As discussed in chapter 5, compressible ows represent a broad range of uid ows of relatively high speeds. Although compressibility in liquid uids is oen negligible, there is a situation where the pressure variation in the ow eld is large enough to cause substantial changes in the density of the uid. is is known as the cavitation phenomenon, where the pressure variations in the ow are large enough to cause a phase change. For liquids, whether the incompressible assumption is valid depends on the uid properties, particularly the pressure and temperature of the uid and how close they are to the critical pressure and temperature. However, the majority of the practical compressible ows are gas ows. For ow of gases, the compressibility needs to be taken into account at Mach numbers above approximately 0.3. Such compressible ows are of great importance to aerospace engineering and many other high-speed ow applications.