Compressibility of fluids are encountered in many applications in aerospace and mechanical engineering. Some examples are flows in nozzles, compressors, turbines, and diffusers. In aerospace engineering, in addition to these examples, compressible flows are seen in external aerodynamics, aircraft, and rocket engines. In almost all of these applications, air (or some other gas or mixture of gases) is the working fluid. However, steam can be the working substance in turbomachinery applications. Thus, the range of engineering applications in which compressible flow occurs is quite large and hence a clear understanding of the dynamics of compressible flow is essential for engineers.
All fluids are compressible to some extent or other. The compressibility of fluids is defined as
where v is the specific volume and P is the pressure. The change in specific volume corresponding to a given change in pressure, will, of course, depend upon the compression process. That is, for a given change in pressure, the change in specific volume will be different between an isothermal and an adiabatic compression process.
The definition of compressibility actually comes from thermodynamics. Since the specific volume v = v(T, P), we can write:
It is well known from high school physics that sound (pressure waves) propagates in any medium with a speed that depends on the bulk compressibility. The less compressible the medium, the higher the speed of sound. Thus, speed of sound is a convenient reference speed, when flow is involved. Speed of sound in air under normal atmospheric conditions is 330 m/s. The implications of this when there is flow are as follows. Let us say that we are considering the flowof air around an automobile traveling at 120 kph (about 33 m/s). This speed is 1/10th of the speed of sound. In other words, compared with 120 kph, sound waves travel 10 times faster. Since the speed of sound appears to be high compared with the highest velocity in the flow field, the medium behaves as though it were incompressible. As the flow velocity becomes comparable to the speed of sound, compressibility effects become more prominent. In reality, the speed of sound itself can vary from one point to another in the flow field and so the velocity at each point has to be compared with the speed of sound at that point.
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