Fluids: continuous or discrete?

[Nabla1]

After looking at some fluid dynamics basics, the maths seems to be centered around three main (partial differential) equations:

The continuity equation (rate of mass flow)
The Navier-Stokes equations (rate of change of momentum)
The energy equations (rate of energy transfer)

These equations treat the various properties of fluid (velocity, density, momentum etc..) as physical scalar (e.g. density) or vector (e.g. momentum) fields. The fluid is treated as a continuum, and is hence differentiable, which is why the above equations work.

My question: If fluids are CONTINUOUSLY variable in all of their properties, then why do many sources talk about fluid being LAYERED? This suggests that the fluid is not continuous and differentiable, but is actual DISCRETE.

(Many sources I have read talk about things like "layered flow", "boundary layers", and "random particle movement between layers")

Thanks, help is much appreciated.

 

[aspearin1]

Some equations must assum turbulent flow, where friction along pipe walls creates enough eddies in the flow to make it uniform. This occurs best in high flows of low viscosity liquid. Low flows, known as laminar flow, have boundary layers. Essentially, their is a velocity gradient across the the pipe diameter. Max fluid velocity is at the center, min (or zero)velocity at the pipe wall. The flow profile is parabolic in shape. It's been a while, but there are equations specific to laminar flow as well. But I wouldn't consider the "layered" aspect of flow to be discrete. In my comprehension, it's very much a continuum. The only true boundary layers are at the interface of imiscible fluids or contact with different phases.

Aaron A. Spearin
ASQ CSSBB
Engineering Six-S'$

http://www.Engineering6ss.com

"The only constant in life is change." -Bruce Lee

 

[rb1957]

"layered flow" is a term i'm unfamiliar with, tho' it might refer to stratified flow, where there is some property of the fluid preventing it form being the coontinuous fluid you're used to seeing.

"boundary layer" is the specific region close to a surface where the velocity profile of the fliud is constrained by viscousity, the fluid velocity quickly increases from the surface condition (usually, but not always 0)to the free stream velocity. the fliud dynamics in this layer is clearly very different to the far-field fluid.

"random particle motion between layers" suggests something like newtonian fliuds, where the molecules are far enough apart it act like individual particles. maybe in this field it makes sense to artifically divide the "fluid" into layers.

 

[Compositepro]

Fluid flow is a continuum. The reference to layers is merely a convenient way to refer to locations where the fuild flow is very similar in terms of velocity.