The differential equations that are generally used in the solution of problems relevant to low-speed aerodynamics are a simplified version of the governing equations of fluid dynamics. Also, most engineers when faced with finding a solution to a practical aerodynamic problem, find themselves operating large computer codes rather than developing simple analytical models to guide them in their analysis. For this reason, it is important to start with a brief development of the principles upon which the general fluid dynamic equations are based. Then we will be in a position to consider the physical reasoning behind the assumptions introduced to generate simplified versions of the equations that still correctly model the aerodynamic phenomena being studied. It is hoped that this approach will give the engineer the ability to appreciate both the power and the limitations of the techniques that will be presented in this text. In this chapter we will derive the conservation of mass and momentum balance equations and show how they are reduced to obtain the equations that will be used in the rest of the text to model flows of interest to the low-speed aerodynamicist.

Description of Fluid Motion

The fluid being studied here is modeled as a continuum, and infinitesimally small regions of the fluid (with a fixed mass) are called fluid elements or fluid particles. The motion of the fluid can be described by two different methods. One adopts the particle point of view and follows the motion of the individual particles.