The many forms of Navier-Stokes

[@BatistaR0X]

I have only watched two of your videos and they are of superior quality in terms of your way of explaining man. And i am really impressed by your level of humbleness by saying leave any criticism comments. Your videos are really helpful for fluid mechanics students

[@yassinkissami9126]

Man, you have literally saved me after I have been going crazy with these books that cant explain anything clearly!! Thanks Alot bruv..

[@engineer_leo]

You're welcome!

[@antoine1407]

One of the best video about Navier- Stokes equations, thank you so much

[@toseektruth3764]

Leonardo: Please check in 30:44. I think there is a correction in convective acceleration term numbering. It should u1, u2 and u3 in the matrix form. Please correct me if I am wrong.

[@engineer_leo]

You are correct. Each line corresponds, respectively, to the derivatives of u1, u2 and u3.

[@oskarloeprecht7579]

Thanks a lot man! I've been trying to understand the navier stokes equation in einsteins notation for hours, now i've got it!

[@engineer_leo]

You're welcome!

[@erisawante1328]

Thanks for these well explained videos on Navier-Stokes aquations, I appreciate your work and your time, I salute you Professor . Do you have a video on axisymmetric Navier-Stokes equations?

[@djdelta777]

Just what I needed. And so clearly explained. Thanks

[@engineer_leo]

Glad it helped!

[@bomgulder]

Thank you very much for your time. I have benefited from it

[@vioco]

I was looking for the Stokes form of NS.

[@omarasbun9188]

Hello loved your videos, is there any way to download the notes you made for this video?

[@trololollolololololl]

very nicely made, especally einsteins notation now I understand it

[@pameladahl9588]

Muito didático, Leonardo! Vou passar para meus colegas do LASME/PEN na UFRJ.
Maybe later, something for compressible fluids?

[@engineer_leo]

Muito obrigado! Thanks! I'll try to make some video about compressible fluids later. Best regards

[@CallumSamuels]

Great video! Thanks

[@slim590]

can you talk abour kronecker delta ?

[@turtleindia417]

Hey Leonardo, thanks again for detailed mathematical forms of NS. :)
Just one clarification reqd: towards the end of the video, in the compact form of NS, shouldn't the RHS be "Partial Diff of [Sigma]ij wrt xj", you used "xi" !

[@engineer_leo]

You are correct. It is "j" instead of "i" in the partial derivative of the stress tensor.

[@fetenadisasadiribsa9704]

it is helpful lecturer. but how can we drive Navier-Stokes equation of elastic solid body??????

[@engineer_leo]

Then it is not called "Navier-Stokes" equation. There is something called "Navier equations", which is the equations Navier derived for elasticity (solids). It would be a interesting topic for a video.

[@AmirrezaEghbali-w4r]

i just can appreciate you , 👍🙏🌹

[@dilharawickramasinghe7121]

Very helpful. Thank you.

[@engineer_leo]

You're welcome!

[@williamschacht]

Excellent work!

[@engineer_leo]

Thanks!

[@LiuyoMZ]

Ótimos vídeos!

[@slim590]

you have made a mitake in the equation around 31 mins. mistake is in du1/dx1 vectors

[@yasirghani7017]

thank you

[@slim590]

Thank you 💓💓💓💓 (no homo)