Fluids: continuous or discrete?
Fluids: continuous or discrete?
(OP)
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.
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.





RE: Fluids: continuous or discrete?
Aaron A. Spearin
ASQ CSSBB
Engineering Six-S'$
www.Engineering6ss.com
"The only constant in life is change." -Bruce Lee
RE: Fluids: continuous or discrete?
"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.
RE: Fluids: continuous or discrete?