A Nonlinear System of Differential Equations in Supercritical Flow Spread Problem and Its Solution Technique

Abstract

A nonlinear system of differential equations in the problem of free flowing of supercritical flow is considered and a method of its solution is proposed. The analytical method is based on the introduction of the velocity hodograph plane and the obtaining of analytical solutions for the system of partial differential equations. It is pointed out that apart from being purely analytical, the potential flow model has a great practical demand due to its use as a base for the further research of the flow resistance forces. The proposed model can be developed by taking into account flow resistance and gradient, the bottom of the diverting channel flow. The theoretical results are complemented by numerical experiments and compared with experimental data.

Keywords

• mathematical model
• hydraulic structures
• hydrodynamics analysis
• channel flow
• open-channel hydraulics
• analytical solution