Fluid as a continuum                    

In the definition of the fluid the molecular structure of the fluid was not mentioned. As we know the fluids are composed of molecules in constant motions. For a liquid, molecules are closely spaced compared with that of a gas. In most engineering applications the average or macroscopic effects of a large number of molecules is considered. We thus do not concern about the behavior of individual molecules. The fluid is treated as an infinitely divisible substance, a continuum at which the properties of the fluid are considered as a continuous (smooth) function of the space variables and time.

To illustrate the concept of fluid as a continuum consider fluid density as a fluid property at a small region.(Fig.L1.2(a)). Density is defined as mass of the fluid molecules per unit volume. Thus the mean density within the small region C could be equal to mass of fluid molecules per unit volume. When the small region C occupies space which is larger than the cube of molecular spacing, the number of the molecules will remain constant. This is the limiting volume above which the effect of molecular variations on fluid properties is negligible. A plot of the mean density versus the size of unit volume is illustrated in Fig.L1.2(b).

Note that the limiting volume  is about  for all liquids and for gases at atmospheric temperature. Within the given limiting value, air at the standard condition has approximately  molecules. It justifies in defining a nearly constant density in a region which is larger than the limiting volume.

In conclusion, since most of the engineering problems deal with fluids at a dimension which is larger than the limiting volume, the assumption of fluid as a continuum is valid. For example the fluid density is defined as a function of space (for Cartesian coordinate system, x, y, and z) and time (t ) by . This simplification helps to use the differential calculus for solving fluid problems.