# Questions tagged [navier-stokes]

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

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### What are the Lorenz Equations used for?

In fluid dynamics I have come across two sets of equations, the Navier-Stokes equation and the Lorenz equations. From what I have read the Navier-Stokes equations always holds. So why do we need the ...
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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 ...
2answers
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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 ...
2answers
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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 ...
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 ...
0answers
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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 ...
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 ...
1answer
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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. ...
1answer
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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. ...
1answer
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### Divergence of Cauchy Stress Tensor [closed]

On the wikipedia page for the Cauchy Momementum Equation, it's stated that the equation can be written as $$\rho \frac{D\,\textbf{v}}{D\,t} = \nabla \cdot \sigma + \textbf{f}$$ Where $\sigma$ is ...
0answers
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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 ...
1answer
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### Instantaneity of Stokes Flow

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 ...
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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} = -\...
2answers
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1answer
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### About turbulence modeling

I have some questions about this paper: Lagrangian/Hamiltonian formalism for description of Navier-Stokes fluids. R. J. Becker. Phys. Rev. Lett. 58 no. 14 (1987), pp. 1419-1422. After reading the ...
1answer
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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 $$\frac{\partial (\rho u)}{\partial x}+\frac{\partial (\rho v)}{\partial y}=0$$ ...
1answer
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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 ...
2answers
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### Viscosity and energy balance

When solving Navier Stokes equations for viscous fluid over rigid surface, the viscous term in the momentum equation accounts for the momentum transfer between the fluid and surface in the near wall ...
0answers
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### Fluid simulation - why gradient of pressure is the term $\delta q$ in the projection step?

I'm learning stable fluids by reading Stam's paper. In the paper, it says, according to Helmholtz-Hodge Decomposition, I vector field $w$ could be decomposed to a divergence-free field and a curl-...
3answers
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### Physical Meaning of Divergence of Convective Velocity Term

When taking the divergence of the convective velocity term, I get the following: \begin{align} \nabla\cdot\left[\mathbf u\cdot\nabla\mathbf u\right]&=\frac{\partial}{\partial x_i}\left[u_j\frac{\...
0answers
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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 ...