Understanding the Navier Stokes Equations

On this video I talk about the principles behind the Navier-Stokes equations and some common misconceptions. General properties of the Navier-Stokes equations are derived from the Newton's Second Law of motion. Please comment and subscribe!

[Auday]

Leonardo, Great Video for a complex subject, I can see that you tried a very good level of explanation to ease things up for us, (Navier - Stokes) are just a little complicated unless you are working with them on regular basis
Area for improvements:
1. Put some grease to the chair to stop squeaking :)
2. Try to make more graphical presentations to explain your ideas in simple manners.
3. Write on your presentations, the assumptions and limitations with the boundary conditions required to satisfy each equations.
4. Try to make each video shorter.

Please keep making these good videos and thank you very much for your efforts.

[artemiyf]

Sir, your explanation beats all I had seen before. Easy, logical, consequent. Thank you so much!

[JohnLittle]

Dear Brother Engineer Leo,
I just want you to know that I really like this video and your presentation in it. It is helpful for me because you explained the reasoning of your argument clearly and simply and in a good order and at a pace (not too fast) which I can follow.
Thank you very much!

[VinayakKuttu]

I've been trying to understand the essence behind these complex set of equations and after watching your video, I feel confident
Thank You @engineerleo and keep posting informational videos.

[oldhounddog]

It's sad that there are only 102 comments here. I've spent a lifetime studying math and science. The Navier-Stokes equation is the hardest thing I have studied. The fact that it comes from F=ma does not make it any simpler. Yours is the best explanation I have seen online for how the equation is developed.
I will keep going at it till I get it. Thanyou!

[ahmedalnemr]

Good explanation, especially the term convective acceleration ' velocity is the transporter of itself '

[BatistaRX]

Dude.. this is really helpful for my thermfluids 2 class here in the UK! Thanks for your work

[neeldutta]

Great video! It really helps that you point and click and rearrange terms as you work with them. In class, the powerpoint only moves in one direction, and doesn't give an indication as to how things fit together.

[MaarceloHenrique]

Leonardo, meus parabéns cara!
Fez algo que até então eu achava super complicado ficar simples e palpável pra mim!

Pretendo iniciar um canal no youtube como o seu, falando sobre engenharia e explicando conceitos assim como você fez neste vídeo, muito obrigado pelo conhecimento compartilhado e pela inspiração!

[viniciusgoncalves]

Excellent! Really clean explanation. Please continue doing more videos!!

[ThePlasmatech]

Excellent work! Look forward to this exciting series. Thank you very much!

[gkzjthh]

very clear and perfect explanation!!thank you so much

[beatricemunera]

Leo, very good, down to earth presentation. Please use more graphics, for instance for the stress tensor. I will follow you.

[BlackIcexxi]

Best explanation on Youtube. Thank you very much

[toseektruth]

Amazing work! waiting for next video. Thanks a lot

[MrChemenger]

You explain this very well thanks please post more

[MohammedKhantheacademician]

Thanks for such an understandable video.

[Igdrazil]

Little mistake with NABLA operator which is not the divergence operator d/dx + d/dy + d/dz as you wrote it (as a sum) but a vector.
And it is at minimum dangerous, and "gramatically" illicite, to write the convective accélération in the form : u•Du ! Without parenthesis it can lead to confusions..It should be writen (u•D)u, where the formal scalar product u•D acts like a linear map, on the right input, which is again the vector u, in this context. In components, this LINEAR MAP (which is a second rank (1, 1) TENSOR), acts like a 2 by 2 matrix on the right input u vector components; the result, the output, the image of this action, gives à vector. So the parenthesis are NECESSARY to write things correctly : (u•D)u .
Best regards

[kiliandietrich]

Thank you for explaining it so well =)

[shafagh_projects]

great tutorial and informative. Thanks a lot