I Claude Naiver work on Navier-Stokes equations

  • I
  • Thread starter Thread starter user079622
  • Start date Start date
  • Tags Tags
    equations Stokes
AI Thread Summary
Claude Navier's two works on fluid motion, "Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molecules" (memoire 1) and "Sur Les Lois du Mouvement des Fluides" (memoire 2), were both written in 1821, with the second published in 1822. Memoire 1 is significant for introducing the viscous term μ∇²u, which is crucial for understanding fluid dynamics. However, there is difficulty in locating a PDF of memoire 1, as it appears to be unpublished. The formulation discussed in the thread aligns with Navier's contributions in memoire 1, although the exact notation may differ. Overall, these works laid foundational principles for the Navier-Stokes equations.
user079622
Messages
449
Reaction score
29
I am interested what are main differences/news in two Claude Navier works "Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molecules"- memoire 1 and "Sur Les Lois du Mouvement des Fluides" memoire-2?

Are both works written(not published) in 1821? Does memoire 1 introduced visocus term μ∇2u?

I cant find pdf of memoire 1..

"Sur Les Lois du Mouvement des Fluides"
https://perso.crans.org/epalle/M2/EC/Histoire/Navier1822MemoireSurLesLoisDuMouvementDesFluides.pdf

Is this formulation(dont have to be same notation) what Navier introduced in 1821 memoire 1?
0bZdvG1C.jpg
 
Last edited:
Physics news on Phys.org
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Off resonance driving of a MW/RF cavity'

Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
View full post »

Similar threads

I Assumptions for Navier Stokes equations in this system
Replies
3
Views
1K
A Why are the Navier-Stokes equations inconsistent in this case?
Replies
18
Views
2K
I Deriving Navier-Stokes Equation
Replies
4
Views
2K
I Divergence of the Navier-Stokes Equation
Replies
1
Views
5K
A How to Solve Isothermal Incompressible Navier-Stokes for Compressible Fluid?
Replies
20
Views
6K
Navier-Stokes equation for parallel flow
Replies
1
Views
2K
Solving the Navier-Stokes Equation for v(angular)
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top