I have a long duct with a fan in the middle of it. The fan causes a steady airflow in the pipe which is at low speeds (incompressible) the mean flow in the pipe is about 10 m/s. However the fan blades are spinning very fast with tip speeds up to 100 m/s and looking at the plots of normalised velocity over a segment of the fan blades (similar to the image below) one sees that the Mach number of the flow moving past the fan blades can attain appreciable mach number (i.e. Mach number > 0.3) so that compressible flow may result. It seems like the acceleration of a flow due to curvature over an obstacle can often induce large velocities even if the oncoming flow is incompressible. Is it then the case that most flows are locally compressible? Am I looking at this in the right way?