Fundamentals

Abstract

Fluid dynamics, which is considered in this book to be a branch of physics, consists of the description and study of gas and liquid dynamics in a macroscopic way, and the fluid is considered to be a continuous medium. But any matter is made of microscopic particles and therefore a continuous description must only be an approximation. Even an infinitessimally small element of a continuous fluid, what is commonly referred to as a fluid particle and is considered to be a point mass, contains, no doubt, an extremely large number of true microscopic particles (see below). These really microscopic particles (atoms, molecules, and so forth), comprising fluids, obey statistical kinetic equations, which are the simplest for dilute gases. In principle, fluid dynamics can be derived using those equations. Indeed, this approach is sometimes used, e.g., in reference [3] in the Bibliographical Notes of this chapter, to lay the foundations of fluid dynamics. The procedure is, however, lengthy and far from being trivial. Instead of taking this approach, we choose to describe, in this book, fluids as continua, ab initio. We should remark, here at the outset, that a continuum description is formally a mathematical one. As said above, it is an approximation and has to be treated with care in particular, e.g., at fluid interfaces or shocks (sharp for continua) or in boundary conditions (i.e., no-slip), which may be ideal for mathematics, but not so for physics.