Compressibility of the fluid in the high-speed flow of gases and liquids introduces a new class of flow effects differing from those we so far have seen. We first introduce the speed of sound and the Mach number. The Mach number is the dimensionless parameter that appears repeatedly throughout this chapter. Compressibility effects in liquids are next studied, including the effect of dissolved gases on the sonic speed and compressibility effects in pipe flow. The thermodynamics of ideal gases is briefly reviewed, and the isentropic flows of these gases is then considered. The possibility of nonisentropic flow regions such as shock waves is introduced, and compressible flow in a nozzle is studied. Nozzle flow offers the possibilities of subsonic, sonic, and supersonic flow existing in the same device, along with the possibility of isolated shock waves.