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Fluid motion with negligible changes in density. No fluid is truly incompressible, since even liquids can have their density increased through application of sufficient pressure. But density changes in a flow will be negligible if the Mach number, Ma, of the flow is small. This condition for incompressible flow is given by the equation below, where V is the fluid velocity and a is the speed of sound of the fluid. It is nearly impossible to attain Ma = 0.3 in liquid flow because of the very high pressures required. Thus liquid flow is incompressible. See Mach number
Gases may easily move at compressible speeds. Doubling the pressure of air—from, say, 1 to 2 atm—may accelerate it to supersonic velocity. In principle, practically any large Mach number may be achieved in gas flow. As Mach number increases above 0.3, the four compressible speed ranges occur: subsonic, transonic, supersonic, and hypersonic flow. Each of these has special characteristics and methods of analysis.
Air at 68°F (20°C) has a speed of sound of 760 mi/h (340 m/s). Thus inequality indicates that air flow will be incompressible at velocities up to 228 mi/h (102 m/s). This includes a wide variety of practical air flows: ventilation ducts, fans, automobiles, baseball pitches, light aircraft, and wind forces. The result is a wide variety of useful incompressible flow relations applicable to both liquids and gases. See Compressible flow, Fluid flow