Incompressible Versus Compressible Flows

A flow in which the density p is constant is called incompressible. In contrast, a flow where the density is variable is called compressible. A more precise definition of compressibility will be given in Chapter 7. For our purposes here, we will simply note that all flows, to a greater or lesser extent, are compressible; truly incompressible flow, where the density is precisely constant, does not occur in nature. However, analogous to our discussion of inviscid flow, there are a number of aerodynamic problems that can be modeled as being incompressible without any detrimental loss of accuracy. For example, the flow of homogeneous liquids is treated as incompressible, and hence most problems involving hydrodynamics assume p = constant. Also, the flow of gases at a low Mach number is essentially incompressible; for M < 0.3, it is always safe to assume p = constant. (We will prove this in Chapter 8.) This was the flight regime of all airplanes from the Wright brothers’ first flight in 1903 to just prior to World War II. It is still the flight regime of most small, general aviation aircraft of today. Hence, there exists a large bulk of aerodynamic experimental and theoretical data for incompressible flows. Such flows are the subject of Chapters 3 to 6. On the other hand, high-speed flow (near Mach 1 and above) must be treated as compressible; for such flows p can vary over wide latitudes. Compressible flow is the subject of Chapters 7 to 14.

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