When one talks about the pressure of a flowing fluid, I get confused. For example, say I want to measure the pressure in a flowing river. I can think of 2 ways of measuring the pressure at a point in the flowing river.
(1) Stick a pressure probe in the river and measure the pressure while keeping the probe fixed relative to the ground.
(2) Stick a pressure probe in the river while traveling with the river on a boat and measure the pressure while moving with the river.
Surely, these two would give you different pressure readings. With that said, when one talks about the pressure field of a flowing fluid, are they talking about the pressure felt by a stationary probe or the pressure felt by one that is flowing with the fluid?