On forces in fluids

Abstract

The role of forces in classical mechanics in general is shown in the first part of the paper. The paradigm of classical mechanics is formulated using the three Newton's laws of motion. Then, the paper is focused on forces in fluid dynamics in context of the basic mathematical models and their description. The Navier-Stokes equations are identified as the mathematical form of forces equilibrium acting on a fluid elementary volume. The Reynolds transport theorem is the forces equilibrium equation written for any finite control volume. The forces’ types are defined both from the point of view of physical mechanisms behind their origin and their topological features. The volumetric forces are inertial and external, while surface forces are represented by the friction forces and pressure forces, respectively. The volumetric interpretation of the surface forces and their relation are shown. A special attention is devoted to the inertial force, which is defined by the second Newton's law. The two canonical flows, laminar flow in a pipe and constant pressure laminar boundary layer on a flat plate, are presented as the demonstration of the forces physical meaning. Link to the Reynolds number is shown in the end of the paper.