17 Compressible flow

Even if air and other gases appear to be quite compressible in our daily doings, we have until now only analyzed incompressible flow and sometimes applied it to gases. The reason is— as pointed out before—that a gas in steady flow “prefers to get out of the way” rather than become compressed when it encounters an obstacle. Unless one entraps the gas, for example in a balloon or bicycle tire, it will be effectively incompressible in steady flow as long as its velocity relative to obstacles and container walls is well below the speed of sound. But when steady flow speeds approach the speed of sound, compression is unavoidable. At such speeds the air has, so to speak, not enough time to get out of the way. Normal passenger jets routinely cruise at speeds just below the speed of sound and considerable compression of air must be expected at the front end of the aircraft. High speed projectiles and fighter jets move at several times the speed of sound, while space vehicles and meteorites move at many times the speed of sound. At supersonic speeds, the compression at the front of a moving object becomes so strong that a pressure discontinuity or shock is formed which trails the object and is perceived as a sonic boom. In unsteady flow the effective incompressibility of fluids cannot be counted on. Rapid changes in the boundary conditions will generate small-amplitude compression waves, called sound, in all fluids. When you clap your hands, you create momentarily a small disturbance in the air which propagates to your ear. The diaphragm of the loudspeaker in your radio vibrates in tune with the music carried by the radio waves and the electric currents in wires connecting it to the radio, and transfers these vibrations to the air where they continue as sound. In this chapter we shall begin by investigating compressible flow in ideal fluids, first for harmonic sound waves, and next for sonic and supersonic steady flow through ducts and nozzles. The chapter ends with a discussion of the role of viscosity in compressible flow and the attenuation it causes in harmonic wave propagation.