ABSTRACT
In Chapter 6, we studied incompressible, unidirectional flows in which the equations of motion can be solved analytically. In bidirectional or tridirectional flows, the governing equations can rarely be solved analytically. One can, of course, solve such problems numerically by using finite elements or finite differences or other methods. Another alternative, however, is to use approximate methods. The most widely used approximate techniques are the so-called perturbation methods. These are based on order of magnitude analyses of the governing equations. Individual terms are first made comparable by dimensional analysis, and relatively small terms are then eliminated. This simplifies the governing equations and leads to either analytic solutions to the truncated form of the governing equations, or to the construction of approximate solutions.
