Rotary vane compressors are kinda sorta like a positive displacement compressor, but not true in nature as a piston compressor would be.
The affinity laws would not apply to either of these, but they would on a centrifugal water pump and air moving devices like fans and blowers. Ring compressors (Regenerative Blowers) are a different animal as well.
Nice thing if you get a decent VFD to run your pumps and compressors with, you don't need sensors for pressure or flow. SVC (Sensorless Vector Control) has made some pretty impressive improvements over the years.
