Concept of Continuum

Any material, solid, liquid or gas is composed of billions of individual molecules, in a very small region, separated by empty spaces in between them. The continuum assumption considers that matter is continuously distributed and fills the entire region of the space it occupies.

A continuum material can be continually sub divided into infinitesimal elements with properties being those of the bulk material. Properties such as density, pressure, temperature and velocity are taken to be well-defined at infinitely small points.

For a continuum fluid, at each point of the region of the fluid it is possible to construct one volume infinitesimally small enough compared to the region of the fluid and still big enough compared to the molecular mean free path. This condition is mathematically expressed using a non dimensional number known as a Knudsen number.

Describing a fluid flow quantitatively makes it necessary to assume that flow variables, such as pressure and velocity, and fluid properties vary continuously from one point to another. Mathematical description of flow on this basis have proved to be reliable and treatment of fluid medium as a continuum has firmly become established.