Navier stokes Definition and 49 Threads

The Navier-Stokes equation is solved in a vector grid in a Cartesian coordinate system. That is, rectangular. But does a rectangular mesh relate to what happens in a gas or liquid, and is it better to use a triangular mesh? Undoubtedly, it is incredibly difficult to take into account all the...

So I've just started learning about Greens functions and I think there is some confusion. We start with the Stokes equations in Cartesian coords for a point force. $$-\nabla \textbf{P} + \nu \nabla^2 \textbf{u} + \textbf{F}\delta(\textbf{x})=0$$ $$\nabla \cdot \textbf{u}=0$$ We can apply the...

With the assumptions of Inviscid flow, no pressure gradient and no body force terms in 1-D Navier Stokes becomes 1-D nonlinear convection equation; And if we assume velocity of wave propagation is constant value c, equation becomes 1-D linear convection equation; This is online derivation and...

Hi PF! I'm running a CFD software that non-dimensionalizes the NS equations. The problem I'm simulating is a 2D channel flow: relaxation oscillations of an interface between two viscous fluids, shown here. I'm trying to see what they are non-dimensionalizing time with, which is evidently just...

Does anyone know of a differential equation, similar to Navier-Stokes, that encompasses incompressible fluid flow with spatially varying viscosity? Viscosity is treated as a global constant in NS; I've found some papers online that address NS with viscosity as a function of velocity, but I can't...

Hello everyone, Attached is the homework problem (FluidHmk.PNG) as well as the attempt (Attempted 1 and 2). Just wanted to know if this is method to approach the problem Thanks in advance.

Just trying to derive the Navier-Stokes equation. (1)The velocity at any point in space of an infinitesimal fluid element is v(x,y,z,t) (2) acceleration ##\frac{dv}{dt}=\frac{\partial v}{\partial t}+\sum_i\frac{\partial v_i}{\partial x_i}{\dot x_i}## ##a=\frac{dv}{dt}=\frac{\partial v}{\partial...

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 Asymmetric Stress Tensor In Fluid Flow http://www.dtic.mil/dtic/tr/fulltext/u2/a181244.pdf...

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?

Homework Statement [/B] Homework Equations Navier strokes theorem The Attempt at a Solution May I ask why would there suddenly a "h" in the highlighted part? "h" wasnt existed in the previous steps, which C2=0 shouldn't add height of the liquid as a constant in the formula... thanks

Hi, in first attachment/picture you can see the generalized navier stokes equation in general form. In order to linearize these equation we use Beam Warming method and for the linearization process we deploy JACOBİAN MATRİX as in the second attachment/picture. But on my own I can ONLY obtain the...

An article in Quanta Magazine discusses the math behind the Navier Stokes equations, why they are so difficult to solve and whether they truly represent fluid flow: https://www.quantamagazine.org/what-makes-the-hardest-equations-in-physics-so-difficult-20180116/

Hello, After Favre averaging the momentum equation for an inviscid flow, the following can be obtained: $$\frac{\partial}{\partial t} \left(\overline{\rho}\tilde{u}_i \right) + \frac{\partial}{\partial x_j}\left( \overline{\rho}\tilde{u}_i \tilde{u}_j \right) + \frac{\partial...

I'm studying the Navier Stokes equations right now, and I've heard that those set of equations are invalid in some situations (like almost any mathematical formulation for a physics problem). I would like to know in which situations I cannot apply the NS equations, and what is the common...

I am pretty confused about how to write Navier-Stokes Equation into conservation form, it seems that from my notes, first, the density term with the pressure gradient dropped out. and second, du^2/dx seems to be equal to udu/dx. Why is it so? I attached my notes here for your reference.

Can you derive the heat conduction equation from the navier stokes equations (particularly the energy eqn)?

Hi all I am conducting a fluid analysis on water flowing through a subsea pipe. Having used navier stokes equation, i derived the equation for velocity in the r-direction (using cylindrical coordinates. But when initially solving the energy equation to determine temperature distribution I...

I was watching a lecture in which the professor derived the Navier Stokes Equations for const density and viscosity. He however skipped a step and directly went from one equation to another without giving any explanation. I have attached an image file in which the 2nd equation is derived from...

Homework Statement [/B] (a) Show that for an incompressible flow the velocity potential satisfies ##\nabla^2 \phi = 0##. Show further the relation for the potential to be ## \frac{\partial \phi}{\partial t} + \frac{\nabla \phi \dot \nabla \phi}{2} + \frac{p}{\rho} + gz = const.## (b)Write out...

Homework Statement Compare the COMSOL results to the analytical solution for laminar flow between flat plates. Assume no effect of gravity on the flow (g = 0). The comparison will involve obtaining the velocity at a point in the flow field and the ΔP/L term. For example, you can compare the...

Homework Statement Consider steady, incompressible, parallel, laminar flow of a film of oil falling down an infinite vertical wall (Figure P-1). The oil film thickness is “h” and gravity acts in the negative Z-direction (downward on the figure). There is no applied pressure driving the flow –...

hey pf! so when deriving navier stokes we have, from Newton's second law, \sum \vec{F} = m\frac{d \vec{V}}{dt} when deriving the full navier stokes (constant density) the acceleration term can be thought of as two pieces: a body change of velocity within the control volume and a mass flow...

Hi guys. Can somebody give mé examples for what the navier stokes equation normally are uset for.? I do not understand or Can see, what we use it for.? And Can someone help mé understand the equation? Like what each term is?

Homework Statement Good evening. First post on this forum! The problem I wish to state would take too long to write by hand so I thought it best to do so via attachment. The question I am stuck on is part d and, in fact, part e also. Homework Equations All relevant equations are given...

hey pf! i am studying fluid mechanics and was wondering if any of you are familiar with a flow around some geometry? for example, perhaps a 2-D fluid flowing around a circle? if so please reply, as i am wondering how to model the navier-stokes equations. i'll be happy to post the equations...

hey pf! i am studying fluid mechanics and we are reviewing navier/stokes equations. we have gone over a few problems, but i could definitely use practice on more. do you all have any suggestions that include solutions, not just answers, so if I am stuck i can see how to solve? problems...

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

I have been doing some serious review of fluids in order to prep for some CFD. I have been re-deriving the NS Equations in all of their various forms. Something seems to have cropped up that I have worked myself in circles about. Let's take the momentum equation in Conservative Integral form...

Does anyone know of a program that can give a good approximation of fluid flow based on the Navier Stokes equations? I know there are FEA programs out there that do linear flow, like in pipes, but what I'm looking for is general flow, for applications that aren't constrained to a pipe. Does such...

I need to solve 0=u[(d/dr)((1/r)*(d/dr)(r*Vo))] for Vo the prof gets Vo=Co*r/2+C1/r I don't get the same answer as him, does anyone know how to do this?

Hello! :smile: I am doing some review and it has occurred to me that I always confuse myself when I derive the the momentum equation in integral form. So I figure I will try to hammer through it here and ask questions as I go in order to clarify certain points. I know that there are many...

I recently came across the NS millennium problem and I read that uniqueness for the NS equations is unknown. I have two questions. First question, if solutions are found to be non-unique, would the NS equations have to be corrected? Second question, since uniqueness is unknown, if someone...

Hi I was reading Introduction to Fluid Mechanics by Nakayama and Boucher and I got lost in their derivation of the Navier Stokes Theorem. They basically started out with a differential of fluid with dimensions dx, dy, and b. Then they say that the force acting on it F = (F_x, F_y) is F_x...

Hi, If the viscosity in the NS equations was a variable, what extra equation is used to solve the NS equations? Thanks.

Homework Statement An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates. The two plates move in opposite directions with constant velocities U1 and U2. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. Use...

Hey!, I was repeating for myself a course I had from a earlier year, fluid mechanics. I looked at the derivation of the navier stokes equations, and there is one term that does not give meaning to me. Take a look at the x-momentum equation here...

Hi every one, I am having a few problems with some research I am doing. I put this in the PDE section as it seams related, but it is for a specific application and I am not sure that it wouldn't be better suited to the mechanical engineering section. I am wanting to find the pressure...

Hello! The incompressible Navier Stokes equation consists of the two equations and Why can't i insert the 2nd one into the first one so that the advection term drops out?! \nabla\cdotv = v\cdot\nabla = 0 => (v\cdot\nabla)\cdotv = 0

Hello! :smile: I am going over an example in my fluid mechanics text and I am confused about a few lines. My question is more about the math then the fluid mechanics. In fact, I doubt you need to understand the FM at all; if you understand Diff eqs, you can probably answer my question. I am...

I wasn't sure whether to put this in Aerospace, but decided on physics in the end. 1.) How do you factor a chemical reaction into the solution for the Navier Stokes equations? More precisely, how can you include the affects of a heat absorbing (endothermic), or heat releasing (exothermic)...

Hi, I've been doing some work with the NS equations. I've read a few papers by fellow undergrads that imply a relationship between the helmholtz-hodge decomposition and the pressure equation. As far as I can see, they're both separate ways of resolving the problem of keeping the flow...

(This is from the perspective of Geophysical Fluid Dynamics) In the Navier Stokes equations I am confused as to why there is both a pressure term and a gravity term. Is this pressure resulting from differences in densities and temperature differences alone? I would think that the gravity term...

Hello, I want, for obscur reasons which would lead us too far to explain, to split my flow into two component, one steady and another one non-steadyv = v_0 + v' I'm looking for a simple equation governing the evolution of this non steady components. The complete momentum equation gives...

Hello, I haven't studied PDEs much yet, but checked out what the Navier Stokes equations are. I think I understood meaning of the terms in Navier Stokes equations, and what is their purpose in defining the time evolution of velocity of the fluid, but I couldn't see any conditions for the...

Consider a stationary body within the flow of some fluid. I want to calculate pressure on the surface of the body. From the Navier Stokes (incompressible, stationary, no volume forces) equations, you would get something like: dp/dx=-rho(u du/dx+v du/dy+w du/dz)+eta(d²u/dx²+d²u/dy²+d²u/dz²)...

Hello, I need the Navier Stokes equations for compressible flow (Newtonian fluid would be ok) in cylinder coordinates. Can anybody help? Thanks

Hi, I'm trying to understand how to convert the cartesian form of the N-S equation to cylinderical/spherical form. Rather than re-derive the equation for spherical/cylindrical systems, I am trying to directly convert the cartesian PDE. I'm ok with converting the d/dx and d2/dx2 terms. What...

I recently came across the vector version of the Navier Stokes equations for fluid flow. \displaystyle{\frac{\partial \mathbf{u}}{\partial \mathbf{t}}} + ( \mathbf{u} \cdot \bigtriangledown) \mathbf{u} = v \bigtriangleup \mathbf{u} - grad \ p Ok, all is well until \bigtriangleup. I know...