Questions tagged [navier-stokes]
The Navier-Stokes equations describe fluid flows in continuum mechanics.
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How does one calculate the viscous term in the integral form of navier stokes?
I learned about the integral form of the navier stokes equation and I am trying to find an explanation for this viscous term at the end but I've searched everywhere and I can't find anything. The ...
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Modeling fluid flow in extremely small pores (or channels) compared to the component
I want to model a non-wetting fluid flowing into tiny pores of a component using Navier-Stokes.
Just for you to visualize, say I have a 2D rectangular component of dimensions $L*W$, and within that ...
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Confusion about the Navier-Stokes equation
so I am learning some stuff about fluid dynamics and I am confused on the 3D navier stokes equation. The full equation (of my knowledge) is defined like this: $$\frac{\partial}{\partial t}\bigg(V(x,t)\...
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Questions regarding the derivation procedure of the Karman-Howarth-Monin relation
I was reading the book "Turbulence" written by Uriel Frisch (1995) and got stuck in following the proof of the Karman-Howarth-Monin relation. Although there is already a thread about it, I ...
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Non-dimensionalisation of Navier-Stokes Equations [closed]
I am trying to numerically simulate a flow in which a fluid with kinematic viscosity $\nu=0.00001167$ m$^2$/s is injected into a cylindrical tube of diameter 0.00745m at a velocity of 45.9 m/s. Thus, ...
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Derive Navier-Stokes equation from the action principle (Euler-Lagrange's equation) [duplicate]
Navier-Stokes equations are the most general equations in fluid dynamics:
We ususlly derive it by the consevation laws and $F=ma$. But how to derive it from the Action principle or equivalently Euler-...
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Is there specific form of Navier-Stokes equation for which mass can cross bounding surface?
In my textbook, we learned that Navier-Stokes (NS) equations can be derived from Reynolds transport theorem where the control volume is assumed to be fixed. But when the control volume is moving, can ...
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Stress Tensor Normal Component (Newtonian Fluid) [duplicate]
I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid.
The stress on the x face in the x direction is
$$\sigma_{xx} = 2*\mu\frac{\partial u}{...
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How to calculate pressure $p$ in the Navier-Stokes equation to simulate the time evolution of a fluid?
I wanted to simulate the motion of a fluid (continuously filling the entire space) in a given space, say $3$-dimensional Euclidean space. To calculate the dynamics of fluid motion, I used the Navier-...
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Why are the Navier-Stokes equations inconsistent in this case?
Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of ...
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Normal Stress Components of Viscous Stress Tensor for Incompressible Fluid
I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid.
The stress on the x face in the x direction is
$$\sigma_{xx} = 2*\mu\frac{\partial u}{...
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Navier-Stokes Equation confusion
I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid.
The stress on the x face in the x direction is
$$\sigma_{xx} = 2*\mu\frac{\partial u}{...
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1
answer
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How do I calculate the Reynolds Number of fluid parcels around an aritrary object (with respect to CFD)? [closed]
Purpose: I am trying to create my own simplified rapid CFD software for custom purposes.
Given an arbitrary object surrounded by a moving fluid (from an arbitrary direction in 3D), how would I best ...
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Deriving the heat equation from compressible Navier Stokes equations
Starting from the compressible Navier-Stokes equations, I want to derive the standard form the instationary heat equation.
The energy equation in general form can be written as
$$
\begin{align}
\frac{\...
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What does thermodynamically consistent mean?
I am currently dealing with Cahn-Hilliard-Navier-Stokes equations. Many paper regarding these kind equations talk about the "thermodynamical consistency" of the presented models. For example,...
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Freedoms in non-dimensionalization of Navier-Stokes equation and their usage in normalization
When we non-dimensionalize NS equation, we typically take some characteristic scales of length, velocity etc, say the size of the box, average speed of the fluid in the flow direction etc. Once we ...
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Two ways of non-dimensionalizing Navier Stokes equation
I can see two ways of non-dimensionalizing Navier Stokes equation. One of them is from Wikipedia where one can see that the non-dimensionalization is performed by taking $p^*=\frac{p}{\rho U^2}$ where ...
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Can irreversibility arise from systems that are microscopically reversible? [duplicate]
I was reading about Feynman's sprinkler problem, and came across a paper that discussed irreversibility in ideal fluids. It quoted the fact that
When a real fluid is expelled quickly from a tube, it ...
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Time dependence in Eulerian description of fluid flow
In the Eulerian description of velocity field, suppose $x,y,z$ are fixed coordinates, the velocity at that point at time $t$ is $\mathbf{u}(x,y,z,t)$.
I am confused whether $x,y,z$ depend on time or ...
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Fluid compression against wall
A compressible fluid within a fixed cubic container is compressed at time $t=0$ by a spatially homogeneous force against one face of the cube. After a long time the mass distribution of the fluid ...
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Flow down an incline - Understanding boundary conditions
After working with some problems regarding flow, I came up to a similiar problem as the one presented here:
In solving the problem, we assume a laminar flow in steady state.
When using Navier-Stokes ...
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Can someone explain the creeping flow approximation?
Hello I’m a HS student so I apologize if my knowledge isn’t adequate enough, or if you have to dumb down concepts for me.
I’m writing an IB extended essay, and right now I’m trying to understand ...
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In Stoke's second problem, why can the pressure gradient be set to 0?
In every derivation of solution to Stokes second problem (where we need to find the flow of a fluid under an oscillating plate on the $x$-axis), the pressure gradient is always taken to be 0 to ...
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Derivation of velocity profile between two parallel cylinders
Recently, I started learning about different flows such as Coutte, Poiseuille and Hagen-Poiseuille. When searching for the latter, I found this interesting image:
I thought that I might be able to ...
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Inner product of the material derivative [duplicate]
I have question about the inner product of the material derivative.
$$\frac{D\mathbf{v}}{Dt}=\frac{d\mathbf{v}}{dt}+\mathbf{v}\cdot\nabla\mathbf{v}.$$
How can you calculate the second term inner ...
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How to calculate pressure change at a U bend of a rectangular duct, with a compressible fluid?
This is not homework, just a home project that I'm working on - although I'd like to get to the end result myself.
I'm familiar with Bernoulli's and Navier-stokes equations, it's just been a while and ...
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What Assumptions in the Bernoulli Equation Lead to the Difference to the Two-Phase Equations?
Why is it that the acceleration pressure drop term in the Bernoulli equations take the form $\tfrac12 \rho v^2$, where as for stratified two phase flow, condensed down to single phase the resultant ...
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Flow in a pipe: shall I counterbalance the ram pressure, or the dynamical pressure?
I'm getting a bit confused between the ram and dynamical pressure. If I consider the stress tensor
$T_{ij} = P\delta_{ij} + \rho v_i v_j$
and I consider the simplest case of fluid flowing into a pipe, ...
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Fluid viscosity, mass diffusion and Navier-Stokes equation
With the increase of fluid viscosity, mass diffusion of a fluid decreases. Then how the diffusion term in Navier-Stokes equation has a dominant effect at high viscosity? Also how the mass convection ...
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Necking stage in bubble detachment
The first image is the bubble dynamics in nucleate boiling, in a) you can see that the bubble is detaching by minimizing contact line with surface until zero, while in b) the bubble is enlongate and ...
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Convective term in Navier-Stokes
In the Navier-Stokes equations, there's a well-known convective term of the form:
\begin{equation}(\mathbf{v}\cdot\nabla)\mathbf{v}\end{equation}
I'm not able to understand it. As far as I know, the ...
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Simplifying 2D Navier stokes equation over the top and bottom part of an airfoil - assumptions incompressible, steady, very high viscosity
I am trying to simplify the Navier-Stokes equations with my assumptions, to be able to solve them numerically:
I'm trying to model an airfoil flying through a very viscous fluid at relatively low ...
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$\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do? [closed]
I'm trying to teach myself Smoothed Particle Hydrodynamics. Unfortunately, my background is in electronics, so the Navier Stokes equations are somewhat alien to me, as is vector calculus. The video I'...
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What do equations involving infinitesimals say?
I am reading this note on the Bernoulli equations with the following derivations:
I am struggling to find a calculus based meaning for the above equations involving the infinitesimal $\delta V$: I ...
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Momentum Conservation in Lighthill Acoustic Analogy
I have a question of Lighthill Acoustic Analogy. In his paper, the approximate equation of momentum is
$$\frac{\partial}{\partial t} (\rho v_i) + a_0^2 \frac{\partial \rho}{\partial x_i} = 0 $$
Would ...
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Plane Couette Flow of Ice
I am trying to solve the following problem:
The simplified Navier Stokes equation for plain Couette flow reads:
$0 = \frac{1}{\rho}\frac{\partial \tau_{xy}}{\partial y}$
(at $y = 0$ fixed plate and ...
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Fluid dynamics: Euler equation and turbulence
I have a doubt, a sort of paradox. It is known that the classical Navier-Stokes equation in the limit of Reynolds number that goes to infinity - the high Reynolds regime - gives the classical Euler's ...
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What is the correct formulation of momentum balance for a body of continuum?
What is the correct form of the momentum balance equation
for a continuum body $\mathscr{B}$
whose particles are
fixed,
and occupies volume $V(t)$ at time $t$?
\begin{align}
&\frac{\mathrm{d}}{\...
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Assumed width for 2D Navier-stokes and energy equation
Let us consider the two-dimensional Navier-Stokes equation being solved for a channel of height $d$ and length $L$, wherein a fluid enters with an average velocity $u$. These dimensions are $L=40 \ mm,...
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Why doesn't viscosity depend on pressure in the Navier-Stokes equations? [duplicate]
In the incompressible Navier-Stokes equations, we make an assumption on the stress in the fluid:
$$
\begin{align*}
\frac{Du}{Dt} &= \nabla \cdot \sigma\\
\sigma &= -pI + 2\mu e\\
e &= \...
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Turbulence from a sphere spinning in an incompressible liquid
When I look online I can find plenty of simulations of Stokes flow: incompressible liquid flowing past a spherical object. What I'm interested in is the problem of a sphere (of given size) spinning (...
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Derivation of Ladenburg correction (to calculate viscosity of fluid with Stoke's Law)
I am creating a lab report investigating the amount of time it takes for a marble ball to sink to the bottom of a cylinder container filled with sugar syrup. I recorded the amount of time it takes for ...
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Oldroyd fluid with negative term of memory
I am looking for physical sense for the Stokes equation with memory
$$\frac{d}{dt}u+u\cdot \nabla u-\mu \Delta u+\int_0^te^{-(t-s)}\Delta u(x,s)ds=f(u,t)$$
Where for now i am considering $f\equiv 0$. ...
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Navier-Stokes equation (notation for convection term)
Incompressible Navier-Stokes in vector notation is written as
$${\partial U \over \partial t}+(U\cdot\nabla)U =-\frac{1}{\rho} \nabla P + \nu \nabla^2(U),$$
where $U$ is velocity vector field $U=(u,v)...
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Why the derivative of the coordinate of a volume control is not zero?
When deducing the Navier-Stokes equation, for conservation of momentum, in an Eulerian frame (a control volume)
the derivative of fluid velocity $U_{(t)}$ is calculated
$$\frac{\mathrm{dU} }{\mathrm{...
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Hydrodynamic equation to Boltzmann's equation
How to get the four-velocity of a fluid in terms of its microscopic distribution function $f(x^{i},\vec{p})$?
For the sake of initial simplicity, the fluid can be thought of to be single component.
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When are my fluid approximations wrong?
I did some classical approximations of the Navier Stokes equations, fluid is:
non-viscous
incompressible
irrotational
When are these approximations wrong? and particularly is there a "general ...
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Navier-Stokes equations - operator $P$ which projects any vector field $w$ onto its divergence free part $u=Pw$
I have question about Navier-Stokes equation, but firstly some details:
given Navier-Stokes equations:
$\nabla \cdot u = 0$
$\dfrac{\partial u}{\partial t}=-(u\cdot \nabla )u - \dfrac{1}{\rho }\...
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To find divergence and Laplacian of the Oseen tensor for given point force in a fluid
In fluid dynamics, the velocity of the fluid due to a point force is related to it by Oseen's Tensor. I want to find the solution to stokes equation i.e. velocity field at a low Reynolds number in a ...
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Probability density of delta-correlated Gaussian white noise
The delta correlated Gaussian white noise $\eta(t)$ used in the study of stochastic processes is defined as the "derivative" of the Weiner process whose conditional probability density is ...
