Navier-stokes Definition and 77 Threads

The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces. So, for example, in a shearing flow where there is a moving surface, the fluid velocity at the fluid/surface interface has to...

In layman's terms, can someone explain what the Navier-Stokes Equations express? And also, can someone explain to me, what the real problem is in trying to understand the Navier-Stokes problem/Turbulence?

I am currently trying to provide a mathematical model that describes the flow through a diverging square pipe. I am trying to simplyfy the navier stokes equations by usings assumptions but am unsure if my current progress is correct. The problem is as follows: Fluid enters a section of a...

Homework Statement In [1], problem 2.3 (ii), we are asked to show that for a pipe with circular cross section r = a and constant pressure gradient P = -dp/dz one has u_z = \frac{P}{4 \mu}\left( a^2 - r^2 \right) u_r = 0 u_\theta = 0 References: [1] D.J. Acheson. <em>Elementary fluid...

I was given an assignment in my Fluid Mechanics Module with the title: Application of the Navier-Stokes Equations in Tribology Applications Yet the lecture has given no starting point and we haven't yet done anything to do with Navier-Stokes Can anyone help me on where to start?

The energy-momentum tensor for a perfect fluid is T^{ab}=(\rho_0+p)u^au^b-pg^{ab} (using the +--- Minkowski metric). Using the conservation law \partial_bT^{ab}=0, I'm coming up with (\rho+\gamma^2p) [\frac{\partial\mathbb{u}}{{\partial}t}+ (\mathbb{u}\cdot\mathbb{\nabla})\mathbb{u}]=...

Hello, I have Navier stokes in 1D \rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}\right)=-\frac{\partial p}{\partial x}+\mu\frac{\partial^2u}{\partial x^2} Condition of imcompressibility gives \frac{\partial u}{\partial x}=0 So I have Navier stokes...

Hello everyone I'm for the first time trying to model using the Navier-Stokes equations. I want to model a 2D problem where I have an incompressible, non viscous fluid. I have a region (a segment of line) where a force is applied to the fluid. For example: a rectangular box with size 2L x L. In...

Notation "(v*gradient operator)v" in Navier-Stokes What does \left( \textbf{v} \cdot \nabla \right) \textbf{v} mean, assuming knowledge of the gradient operator? And, specifically, how would that be expanded? In general, I'm ignorant of the notation \left( f \left( y, \frac{d}{dx}...

First post; I am starting to read the official problem description of the http://www.claymath.org/millennium/Navier-Stokes_Equations/navierstokes.pdf" and am having trouble understanding the units involved in the first equation :rolleyes: The equation, verbatim, is \begin{equation}...

It has been a while since I've had calculus. I am working on a fluid mechanics problem: I have reduced the Navier-Stokes equation and this is what I have: mu [d/dr (1/r d/dr (r v(angular)))] = 0 How do I solve for v(angular) ?

I'm looking to get a full solution to the Navier-Stokes equation to describe fluid flow through a pipe with moving surfaces. For now I am just concerned with a two dimensional system. The upper and lower boundaries are parallel to the x-axis. The surfaces of the boundaries move sinusoidally...

I was wondering if someone could help me this Navier-Stokes Equation. f[(δv/δt) + v.Dv] = -DP + Dt + f Could someone maybe explain the symbols and what it means. I'm not sure but I think Navier-Stokes equations describe fluid motion. (The P could be ρ. I'm not too sure) Thanks

Hello all, Still at my frisbee modeling program, I started to ask myself how I could get better approximations of stuff like COP versus angle-of-attack, drag/lift coefficients, etc. I've been checking out the Navier-Stokes equations because I understand they can be used to model fluid flow...

Do the navier-stokes equations inlude the seven that have not been solved and, if you successfully solve them, you get a prize of $1 Million per equation? Thank you.

What does it take to look at the well poseness problem of the Navier stokes equations? Besides knowledge in PDEs.

Hey guys, Just trying to non-dimensionalise the navier stokes equation. We were taught how to do it when you scale x,y,z with one reference length L...just wondering how to do it if I scale x,y,z with a,b,c respectively. Edit - this is what I already know...

I've been trying to figure out how I can start with the Navier-Stokes equation and end up at the Reynolds Transport Theorem. Could anyone provide a link to a derivation of this? or some advice of some sort?

As show below the Fourier Transform of Naiver-Stokes equation. I wonder if the pressure should be in the Fourier transform? In the below transformation there is no pressure. N-S \frac{\partial\vec{u}}{\partial t}\+(\vec{u}\bullet\nabla)\vec{u}=-\frac{\nabla P}{\rho}+\nu\nabla^{2} N-S in...

I'm trying to find a simply derivation of the incompressible navier-stokes equations, as stated in the official problem description at the cmi website, or in "The Millenium Problems", by Keith Devlin: \frac{\partial u}{\partial t}+(u\cdot\nabla)u=f-\nabla p+\nu\Delta u \nabla\cdot u=0 I...

navier-stokes smoothness problem almost solved Penny Smith has made progress with showing that smooth conditions exist for all time in a domain for the Navier Stokes equations http://notes.dpdx.net/2006/10/06/penny-smiths-proof-on-the-navier-stokes-equations/ However a flaw was found in the...

What are Navier-stokes equations and why are they difficult to solve?

I've reduced a portion of the Navier Stokes to solve a flow problem, and am left with the following ODE: u (\frac {\partial^2 Vz} {\partial^2 r}) + \frac {r} {u}\frac {\partial Vz} {\partial r} = 0 I tried to solve this equation by assuming a power law solution with Vz = Cr^n Which...

I am surprised that nobody has posted yet of the hottest hews in PDE's, Penny Smith's proposed proof that smooth, "immortal" solutions of the N-S equations exist. If it pans out, this will collect one of the famous Clay Millennium Prizes, a cool million. Smith says that unlike Perelman, she'd...

i'm revising for my exams, and i didn't go to many of my fluids lectures, now I'm well confused. in the navier-stokes equation for viscous fluid flow, there is a term: v(del squared)u where v is the kinematic viscosity and u is the velocity field of the fluid. at this point in my notes, the...

The Clay Institute wants a proof that an initially smooth flowing fluid stays free of turbulence in the long run. Can the Navier-Stokes equations, which describe a fluid that initially has no turbulence in it, be equivalent to a set of equations describing vortices, with the vortices...

Help me find solutions for the Navier-stokes equations and you could get rich. The problem is this: A fluid enters a pipe and flows through it smoothly at the outset. Will it keep flowing smoothly? Sounds easy to solve but it isn't because nobody has won the million dollars yet. Here is...