Governing Equations and Boundary Conditions for Fluid Flows

Abstract

The objective of this chapter is to give a brief description of the basic equations of fluid mechanics. The main method used to analyse the fluid motion is the construction of phenomenological macroscopic theories, based on experimentally established common relations and hypotheses. The fundamental theory of fluid dynamics is based on the three basic conservation laws of mechanics, of matter, momentum and energy, whose modification for fluid flow will be given in the next section 1.2. The laws that we shall use to obtain these equations are of such a fundamental nature that they cannot be proven in the mathematical sense. They are sufficiently general to be applied to all substances including both rigid bodies and fluids. The truthfulness of these basic laws has been established through scientific evolution over a very long period of time. Through the years these laws, as well as the concepts on which they are based, have undergone serious changes. Although fluid mechanics now has a developed content, the major part of the phenomena treated by fluid mechanics is still not sufficiently understood. The derivation of basic laws is in fact the mathematical formulation of the relations between some physical concepts. The final forms of these laws are the differential equations valid for each point inside the considered region.