Asupra deducerii ecuaţiilor Navier–Stokes pentru mişcarea laminară a fluidelor vâscoase incompresibile [Articol]

Abstract

Starting from the fundamental laws of classical dynamics and molecular physics, an alternative variant of derivation of the Navier–Stokes equations for the laminar motion of incompressible viscous fluids is presented, focused on the application of d’Alembert’s principle to the forces exerted on a volume of fluid limited by a closed surface and Newton’s law of linear deformation for unidirectional motion. To transform surface integrals into volume integrals, the gradient integral relation and Green’s first integral identity are used. The method stands out for its simplicity and clarity, which can give it a wide applicability among the existing methods in the specialized literature. The demonstration is preceded by a brief analysis of the main methods used today to deduce the fundamental equations of hydrodynamics. It is shown that including the phenomenon of internal friction in the equations of motion was a difficult problem, due to the fact that these equations describe the macroscopic velocity flow of the fluid, while energy dissipation occurs at the microscopic level.