Analysis of one assumption of the Navier-Stokes equations

TL;DR

This paper critically examines the assumptions about pressure forces in the Navier-Stokes equations, assessing their reasonableness and impact on fluid motion calculations, especially at low Reynolds numbers and in computational solutions.

Contribution

It analyzes the validity of pressure-related assumptions in Navier-Stokes equations and explores additional equations needed for accurate fluid motion modeling.

Findings

Identifies causes of discrepancies in low Reynolds number solutions

Highlights the need for supplementary equations beyond Navier-Stokes

Describes three methods for solving the extended problem

Abstract

This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact on the results of the analytical calculation. The connections between equations, causes of discrepancies in exact solutions of the Navier-Stokes equations at low Reynolds numbers and the emergence of unstable solutions using computer programs are also addressed. The necessity to complement the well-known equations of motion in mechanical stress requires other equations are substantive. It is shown that there are three methods of solving such a problem and the requirements for the unknown equations are described. Keywords: Navier-Stokes, approximate equation, closing equations, holonomic system.