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Chapt09 - The Concorde 264 supersonic airliner Flying more...

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570 The Concorde 264 supersonic airliner. Flying more than twice as fast as the speed of sound, as discussed in the present chapter, the Concorde is a milestone in commercial aviation. However, this great technical achievement is accompanied by high expense for the traveller. (Courtesy of Don Riepe/Peter Arnold, Inc.)

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9.1 Introduction Motivation. All eight of our previous chapters have been concerned with “low-speed’’ or “incompressible’’ flow, i.e., where the fluid velocity is much less than its speed of sound. In fact, we did not even develop an expression for the speed of sound of a fluid. That is done in this chapter. When a fluid moves at speeds comparable to its speed of sound, density changes be- come significant and the flow is termed compressible . Such flows are difficult to obtain in liquids, since high pressures of order 1000 atm are needed to generate sonic veloci- ties. In gases, however, a pressure ratio of only 2 1 will likely cause sonic flow. Thus compressible gas flow is quite common, and this subject is often called gas dynamics . Probably the two most important and distinctive effects of compressibility on flow are (1) choking , wherein the duct flow rate is sharply limited by the sonic condition, and (2) shock waves , which are nearly discontinuous property changes in a supersonic flow. The purpose of this chapter is to explain such striking phenomena and to famil- iarize the reader with engineering calculations of compressible flow. Speaking of calculations, the present chapter is made to order for the Engineering Equation Solver (EES) in App. E. Compressible-flow analysis is filled with scores of complicated algebraic equations, most of which are very difficult to manipulate or in- vert. Consequently, for nearly a century, compressible-flow textbooks have relied upon extensive tables of Mach number relations (see App. B) for numerical work. With EES, however, any set of equations in this chapter can be typed out and solved for any vari- able—see part ( b ) of Example 9.13 for an especially intricate example. With such a tool, App. B serves only as a backup and indeed may soon vanish from textbooks. We took a brief look in Chap. 4 [Eqs. (4.13) to (4.17)] to see when we might safely neglect the compressibility inherent in every real fluid. We found that the proper cri- terion for a nearly incompressible flow was a small Mach number Ma V a 1 where V is the flow velocity and a is the speed of sound of the fluid. Under small-Mach- number conditions, changes in fluid density are everywhere small in the flow field. The energy equation becomes uncoupled, and temperature effects can be either ignored or 571 Chapter 9 Compressible Flow
put aside for later study. The equation of state degenerates into the simple statement that density is nearly constant. This means that an incompressible flow requires only a mo- mentum and continuity analysis, as we showed with many examples in Chaps. 7 and 8.

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Chapt09 - The Concorde 264 supersonic airliner Flying more...

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