The concept of continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables. Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.
Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure , velocity etc.) 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. For example density at a point is normally defined as
Here Δ is the volume of the fluid element and m is the mass
If Δ is very large ρ is affected by the inhomogeneities in the fluid medium. Considering another extreme if Δ is very small, random movement of atoms (or molecules) would change their number at different times. In the continuum approximation point density is defined at the smallest magnitude of Δ, before statistical fluctuations become significant. This is called continuum limit and is denoted by Δc.
is the volume of the fluid element and m is the mass
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