The thermodynamic definition of pressure is just how much work it takes to compress the system. This definition still works locally, you can just imagine compre

The thermodynamic definition of pressure is just how much work it takes to compress the system. This definition still works locally, you can just imagine compressing a small volume of gas. I'm not 100% sure if fluid dynamics uses a subtly different definition (though how hard the medium is to compress is a fairly universal definition). Obviously thermodynamics does break down if you've only got a small number of particles, but then 'pressure' also kind of stops working as a concept when you've got mostly vacuum.