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Chapter 11

# Chapter 11 - Flow past a sphere at Mach 1.53 An object...

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Flow past a sphere at Mach 1.53: An object moving through a fluid at supersonic speed 1 Mach number greater than one 2 creates a shock wave 1 a discontinuity in flow conditions shown by the dark curved line 2 , which is heard as a sonic boom as the object passes overhead. The turbulent wake is also shown 1 shadowgraph technique used in air 2 . 1 Photography courtesy of A. C. Charters. 2

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Most first courses in fluid mechanics concentrate on constant density 1 incompressible 2 flows. In earlier chapters of this book, we mainly considered incompressible flow behavior. In a few instances, variable density 1 compressible 2 flow effects were covered briefly. The notion of an incompressible fluid is convenient because when constant density and constant 1 in- cluding zero 2 viscosity are assumed, problem solutions are greatly simplified. Also, fluid in- compressibility allows us to build on the Bernoulli equation as was done, for example, in Chapter 5. Preceding examples should have convinced us that nearly incompressible flows are common in everyday experiences. Any study of fluid mechanics would, however, be incomplete without a brief intro- duction to compressible flow behavior. Fluid compressibility is a very important consider- ation in numerous engineering applications of fluid mechanics. For example, the measurement of high-speed flow velocities requires compressible flow theory. The flows in gas turbine en- gine components are generally compressible. Many aircraft fly fast enough to involve a com- pressible flow field. The variation of fluid density for compressible flows requires attention to density and other fluid property relationships. The fluid equation of state, often unimportant for incom- pressible flows, is vital in the analysis of compressible flows. Also, temperature variations for compressible flows are usually significant and thus the energy equation is important. Cu- rious phenomena can occur with compressible flows. For example, with compressible flows we can have fluid acceleration because of friction, fluid deceleration in a converging duct, fluid temperature decrease with heating, and the formation of abrupt discontinuities in flows across which fluid properties change appreciably. For simplicity, in this introductory study of compressibility effects we mainly consider the steady, one-dimensional, constant 1 including zero 2 viscosity, compressible flow of an ideal gas. In this chapter, one-dimensional flow refers to flow involving uniform distributions of fluid properties over any flow cross-section area. Both frictionless and frictional compressible flows are considered. If the change in volume associated with a change of pressure is considered a measure of compressibility, our experience suggests that gases 1 m 0 2 1 m 0 2 679 11 C ompressible Flow Compressible flow phenomena are sometimes surpris- ing; for example, friction can accel- erate fluid.
and vapors are much more compressible than liquids. We focus our attention on the com- pressible flow of a gas because such flows occur often. We limit our discussion to ideal gases,

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Chapter 11 - Flow past a sphere at Mach 1.53 An object...

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