An Introduction to Compressible Flows

In your previous fluids classes, the working fluids (in most cases air) were treated as incompressible - a flow in which the density was considered constant.  However, as you probably learned in earlier cases that this simplifcation (density being considered as precisely constant), does not occur in nature. 

Incompressible Flows

The assumption that density was a constant was a good approximation for a wide variety of problems.  This assumption significantly eases the solution of many fluid flows.   Assuming the density to be constant allowed:

In reality, all fluids are compressible.  This means that as the pressure exerted on a fluid element increases, the density also increases.  Therefore, if the fluid flow experiences small pressure changes, then the changes in density may be small as well (i.e. can assume there is no change in density).