Originally Posted by aeronaut999
does that pressure involve momentum?
I think you're getting to the heart of the question. At a microscopic level, as I'm sure you know, pressure from a fluid on a body comes from the fluid molecules colliding with the surface of the body and, therefore, transferring their momentum. However, take this example.
When you are about to enter a room and do so by quickly opening the door, you can hear the other doors in the room slam shut if they were barely cracked open. The result is seemingly instantaneous. The pressure "information" travels at the speed of sound, not at the speed you were shutting the door, and not at the speed the air pushed by the door traveled.