is air an incompressible fluid
Incompressible flows do not have such a variation of density. The key differentiation between compressible and incompressible is the velocity of the flow. A fluid such as air that is moving slower than Mach 0.3 is considered incompressible, even though it is a gas. A gas that is run through a compressor is not truly considered compressible (in the thermodynamic sense) unless its velocity exceeds Mach 0.3.