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Ebook Fluid mechanics: Part 2

(BQ) Part 2 book "Fluid mechanics" has contents: Compressible flow, open channel flow, turbomachinery, physical properties of fluids, compressible flow tables, conversion factors, equations of motion in cylindrical coordinates, introduction to EES. | Chapter 9 Compressible Flow 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 become 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 velocities. In gases, however, a pressure ratio of only 2Ϻ1 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 familiarize 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 invert. 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 variable—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. 9.1 Introduction 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