| Issue |
E3S Web Conf.
Volume 264, 2021
International Scientific Conference “Construction Mechanics, Hydraulics and Water Resources Engineering” (CONMECHYDRO - 2021)
|
|
|---|---|---|
| Article Number | 03025 | |
| Number of page(s) | 8 | |
| Section | Hydraulics of Structures, Hydraulic Engineering and Land Reclamation Construction | |
| DOI | https://doi.org/10.1051/e3sconf/202126403025 | |
| Published online | 02 June 2021 | |
Transfer equation for the strain rate tensor and description of an incompressible dispersed mixture (incompressible fluid) by a system of equations of dynamic type
1 Bukhara Branch Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Bukhara, Uzbekistan
2 Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Tashkent, Uzbekistan
* Corresponding author: askar021954@mail.ru
It is known that the application of the vector operation rot to the equations of hydrodynamics leads to the Helmholtz-Friedman equation for a vortex. A dispersed mixture, tensor transformations are used, in a certain sense generalizing the vector operation rot, which gives more than one, a couple of equations. One of them describes the transfer of vorticity is the well-known Helmholtz-Friedman equation. The second equation was obtained for the first time, and it describes the transfer of the strain rate tensor. Any tensor decomposes into symmetric and antisymmetric parts. By definition, the symmetric part of the tensor U is the strain rate tensor. The antisymmetric part of U is a tensor whose components are related in a known manner to the pseudovector angular velocity.
© The Authors, published by EDP Sciences, 2021
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