What is a Fluid?

A *plastic* material, such as clay,
also possess some degree of rigidity. However, the critical shear stress at which it yields is relatively
small, and once this stress is exceeded the material deforms continuously and
irreversibly, and does not recover its original shape when the stress is relieved.

By definition, a *fluid* material possesses no rigidity at all.
In other words, a small fluid element is unable to withstand any tendency of an applied shear stress to
change its shape. Incidentally, this does not
preclude the possibility that such an element may offer resistance
to shear stress. However, any resistance must be incapable of preventing the
change in shape from eventually occurring, which implies that the force of resistance
vanishes with the rate of deformation. An obvious corollary is that the shear stress must
be *zero* everywhere inside a fluid that is in mechanical equilibrium.

Fluids are conventionally classified as either *liquids* or *gases*. The most important difference
between these two types of fluid lies in their relative *compressibility*: *i.e.*, gases can be compressed much
more easily than liquids. Consequently, any motion that involves significant pressure variations is generally accompanied by much larger changes in mass density in the case of a gas than in the
case of a liquid.

Of course, a macroscopic fluid ultimately consists of a huge number of individual molecules. However, most practical
applications of fluid mechanics are concerned with behavior on length-scales
that are far larger than the typical intermolecular spacing. Under these circumstances, it
is reasonable to suppose that the bulk properties of a given fluid are the same as if
it were completely *continuous* in structure. A corollary of this assumption is that
when, in the following, we talk about infinitesimal volume elements, we really mean elements which are
sufficiently small that the bulk fluid properties (such as mass density, pressure, and velocity) are approximately constant across them, but are still sufficiently large that
they contain a very great number of molecules (which implies that we can safely neglect any statistical variations
in the bulk properties). The continuum hypothesis also requires infinitesimal volume elements to be much
larger than the molecular mean-free-path between collisions.

In addition to the continuum hypothesis, our study of fluid mechanics is premised on three major assumptions:

- Fluids are
*isotropic*media:*i.e.*, there is no preferred direction in a fluid. - Fluids are
*Newtonian*:*i.e.*, there is a linear relationship between the local shear stress and the local rate of strain, as first postulated by Newton. It is also assumed that there is a linear relationship between the local heat flux density and the local temperature gradient. - Fluids are
*classical*:*i.e.*, the macroscopic motion of ordinary fluids is well-described by Newtonian dynamics, and both quantum and relativistic effects can be safely ignored.