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Questions tagged [navier-stokes]

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

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Time independence in non-dimensionalized Navier-Stokes equations

I was looking into the creeping motion equation: $$Re \frac{\mathrm{D} \mathbf{u^*}}{\mathrm{D} t^*} = -\nabla^* p^* + \nabla^{*2} \mathbf{u^*}$$ In the case of $Re << 1$ this equation ...
65 views

Comparing the complexity of Einstein's field equations with the Navier-Stokes equations

I know litte about the Navier-Stokes equations, but it seems to me that questions related to Navier-Stokes are more fundamental (e.g. do solutions exist for a set of initial conditions) than the ones ...
24 views

Adapting the “12 steps to navier stokes” cfd to find a drag coefficient by finding drag force and rearanging

I am using the 12 steps of navier stokes from here to learn the basics of cfd for a rocket simulation project where I would like to find a static coefficient of drag to use. Is there anyway to do this ...
72 views

Navier-Stokes Derivation

Someone knows where can I found a physical derivation of the Navier-Stokes equation? Mainly the stress tensor. A lot of authors simply "jumps" the stress tensor and it's the more important of physical ...
120 views

Analogies between equations [closed]

What properties of fields and matter are related to the analogy of the Schrödinger equation and the Navier-Stokes equation, between the equation of general relativity and the Navier-Stokes equation? I ...
532 views

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?
1k views

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 ...
140 views

Is Stokes equation a reduction of Navier-Stokes equations?

The following Stokes problem: $$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$ is a reduction of the Navier--Stokes equations? ...
228 views

Governing equations and boundary conditions for a steady-state compressible viscous flow in an axisymmetric annular orifice

I'm trying to simulate a 2D axisymmetric model of steady-state compressible viscous flow using Mathematica, but I get some errors. There is a chance that I'm making some mistakes with the governing ...
333 views

Pressure generation due to opposing flows

If two fluids are flowing at unequal velocities towards each other in a circular pipe, will a pressure be generated at the intersection? If yes, what will the direction of this pressure generated and ...
1k views

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 ...
40 views

External force in the Navier-Stokes momentum equation

The Navier-Stokes momentum equation is $$\rho\frac{\partial \bf{v}}{\partial t}+\rho(\bf{v} \cdot \nabla\bf{v})=-\nabla P + \nabla\cdot \bf{\tau} +\bf f$$ where $\tau$ is the deviatoric stress ...
338 views

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 ...
46 views

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 ...
250 views

What is the physical explanation as to why the kinematic boundary condition must hold at the free surface of a wave?

The kinematic boundary condition at the surface of a water wave is given as: "a particle on the free surface remains there always". This is then written as the material derivative of the free surface ...
210 views

How can I derive the stress tensor for a Newtonian fluid in more physical terms?

The question is quite fundamental and more on a beginner's level (not sure if good in this high-level-forum, but I try): I have big problems in understanding the stress tensor for Newtonian fluids in ...
137 views

Velocity field to a permeability field using poisson pressure equation

I have a velocity field and I want to get a pressure field. In my experiment we're controlling the pressure at the inlet and the outlet. I have Dirichlet boundary conditions at the inlet and outlet ...
30 views

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, ...
39 views

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 ...
165 views

How do I calculate the change of pressure on a fluid moving on block?

Lets assume block motion for a fluid. From Navier-Stokes equation we got $\vec \nabla p = \rho (\vec g - \vec a)$ Lets say s is the direction where pressure has the steepest increase. How do you ...
68 views

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 ...
1k views

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} = ...
42 views

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 ...
160 views