# Questions tagged [navier-stokes]

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

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### Is there a formulation for (self-)accelerating fluid flow through permeable medium?

I have a permeable system where is an accelerating fluid flow. Imagine a sponge that is squeezed. The fluid starts at rest, accelerates and flows out from the sponge. How to calculate the fluid speed? ...
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### Stokes law in 2-dimensions

Stokes' law states that force on slow moving sphere (i.e. $Re\ll1$) in liquid is $$F_d = 6 \pi \mu R V$$ In two dimensions we are in trouble (flow around disk in 2d or around cylinder in 3d), ...
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### How does the dissolution of salt affect the solution density?

Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
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### Why is the Reynolds number “the way it is?” Why is its order the way it is?

Why is the Reynolds number “the way it is?” Why is its order the way it is? I'm not sure if this is an appropriate question for this context, but I would like more intuition on this matter and so I'...
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### Velocity profile of a viscously damped wave

For a test case, I want to determine the velocity profile of a viscously damped standing wave. By linearizing the density ($\rho=\rho_0+\rho'$) and velocity ($ux=ux'$), the continuity and Navier-...
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### No diffusion term in conservation of mass in Navier-Stokes equations?

I have followed derivations of the Navier-Stokes equations and I can see how the various terms arise in the "main equation", the momentum conservation equation. However I don't understand why the ...
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### Does a whirlpool(vortex in water) continue in air(vortex in air),and when does a vortex stop?

First part: The question is both about the continuity of the water vortex(whirlpool) to vortex in air in time and in space. About continuity in time,does the vortex of the water slowly produce a ...
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### Why can't the Navier Stokes equations be derived from first principle physics?

At the 109th UCLA Faculty Research lecture, Seth Putterman gave a talk on Sonoluminescence. During the lecture he emphasized that "The Navier Stokes equations cannot be derived from first principles [...
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### Incompressible Navier-Stokes pressure solve in simulations

I am a complete newcomer when it comes to fluid simulations. I'm currently working through some tutorials to understand the idea of of the discretized Navier-Stokes equations for numerical simulations....
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### Solve unsteady state Bernoulli equation for flow in a pipe

I am an engineer studying an unsteady-state flow through a pipe. The Pipeline has been cleanly cut into two halves, without deforming the cylindrical form of the pipe, exposing the contents to ...
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### Exact solution to a 2D/3D Poiseuille flow in a channel

Hi everyone and thank you in advance for any help. I am struggling to find an analytical solution to either a 2D or 3D Poiseuille flow in a rectangular duct. All I can find is 1D example. Can someone ...
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### 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 ...
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### Could Navier-Stokes equation be derived directly from Boltzmann equation?

I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over ...
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### Fluid flow: Force acting on the fluid and the Navier-Stokes equation

Consider a one dimensional fluid flow in a rectangular tube. Typical streams are the poiseuille streams. Consider the case in wich we apply a force on the fluid. The Navier-Stokes equation (for ...
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### Why hydrodynamic turbulence without heat terms matters?

A lot of research is made on turbulence in "pure" Navier-Stokes equations (NSE). There is a notion of energy cascade when energy comes from larger scales to lower scales and than dissipate. However ...
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### Physical interpretation of the change of diffusion term in navier stokes equations

In the Navier-Stokes Equations, there is one term accounting for convective flow and one term for diffusive flow. At high flow rates, the diffusive term becomes much smaller compared to convective ...
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### What is the apparent viscosity in shear thinning turbulent flow through a pipe? [duplicate]

The explanation of shear rate in laminar flow is straightforward: We imagine small layers of fluid that glide on each other. Now, in turbulent flow, this does not work as there are no layers. If I ...
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### What's the shear rate in a turbulent flow?

The explanation of shear rate in laminar flow is straightforward: We imagine small layers of fluid that glide on each other. Now, in turbulent flow, this does not work as there are no layers. I'm not ...
I am looking for the derivation of Momentum Equations for Micropolar Fluid \rho\frac{D\vec V}{Dt}=-\nabla p+(\mu+k_1^*)\nabla^2\vec V+k_1^*(\nabla\times\vec N^*)+\vec J\times\vec B ,\\ \rho j^*\...