The mathematical equations used to describe the motion of fluids can be simplified by omitting effects that are not pertinent to a particular problem. As a consequence of these simplifications a tremendous amount of insight into fluid dynamic behavior can be obtained without having to solve the general equations. In general exact solutions to fluid dynamic problems can only be obtained for the simplified cases.
Fluid dynamics problems are frequently classified by constraints placed on: 1) physical properties such as density and viscosity, 2) the characteristics of the velocity field, 3) the number of dimensions required to describe the velocity field, or 4) constraints placed on thermodynamic parameters. The figure provides a summary of some of the main fluid flow classifications. Entire text books and college level courses are devoted to many of these flow classifications. Modern computational fluid dynamics computer programs are able to obtain approximate solutions to the general equations and are not constrained to work within one or more of these various classifications. However, computational fluid dynamics programs often use terminology associated with these classifications.