# Questions tagged [navier-stokes]

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

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### How do I determine the shape of steam?

When you dip a fork into a plate of hot food right off the stove and pull it out again with a forkful of food, it generates water vapour steam from the temperature difference. I am wondering how the ...
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### Governing equations vs Transport equations

I posted it in computational-science SE site, and it was suggested I shift it here. This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, ...
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### Viscous Flow past a cylinder

I'm trying to solve the incompressible, viscous and small Reynolds number flow past a cylinder. At the surface of the cylinder ($r=R$) the velocity is zero and at infinity it is $v_0 {\vec e}_y$ where ...
1answer
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### Deriving the Integral Form of the Navier Stokes equation

I'm trying to follow the book Turbulence by Davidson. Currently I'm having trouble in converting the differential NS equation to its integral form but I cannot see clearly how the Divergence theorem ...
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### What are the limitations of this form of the Navier-Stokes equation?

$$\frac{∂u}{∂t}+u\frac{∂u}{∂x}+v\frac{∂u}{∂y}+w\frac{∂u}{∂z}=\frac{−1}{ρ}\frac{∂P}{∂x}+gx+ν(\frac{∂^2u}{∂x^2}+\frac{∂^2u}{∂y^2}+\frac{∂^2u}{∂z^2})$$ Why would someone use a form of this equation ...
1answer
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### Why shear stress is assumed constant in the inner layer

In the derivation of the log-law and the viscous sub-layer velocity profiles, it is customary to assume that the shear stress is constant and equal to the wall shear stress. Is there any physical or ...
1answer
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### Inversion of a metric

I am currently reading a paper by Bredberg $et.al$ arXiv:1101.2451 titled "From Navier-Stokes to Einstein". In this paper, the authors have considered a metric of the form \begin{eqnarray}ds^2_{p+2} = ...
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### Should non-relativistic Navier Stokes Equations be modified so that they become pseudo-Lorentz invariant?

Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_* c_*$ where $\rho_*$ is the critical mass density and $c_*$ is ...
3answers
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### Are there any cases where Stokes law does not apply in viscous fluids?

A friend of mine and I are conducting an experiment to find the relationship between terminal velocity and radius of a sphere (i.e trying to confirm Stokes law). We are using spheres ranging from 1....
2answers
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### Stressing Over Stress Tensor Symmetry in the Navier-Stokes Equations

How do we know that the stress tensor must be symmetric in the Navier-Stokes equation? Here are some papers that discuss this issue beyond the usual derivations: Behavior of a Vorticity Influenced ...
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### Navier stokes equation - two dimensional simplified [closed]

The general Navier Stokes Equation is $\dfrac{D\vec{v}}{D t}= \dfrac{d\vec{v}}{d t}+ \vec{v} .\nabla \vec{v} = \vec{g} - \dfrac{1}{\rho} \nabla p + \nu \nabla^2 \vec{v}$ The above equation can be ...
3answers
438 views

### Is Navier stokes a turbulence model?

Is Navier stokes a turbulence model? If yes, what is the use of k-omega model.. if no, what does the Navier stokes equation got to do with the turbulence models ..? I am very new to fluid dynamics... ...
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### How do speed and density change in a turbulent flow?

Suppose a fluid passes from having laminar flow, to having a turbulent flow (like when passing after an object). How do fluid speed and fluid density change after that?
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### What is the meaning of pressure in the Navier-Stokes equation?

I have a hard time to wrap my head around pressure in the Navier-Stokes equation! It may sounds ridiculous but still I cannot understand the true meaning of pressure in the Navier-Stokes equation. Let'...
1answer
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### Non-dimensionalization of Navier-Stokes equations multiphase flows

I am currently dealing with multiphase flows and have to use the non-dimensional form of the Navier-Stokes equations (NSE). In the scientific literature I found various formulations (and almost no ...
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### Derive total energy balance equation from Chapman-Enskog analysis of lattice Boltzmann equation

I'm interested to derive the total energy balance from Chapman-Enskog analysis of lattice Boltzmann equation (LBE). I know, I should go to the second moment of LBE (zeroth moment gives mass ...
1answer
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### Coupling Navier-Stokes and stochastic models for particle tracking in micro-scale free convection?

I have been using a commercially available software to simulate laminar free convection in a specific small domain (let's use channel w/ heated lower wall as an example). The scale is approx 50-100 ...
2answers
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### Zero velocity divergence for incompressible flow is derived from conservation of energy equation or conservation of mass equation?

I'm a bit confused about incompressible flow definition. In many textbooks or scientific articles, they simply claim that the incompressibility condition for Navier-Stokes equation is: \$\nabla \cdot \...
2answers
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### Why does Anderson ignore a derivative of a normal viscous stress?

I am reading "Fundamentals of Aerodynamics" 5th edition, J.D.Anderson. In part 15.6, he said: Consider a steady two-dimensional, viscous, compressible flow. The x-momentum equation for such a ...
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### How can a system of hoses each defined in their own non-inertial reference frame transmit energy information?

Rotating pipes <- image Since energy is frame dependent, I can't find a relationship that makes energy invariant at the hose connection points in respect to each local frame in the general case. ...
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### a flow through a pipe submeged in a moving fluid

There is a classic problem by which a fluid having a uniform velocity profile enters a tube. The pressure at the outlet is atmospheric, and the dimensions of that tube (diameter and length) are known. ...
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### Can someone explain the Navier Stokes equations? [duplicate]

I am doing a research work on the Navier stokes equations but I don't really understand them, as I am a high school student. Could someone explain them to me in an easy way but kind of specific? Thank ...
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### Incompressible Navier-Stokes equation in Fourier Space

I'm trying to derive the incompressible Navier-Stokes equation in Fourier space, given in e.g. Kraichnan & Montgomery (1980), Rep. Prog. Phys. 43 547 (PDF) (but probably countless other places), ...