The subject of compressible flow has wide applications in high speed flows such as those occurring in rocket or gas turbine engines, or the flow around supersonic airplanes; we now turn our attention to the analysis of such flows. With the governing equations discussed in Chapter 1, and a knowledge of the appropriate constitutive laws, it should be possible to carry out the analysis carried out in this chapter for any gas. For reasons of simplicity, however, we shall restrict ourselves to a perfect gas. For a numerical implementation of the equations presented in this chapter, see [50].

As mentioned in Section 1.3.9, under the assumption of incompressibility, the equations of continuity and momentum are sufficient to solve for the velocity and pressure fields. However, for compressible flows, since the density is not constant, the equations of continuity, momentum and energy conservation have to be considered simultaneously in order to obtain a solution to a flow problem.

In reality, every fluid is compressible. However, for liquid flows and for flow of gases with low Mach numbers, the density changes are so small that the assumption of incompressibility can be made with reasonable accuracy. We have pointed out in Section 1.6, following our discussion of the Eckert number, that the assumption of incompressibility can be made when the Mach number M defined as the ratio of the speed of flow to the speed of sound is less than 0.3.

Compressible flows can be classified based on the Mach number as follows:

1. Subsonic flow: The Mach number number is less than one everywhere in the flow. If, further, the Mach number everywhere is less than 0.3, the incompressibility assumption can be made.

2. Transonic flow: The Mach number in the flow lies in the range 0.8 to 1.0. Shock waves appear, and the flow is characterized by mixed regions of subsonic and supersonic flow.

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