MATHEMATICAL METHODS IN THE PROBLEMS OF WATER ENGINEERING

Abstract

The sharp rise in world energy prices highlights the task of minimizing the cost of materials, electricity and other resources in hydraulic engineering, shipping and related industries. The study of such problems is of considerable theoretical and significant practical interest. Mathematical analysis and differential equations are powerful tools for solving a wide range of engineering problems with practical content. Building a mathematical model of the process allows the use of optimization methods. By selecting control parameters in a certain way, you can optimize the target function, which depends on these parameters. Formalization of a practical task allows to reject factors that do not have a significant impact on the process. This makes it possible to make a differential equation to study the physical process. Complementing the problem with initial conditions makes it possible to obtain a single solution. Note that in most cases the obtained differential equations are nonlinear and can be solved only by approximate methods. The paper considers a number of engineering problems with practical content. In particular, the task of minimizing the surface of the channel being washed; study of the speed of the vessel under certain conditions; the task of minimizing the cost of materials in hydraulic engineering and some other tasks. Appropriate mathematical models have been built to solve them. Exact solutions of these problems have been found by methods of mathematical analysis of the function of one and several variables, differential equations. The study of such problems leads to a deeper understanding of physical phenomena and processes and the ability to solve problems arising in engineering and related fields, including aerodynamics, gravity theory and other fields of science and technology.