What is the difference between compressible and incompressible flow?

Incompressible flow assumes constant fluid density regardless of pressure changes, valid when density variation is less than 5% (Mach number < 0.3). Liquids are typically treated as incompressible. Compressible flow involves significant density changes with pressure, important for gases at high velocities. The criterion is Mach number: M = V/c, where c is speed of sound. At M < 0.3, compressibility effects are negligible. Compressible flow analysis is essential for aircraft design, gas pipelines, steam turbines, and high-speed nozzles.