# How does one define the pressure in a flowing fluid?

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?

• What exactly is your question? Do you want to measure the pressure of fluid flowing in pipes? Do you doubt that the Bernoulli equation is correct? Do you need an explanation of why pressure drops when velocity increases? Oct 31, 2021 at 15:57
• I apologize if my question was worded in a confusing way. I have edited to make it more clear. What I want to know is: when one is talking about the pressure field P(x,y,z,t) of a flowing fluid at some point P, are they talking about the pressure felt by a stationary probe at P or one that’s moving with the fluid that at P? Oct 31, 2021 at 17:09
• In scenario 1, you need to place your pressure probe opening parallel to the streamlines. If you place the pressure probe opening normal to the streamlines, you will be measuring the "dynamic pressure," which includes a $\rho \frac{v^2}{2}$ term, over and above the static pressure. Oct 31, 2021 at 20:13