Linked Questions
13 questions linked to/from Navier-Stokes Derivation
12
votes
3
answers
6k
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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, ...
15
votes
1
answer
9k
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 ...
- 1,181
7
votes
4
answers
22k
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What are the assumptions of the Navier-Stokes equations?
I wanted to model a real life problem using the Navier-Stokes equations and was wondering what the assumptions made by the same are so that I could better relate my entities with a 'fluid' and make or ...
- 173
9
votes
4
answers
1k
views
How does hot air rise?
If a balloon is filled with hot air, it is rising due to buoyancy: the mass of the hot air inside the balloon is lower than the mass of the same volume of the cold air outside the balloon cavity.
...
- 65k
2
votes
3
answers
4k
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.
- 21
-2
votes
4
answers
2k
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 ...
- 2,557
7
votes
3
answers
1k
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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?
...
user249451
1
vote
1
answer
770
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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 ...
- 11
1
vote
3
answers
902
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 ...
- 632
2
votes
2
answers
524
views
What is (local) pressure within a gas on the microscopic level?
Fluid dynamics view
Fluid dynamics describes liquids and gases in terms of local pressure (among other variables), which varies from a point to point. While mathematically the concept is well-defined (...
- 65k
2
votes
1
answer
450
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 ...
4
votes
1
answer
238
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, $\...
4
votes
2
answers
397
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 ...
- 43