Linked Questions

10
votes
3answers
2k views

Incompressible fluid definition

In a fluid mechanics course I found that an incompressible fluid flow means literally: $$\rho = \text{constant} \quad \forall \vec r,\, \forall t$$ Where $\vec r = (x, y, z)$ In my understanding, ...
5
votes
1answer
2k views

Deriving Stokes' law ($f_v=6\pi\eta Rv$) in a simple way

Is it possible to derive Stokes' law (Viscous force on a spherical body moving in a fluid $f_v=6\pi\eta Rv$) without using the "$\nabla$" operator (at least not in that form) or other theorems/laws ...
1
vote
3answers
1k views

What is the physical meaning of Navier-Stokes equations?

What is the physical meaning of Navier-stokes equations? I am trying to understand the physical meaning of Navier-stokes equations. But I did not get any reasonable answer so far.
0
votes
1answer
424 views

What are the limitations of this form of the Navier-Stokes equation?

$$ \frac{∂u}{∂t}+u\frac{∂u}{∂x}+v\frac{∂u}{∂y}+w\frac{∂u}{∂z}=-\frac{1}{ρ}\frac{∂P}{∂x}+gx+\nu\left(\frac{∂^2u}{∂x^2}+\frac{∂^2u}{∂y^2}+\frac{∂^2u}{∂z^2}\right) $$ Why would someone use a form of ...
-3
votes
3answers
663 views

In an incompressible Ideal fluid, can the pressure increase with depth?

Ideal Fluid is defined as an "In-Compressible Fluid". Without taking "Compressibility" into account, is it really possible that pressure increases with the depth? When we consider compressibility in ...
4
votes
1answer
332 views

Why does pressure vary with depth in a fluid at microscopic level?

Before asking this question I searched for the answer on the web (in particular on Physics.SE) and here are some that I found: In an incompressible Ideal fluid, can the pressure increase with depth? ...
1
vote
3answers
240 views

Perfect fluid stress tensor

In Thorne and Balndford's new book, they approach the subject of classical physics and tensors from the geometric viewpoint (as in relativity) that is independent from coordinates, instead from a ...
3
votes
2answers
172 views

Lattice Boltzmann Method: How is shear flow handled in D2Q5?

I've implemented 2-dimensional, incompressible, high-reynolds fluid-flow using the Lattice Boltzmann Method on a D2Q9 lattice. My main goal is just visual plausibility, not quantitative accuracy. The ...
3
votes
1answer
125 views

Motivation for pressure term in fluid approximation

A common prescription for the momentum flux $J_{ij}$ of a fluid is the following $ J_{ij} = \rho u_i u_j+p\delta_{ij}-\sigma_{ij} $ where $\sigma_{ij}$ is the viscous stress, $p$ the pressure, $\...
2
votes
1answer
86 views

From Boltzmann equation to Lattice Boltzmann

I'm following the book Lattice Gas Cellular Automata and Lattice Boltzmann models which refers to this paper to explain how to discretize the Boltzmann equation (BE) into the Lattice Boltzmann ...