Aerodynamics: Some Fundamental. Principles and Equations

There is so great a difference between a fluid and a collection of solid particles that the laws of pressure’ and of equilibrium of fluids are very different from the laws of the pressure and equilibrium of solids.

Jean Le Rond d’Alembert, 1768

The principle is most important, not the detail.

Theodore von Karman, 1954

2.1 Introduction and Road Map

To be a good craftsperson, one must have good tools and know how to use them effectively. Similarly, a good aerodynamicist must have good aerodynamic tools and must know how to use them for a variety of applications. The purpose of this chapter is “tool-building”; we develop some of the concepts and equations that are vital to the study of aerodynamic flows. However, please be cautioned; A craftsperson usually derives his or her pleasure from the works of art created with the use of the tools; the actual building of the tools themselves is sometimes considered a mundane chore. You may derive a similar feeling here. As we proceed to build our aerodynamic tools, you may wonder from time to time why such tools are necessary and what possible value they may have in the solution of practical problems. Rest assured, however, that every aerodynamic tool we develop in this and subsequent chapters is important for the analysis and understanding of practical problems to be discussed later. So, as

we move through this chapter, do not get lost or disoriented; rather, as we develop each tool, simply put it away in the store box of your mind for future use.

To help you keep track of our tool building, and to give you some orientation, the road map in Figure 2.1 is provided for your reference. As we progress through each section of this chapter, use Figure 2.1 to help you maintain a perspective of our work. You will note that Figure 2.1 is full of strange-sounding terms, such as “substantial derivative,” “circulation,” and “velocity potential.” However, when you finish this chapter, and look back at Figure 2.1, all these terms will be second nature to you.