation, a practical approach is presented for inviscid, rotational flow. The model is verified by data pertaining to the free overfall and further tested with data on viscous flow in undular jumps, thereby resulting in good agreement.

Keywords:

• Boundary layer
• free overfall
• transitional flow
• undular hydraulic jump
• vorticity

Acknowledgements

The first Author was supported by a contract of modality JAE-DOC of the program “Junta para la Ampliación de Estudios”, CSIC, National Research Council of Spain, co-financed by the FSE.