# Questions tagged [navier-stokes]

The Navier-Stokes equations describe fluid flows in continuum mechanics.

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### Can we derive Stokes' drag law from Navier-Stokes' equation?

So basically Stokes' law states that, "The drag force on a spherical body of radius $r$ and velocity $v$ is $$F_{d}=6\pi \eta rv.$$ My question: $(1)$ Can we derive Stokes' drag law from Navier-...
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### No slip boundary condition in Hele-Shaw Cell

A Hele-Shaw cell can be used to visualise potential flow around a cylinder. See this image from Van Dyke Album of fluid motion with the z axis of the cylinder pointing out of the page: Potential ...
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### Acceleration of fluid in a magnetohydrodynamics vortex

In the following video we see a mercury vortex done by magnetohydrodynamics: https://youtu.be/au4hbUm4mMo In the following manuscript they say that the fluid will accelerate according to (14) ${}^1$: ...
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### How to derive gravitational potential from Navier-Stokes equation?

Starting from the Navier-Stokes equation I want to be able to derive the gravitational potential using the Poisson equation but am unsure how to do it in spherical polar coordinates. This is what I ...
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### Boltzmann Transport Equation existence and smoothness - Is it proved?

Currently, Navier-Stokes Equation, its solution's existence and smoothness is not well established, making the problem as one of famous Millennium Prize Problems. On the other hand, I noticed that ...
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### How does turbulence arise from Navier-Stokes?

I would like to know how turbulence arises from the standard Navier-Stokes equations, both mathematically and also physically. At least I suspect this is the case as many of the "vanilla" ...
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### Impact of total stress tensor's definition on a continuum's linear momentum equation derivation and result

I am reading the book: "The Finite Volume Method in Computational Fluid Dynamics An Advanced Introduction with OpenFOAM® and Matlab®" - DOI 10.1007/978-3-319-16874-6 The section of concern ...
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### Normalisation for pressure for low and high flow speed regimes: what is the explanation behind it?

In the book of Theoretical microfluidics by Bruus, at page 26 it is given that $$p=\frac{\eta V_{0}}{L_{0}} \tilde{p}=P_{0} \tilde{p}$$ Note that a quantity often can be made dimensionless in more ...
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