What does 'flow' refer to in pipe flow problems?

[Benny]

Hi, I'm just trying to get a feel for a subject that I plan to take but I'm unsure about the meaning of a certain term which frequently arises.

The term 'flow' comes up a lot and I'm wondering what it could mean (or refers to) in the context of a pipe flow problem. I know my question is vague but as an example if I'm given a PDE (for the function u(z,t) say) for a pipe flow problem, what am I actually solving for? Would u(z,t) be the velocity of the fluid? Any help would be good thanks.

 

[FredGarvin]

This is kind of tough to answer because a "flow" problem can mean different things to different people.

In your case of the PDE, u is "usually" reference for velocity in one of the 3 orthogonal directions. In Navier-Stokes equations, the notations are $$u_{x}, u_{xx}, u_{y}, u_{yy}, u_{z}, u_{zz}$$ and $$u_{t}$$ for for the x direction equation. The corresponding notations for y and z directions are v and w. These are all velocity vector components. Eventually, one would have to integrate their velocity profile over a surface area to come up with a volumetric flow in the case of something like flow in a pipe.

 

[Benny]

Thanks for the explanation.