ABSTRACT
A flow can be of statistical (i.e., molecular) or of continuum nature, depending on the involved length and time scales. Fluid mechanics is normally concerned with the macroscopic behavior of fluids on length scales significantly larger than the mean distance between molecules, and on time scales significantly larger than those associated with molecular vibrations. In such a case, a fluid can be approximated as a continuum, i.e., as a hypothetical infinitely divisible substance, and can be treated strictly by macroscopic methods. As a consequence of the continuum hypothesis, a fluid property is assumed to have a definite value at every point in space. This unique value is defined as the average over a very large number of molecules surrounding a given point within a small distance, which is still large compared with the mean intermolecular distance. Such a collection of molecules occupying a very small volume is called fluid particle. Hence, the velocity of a particle is considered equal to the mean velocity of the molecules it contains. The velocity so defined can also be considered to be the velocity of the fluid at the center of mass of the fluid particle. The continuum assumption implies that the values of the various fluid properties are continuous functions of position and of time. This assumption breaks down in rarefied gas flow where the mean free path of the molecules may be of the same order of magnitude as the physical dimensions of the flow. In this case, a microscopic or statistical approach must be used.
