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

In summary, the conversation is about the meaning of the term 'flow' in the context of a pipe flow problem. It is explained that 'u' is usually used to represent velocity in one of the three orthogonal directions, and in Navier-Stokes equations, the notations for the different directions are u, v, and w. To determine the volumetric flow, the velocity profile must be integrated over a surface area.
  • #1
Benny
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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.
 
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  • #2
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 [tex]u_{x}, u_{xx}, u_{y}, u_{yy}, u_{z}, u_{zz}[/tex] and [tex]u_{t}[/tex] 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.
 
  • #3
Thanks for the explanation.
 

1. What is viscosity in fluid mechanics?

Viscosity is a measure of a fluid's resistance to flow. It is often described as the "thickness" of a fluid, and is affected by factors such as temperature, pressure, and composition of the fluid.

2. What is the difference between a Newtonian and non-Newtonian fluid?

Newtonian fluids have a constant viscosity, meaning that their resistance to flow remains the same regardless of the force applied. Non-Newtonian fluids, on the other hand, have a varying viscosity that is dependent on the force applied. Examples of non-Newtonian fluids include ketchup, toothpaste, and blood.

3. What is the Bernoulli's principle in fluid mechanics?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle is often applied in the study of fluid dynamics to explain the lift force of airplane wings and the flow of water through pipes.

4. What is the difference between laminar and turbulent flow?

In laminar flow, the fluid particles move in parallel layers with little to no mixing between them. In turbulent flow, the fluid particles mix and move in irregular patterns. Turbulent flow is often characterized by chaotic motion and eddies.

5. What is the Reynolds number in fluid mechanics?

The Reynolds number is a dimensionless quantity that relates the forces of inertia and viscosity in a fluid. It is used to determine whether a fluid flow is laminar or turbulent, with a higher Reynolds number indicating a more turbulent flow.

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