10 questions linked to/from Navier-Stokes Derivation
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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, ...
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### 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 ...
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### 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.
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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 ...
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### 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 ...
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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? ...
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### 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 ...
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### 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 ...
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, \$\...