Crab,
The outcome of the flow equations is the fact that the rotor smoothly accelerates the air, so that half the speed change takes place before the disk, and half afterward. This is similar to the way a wing affects the flow around it, since the flow realigns far ahead of the wing. This is true in subsonic flight for all flow disturbences (in supersonic flight, the wing hits the air before the pressure disturbence can get there).