# Tagged Questions

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

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### Does surface tension attenuate turbulence?

Rapids and several other "white water" systems could be typical examples of turbulent motion. To describe such flows the Navier-Stokes equations must be extended by terms describing the surface ...
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### Solve unsteady state Bernoulli equation for flow in a pipe

I am an engineer studying an unsteady-state flow through a pipe. The Pipeline has been cleanly cut into two halves, without deforming the cylindrical form of the pipe, exposing the contents to ...
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### How does the dissolution of salt affect the solution density?

Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
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### What is the velocity in the Navier-Stokes equation?

I have been looking at the Navier-Stokes equation, and can't seem to find anywhere a clear description of what velocity it represents. From what I have read it could be any of the following: The '...
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### Energy/density fluid/solid boundary condition

Working on solid/fluid couplings (for atmospheric purposes) I try to better understand how things work at the interface between an elastic medium and a compressible fluid. What I understood from ...
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### Non-dimensionalizing incompressible Navier-Stokes

I have a question about non-dimensionalization of the incompressible Navier-Stokes (NS) equations. My understanding is that the purpose of non-dimensionalization is to "collapse" solutions onto one ...
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### Inertial Waves - Why neglecting the advecting term?

I'm trying to derive the dispersion relation for Inertial waves. In Cartesian coordinates: Inviscid and incompressible fluid is rotating uniformly with Angular Velocity: $\Omega = (0, 0, \Omega)$ ...
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### Why is turbulence caused?

In high Reynolds numbers we have turbulent flow. This is because the inertial forces are much greater than the viscous forces. I understand inertial forces to be actually the fictional forces due to ...
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### Navier Stokes : what about angular momentum?

I play with CFD for a while, and suddenly, a transcendantal question raises: :-) Navier Stokes is basically Newton applied on a continuum in Eulerian. For solids, we would consider linear, but also ...
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### Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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### What fluid dynamics equations are like in zero gravity?

I don't know if this is a proper question. I am not so familiar with fluids. I am just curious about what Navier-Stokes equations for fluids will look like in zero gravity. Are they stay the same? If ...
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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 ...
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### Incompressible Navier-Stokes boundary conditions

Let's say I have a unit cube $\Omega\in[0,1]^2$ where the inflow is on the left and outflow on the right, at the top and bottom boundary I have no-slip $u_1 = u_2 = 0$. At the inflow I prescribe ...
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### Why Velocity is referred as momentum? [closed]

In many text books the velocity is referred to as a linear momentum which is being convected. For example the table in the following page My old conception is that the momentum or more precisely ...
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### Numerical model for a Air core Vortex, why it's still so limited? [closed]

The Question can be Formally presented as follows; How is the Numerical Model (CFD, Navier Stokes) of fluid dynamics for Vortexes at in it's limits? At this Publication from 2013 at page 48 is said;...
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### Why is the solution to the Blasius boundary layer problem self-similar?

In every course or textbook that I encountered so far, the authors transform the Navier-Stokes equations of the Blasius boundary layer problem into the Blasius ODE. The problem with many of those ...
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### The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
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### Does a whirlpool(vortex in water) continue in air(vortex in air),and when does a vortex stop?

First part: The question is both about the continuity of the water vortex(whirlpool) to vortex in air in time and in space. About continuity in time,does the vortex of the water slowly produce a ...
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### Reference values for viscosity and density in incompressible NSE

I come from a pure mathematics background, so I have very limited physics knowledge. I'm currently working out the non-dimensional form for the Navier-Stokes equations and have some questions. Where ...
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### Fluid dynamics equations, number of variables and number of equations

Continuity and Navier-Stokes equation for fluid are, \begin{eqnarray} \frac{\partial \rho}{\partial t} + \nabla\cdot (\rho \mathbf{u}) &=& 0 \\ \rho\left(\frac{\partial \mathbf{u}}{\partial t} ...
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### Navier-Stokes: equation or equations [closed]

In textbooks and papers, you see both forms: the Navier-Stokes equation and the Navier-Stokes equations. Which one is correct and why?
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### Visco-elastic fluid | stress/strain relationship

I'm working on a moving visco-elastic fluid with a absorption law (against frequency) that can be represented by a Zener model (Gaussian quality factor). I try to make a numerical modeling of it (...
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### Maximum pressure in a die-less wire drawing apparatus

I ran across this patent: http://www.google.com/patents/US4549421 and was interested by the idea of reducing the cross sectional area of a wire with only shear stress caused by the wire being pulled ...
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### Is there a nice way to write Navier-Stokes equations in exterior calculus

I'm considering to study some high-dimensional Navier-Stokes equations. One problem is to do write the viscous equation for vorticity, helicity and other conserved quantities. I think it might be ...
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### Navier-Stokes system

I have to study this system which name is Navier-Stokes. Can you explain please what means that $p$, $u$ and $(u \cdot \nabla)u$. What represents in reality? Tell me please, how should I read the ...