I What year were Navier-Stokes equations introduced?

[user079622]

Who and when first time introduced below equations(dont have to be in same notation, content is important)?

If this formula is always the same, what is contribution of Navier, what of Stokes, what changes all these years?

 

[Frabjous]

From https://www.amazon.com/Worlds-Flow-history-hydrodynamics-Bernoullis/dp/0199559112/?tag=pfamazon01-20

 

[user079622]

From https://www.amazon.com/Worlds-Flow-history-hydrodynamics-Bernoullis/dp/0199559112/?tag=pfamazon01-20
View attachment 347026View attachment 347027

Are you sure that equations from my post is from 1821?
Main formula remain the same from 1821 until today, what mean equations were rederived many times?

 

[Baluncore]

Between Navier in 1821-2 and Stokes report in 1846, many mathematicians and experimenters were trying to find a more tractable solution. The names dropped by Stokes in his 1846 discussion and summary of that period include; Airy, Cauchy, Challis, Coulomb, Dubuat, Girard, Green, Kelland, Lagrange, Navier, Ostrogradsky, Plana, Poisson, Power, and Russel.

Those attempts involved changing assumptions like the shape of the fluid parcel between square, tetrahedral, sphere and ellipsoid, considering compressibility or not, and how to handle circulation, while investigating viscosity and understanding the boundary layer.

It seems many wanted to avoid Navier's intractable equations, but a better alternative was not found.

 

[user079622]

I find this:

http://physics.uwyo.edu/~rudim/ArchHistExSci56_2002_FiveBirthsOfNavierStokes_Sum15.pdf

"Éléments d’analyse
des articles historiques
de Navier
La contribution historique de Navier aux équations du mouvement des flui-des a fait l’objet d’une présentation à l’Académie des sciences le 18 mars 1822, et se trouve développée dans deux contributions écrites :
– « Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molécules », Annales de chimie et de physique, tome XIX, 1821 ;
– « Sur les lois des mouvements des fluides » (lu à l’Académie des sciences le 18 mars 1822), Mémoires de l’Académie des sciences, sciences mathématiques et physiques, tome VI (1823), 1827.

L’article de 1821, que l’on peut consi-dérer comme article fondateur, secontente de développer les conséquen-ces de l’hypothèse sur l’expression locale de la force de viscosité (il ren-voie d’ailleurs pour les détails à une autre contribution récente de Navier, elle aussi de 1821, relative aux lois de l’élasticité, qui contient une mise en équations et un calcul formellement semblables), puis injecte cette force supplémentaire dans les équations d’Euler."

 

[user079622]

From https://www.amazon.com/Worlds-Flow-history-hydrodynamics-Bernoullis/dp/0199559112/?tag=pfamazon01-20
View attachment 347026View attachment 347027

What is your conclusion/selection, what was birth year, 1821?

 

[user079622]

Can someone explain what are this equations and translate in modern notation?
source: https://gallica.bnf.fr/ark:/12148/bpt6k6571078m/f250.item

 

[Baluncore]

"On the development of the Navier-Stokes equation by Navier"
For the notation used by Navier see:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?lang=en#
Look at section 4 of this text.

My copy of the .pdf came from:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?format=pdf&lang=en

 

[user079622]

"On the development of the Navier-Stokes equation by Navier"
For the notation used by Navier see:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?lang=en#
Look at section 4 of this text.

My copy of the .pdf came from:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?format=pdf&lang=en

What are differences in equations from https://gallica.bnf.fr/ark:/12148/bpt6k6571078m/f250.item and https://perso.crans.org/epalle/M2/EC/Histoire/Navier1822MemoireSurLesLoisDuMouvementDesFluides.pdf?

 

[berkeman]

What are differences in equations from https://gallica.bnf.fr/ark:/12148/bpt6k6571078m/f250.item and https://perso.crans.org/epalle/M2/EC/Histoire/Navier1822MemoireSurLesLoisDuMouvementDesFluides.pdf?

Why don't you read the papers and tell us?

 

[user079622]

Why don't you read the papers and tell us?

Because I dont understand France and cartesian hieroglyphics.

 

[berkeman]

Because I dont understand France and cartesian hieroglyphics.

You are asking too much of others to do your work for you. Thread is closed.