1 Introduction

To this point we have neglected the effects of density variations due to pressure changes. In this chapter we shall examine some elementary aspects of flows in which the compressibility effects are important. The subject of compressible flows is also called gas dynamics, which has wide applications in high-speed flows around objects of engineering interest. These include externalflows such as those around airplanes, and internal flows in ducts and passages such as nozzles and diffusers used in jet engines and rocket motors. Compressibility effects are also important in astrophysics. Two popular books dealing with compressibility effects in engineering applications are those by Liepmann and Roshko (1957) and Shapiro (1953), which discuss in further detail most of the material presented here.

Our study in this chapter will be rather superficial and elementary because this book is essentially about incompressible flows. However, this small chapter on compressible flows is added because a complete ignorance about compressibility effects is rather unsatisfying. Several startling and fascinating phenomena arise in compressible flows (especially in the supersonic range) that go against our intuition developed from a knowledge of incompressible flows. Discontinuities (shock waves) appear within the flow, and a rather strange circumstance arises in which an increase of flow area accelerates a (supersonic) stream. Friction can also make the flow go faster and adding heat can lower the temperature in subsonic duct flows. We will see this later in this chapter. Some understanding of these phenomena, which have no counterpart...