# Fluid mechanics

Fluid mechanics is one of the oldest and broadest fields of engineering. It deals with the properties and behavior of fluids, i.e., liquids and gases at rest (fluid statics) or in motion (fluid dynamics). Because of their ability to flow, liquids and gases have many properties in common not shared by solids. The beginnings of modern fluid mechanics date back to the mid-17th century, when mathematicians began to enunciate its laws.

Engineers use fluid mechanics in the design of bridges, dams, and ships. Physicists use it in studying the structure of the atomic nucleus, and astronomer uses it to explain the spiral structure of some galaxies.

In fluid mechanics, consistently with the classical approach of continuum mechanics, the fluid is considered assimilable to a continuum, which can be associated with characteristic properties varying with continuity from point to point. In fact the matter (solids, liquids, aeriforms) is composed of distinct particles located at large distances from each other with respect to their size: at the scale of molecules the mathematical continuum scheme is not at all meaningful, since the value of each quantity is more or less defined and varies abruptly from point to point and from instant to instant, depending on the presence or absence of a molecule in the point considered.

It is also true that, for most practical problems, the minimum scale of observation is much greater than the molecular one, so that each (small) volume of interest contains a large number of molecules; associating to this volume appropriate average characteristics of the matter contained, the properties thus defined vary with continuity in space and with the variation of the size of the volume itself.

It is therefore possible to consider the matter as a continuous system and describe its behavior with the tools of the mathematics of the continuum. The concept of fluid particle refers to a volume of fluid, however small, containing a large number of molecules, to be considered as a point unit of a continuous system, which are univocally associated with the physical quantities density, velocity, temperature, pressure and so on.

The use of the continuum hypothesis in the study of fluid mechanics has always proved more than acceptable; in fact, most of the problems analyzed have sufficiently small Knudsen numbers.

Fluid statics or hydrostatics includes the study of pressure, density, Pascal’s law, and Archimedes’ principle.

Fluid dynamics includes the study of streamlines (see streamlining), Bernoulli’s law, and the propagation of waves.