Questions tagged [navier-stokes]

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

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Incompressible Fluid Flow around sphere (Stokes)

Stokes solved this 1851. I have a question regarding the derivation. Following Batchelor the equations to be solved are \begin{align} \nabla \left( \frac{p - p_0}{\mu} \right) = \nabla^2 \vec{u} = -\...
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What is the turbulent Navier Stokes equation for cylindrical coordinates?

I am looking for turbulent Navier Stokes equation for cylindrical coordinates. I know that RANS (Reynolds Averaged Navier Stokes) eq. is the solution, I understood the point of it but only for ...
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Friction between 2 fluids in Navier Stokes

I have a system with 2 different fluids, and I want to write a friction/viscosity term between them in their Navier-Stokes equation. Should it be in the form $M(v_{1}-v_{2})$ with $M$ a friction ...
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momentum balance equation for low reynolds number flow

This is a flow in a 2-D microchannel (h/L<<1). Low Reynolds number flow. The mass - conservation equation states $$\frac{\partial (\rho u)}{\partial x}+\frac{\partial (\rho v)}{\partial y}=0$$ ...
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Exact solution of micropolar fluid for Poiseuille flow

I am new here, so i wondered if you could help me with a sytem of ordinary equations with constant coefficients. This model of equations refer to the well known Navier Stokes equations of fluid ...
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Second-order covariant derivative in index notation [closed]

So I'm having problems finding the second order covariant derivitive in index notation. My teacher said to just find the covariant derivative of a covariant derivative, so I first started with finding ...
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Relationship between flow and pressure gradient in a one dimensional compressible fluid

Consider a one dimensional model (tube with diamter $D$) with a compressible viscose ($\mu$) fluid (e.g. air). further assumptions are conduction and radiation are negligible gravity's effect is ...
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Sound speed on Navier-Stokes/Euler equations

I'd like to simulate strong shock (i.e., Rankine Hugoniot conditions) on inviscid condition, using the non-conservative Euler equations and I don't know if I should use the relation,  c^2=\left(\...
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What does it mean that a substance can be smelled from far away?

I thought about this question in the middle of this video. Ok, Thioacetone takes the price for the World's smelliest chemical, I can accept it (why not?), but what about You can smell one drop of ...
Background Info: A steady-state incompressible newtonian Stokes fluid occupying a domain $\Omega \in \mathbb{R}^2$ has flow velocity $\textbf{u}$ and pressure $p$ given by the following system of ...
I have recently learned about the Okubo-Weiss criterion in a ($x,y$) and a ($r,\theta$) coordinate system. Is it possible to recast this criterium in an ($z,r$) system, that is for axisymmetric ...