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.
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!
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.
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!
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.
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!
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
Hi Engineer Leo, many thanks for the great explanation video. But I have one question at 12:16, how can we write dx/dt, dy/dt, dz/dt as u, v and w respectively. This step I could not fully understand.
definition of nabla is wrong, and thank you it was much clear, as a mathematician i was looking for the term of pressure why there is a nabla you did not mention it :(
Hi Leo, Thank you for the playlist. Here you did mention about doing a video set about obtaining the numerical solution for NS equation. If possible, can you please consider doing that 😊
Great video! you have a good ability to explain it well. An example of application would be equally helpful.I am writing a book, and one chapter is about asteroid impacts, the momentum of the impacting object creates incredible pressure and temperature liquefying the impact area and creating a viscous area long enough to create circular ripples. Q. Can we apply the Navier Stokes Equations to an impact crater as its forming? thank you kindly.
I believe so, but some aspects of the rheology of this liquefied area must be considered. Probably it will not be a Newtonian fluid, so the Navier-Stokes in their classical form could not be used. Perhaps a Herschel-Bulkley model or a Power-law model would be more adequate. Good luck on your writing!
I have doubt in the terms you derived for shear stress xz and yz shouldn't stress xz =ų(dw/dx + du/dz) and stress yz = ų( dw/dy + dv/dz). watched another video and confirmed it.
Hello! Can you please explain, why in wikipedia the viscosity term is called "diffusion"? As well as the transportation of the velocity itself term is called "divergence"? en.wikipedia.org/wiki/Navier-Stokes_equations#Incompressible_flow In your explanation everything is so clear. However in wikipedia it is a mess...
I'm trying to program a fluid, and I ran into a problem. can you tell me the input and output of the naiver stokes equations. also is there an version of the navier stokes equation with one unknown? thanks
No, they don't change. To be clear, I wasn't talking about the nature of the forces itself, that's another discussion. On this video I talk about how the forces appear and behave in the context on the Navier-Stokes equation. Regarding your statement about the nature of the forces, I believe only the gravitational force can be considered a volumetric force, which acts on the whole of a small volume of fluid. When deducing the stress tensor, the pressure and viscous stresses act on the surfaces of the control volume.
Well see ruclips.net/video/vxJrb7JKigQ/видео.html you're naming pressure and viscous forces as volumetric forces. Again, even when you are doing a volumetric balance, the nature of the forces doesn't change. Maybe you can say that these are volumetric terms coming from surface forces.
Muito produtivo e been explicativo! Ja quero ver os próximos! (Apenas indicaria um cuidado com o Ingles, pronuncias erradas e muito sotaque, mas isso melhora com a prática (: )
![Kodak Black - Catch Fire [Official Music Video]](http://i.ytimg.com/vi/A4ch-olIuZo/mqdefault.jpg)
Check out our course in Udemy about the Navier-Stokes equations: www.udemy.com/understanding-the-navier-stokes-equations/
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.
Auday Sami Thank you very much for your feedback and suggestions! I'll try to implement them in the next videos. Best regards!
Sir, your explanation beats all I had seen before. Easy, logical, consequent. Thank you so much!
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!
Glad it was helpful!
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.
You're welcome!
Good explanation, especially the term convective acceleration ' velocity is the transporter of itself '
Glad you liked it!
Dude.. this is really helpful for my thermfluids 2 class here in the UK! Thanks for your work
You're welcome! Keep up the feedback!
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!
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.
Thanks for the feedback!
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!
Obrigado! Fico feliz em saber que tenhas te inspirado. Boa sorte com o seu canal. Abraço
Excellent! Really clean explanation. Please continue doing more videos!!
Thanks very much!
Excellent work! Look forward to this exciting series. Thank you very much!
You're welcome! On the next video I'll talk about the many mathematical representations avaiable for Navier-Stokes.
very clear and perfect explanation!!thank you so much
Leo, very good, down to earth presentation. Please use more graphics, for instance for the stress tensor. I will follow you.
Thanks, will do!
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
Best explanation on RUclips. Thank you very much
Thanks!
You explain this very well thanks please post more
Thanks, I will!
BRASIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIL!!!!
Hi Engineer Leo, many thanks for the great explanation video. But I have one question at 12:16, how can we write dx/dt, dy/dt, dz/dt as u, v and w respectively. This step I could not fully understand.
Excellent presentation!!!
Amazing work! waiting for next video. Thanks a lot
Thank you!
Thanks for such an understandable video.
Dear Leonardo, Great explanation and very informative.
Where can I watch the equation for pressure also?
Thank you for your contributions.
I have posted a video about the Poisson equation
Good work. Very clear explanation!
Thank you very much!
definition of nabla is wrong, and thank you it was much clear, as a mathematician i was looking for the term of pressure why there is a nabla you did not mention it :(
Thank you, now i understand about 70%, except for that volume accleration thing (triangle pointing down),consitutive equation and tensor, very strange
great tutorial and informative. Thanks a lot
Glad you enjoyed it!
Thank you for explaining it so well =)
Hi Leo, Thank you for the playlist. Here you did mention about doing a video set about obtaining the numerical solution for NS equation. If possible, can you please consider doing that 😊
Great video! you have a good ability to explain it well. An example of application would be equally helpful.I am writing a book, and one chapter is about asteroid impacts, the momentum of the impacting object creates incredible pressure and temperature liquefying the impact area and creating a viscous area long enough to create circular ripples. Q. Can we apply the Navier Stokes Equations to an impact crater as its forming? thank you kindly.
I believe so, but some aspects of the rheology of this liquefied area must be considered. Probably it will not be a Newtonian fluid, so the Navier-Stokes in their classical form could not be used. Perhaps a Herschel-Bulkley model or a Power-law model would be more adequate. Good luck on your writing!
Thank you kindly
Great explanation!
Overall, a very detailed and understandable video. Keep it up.
A Doubt though: How is Stress tensor (Tau) equal to "Mu times Gradient of v (Mu Del v)"
On this video I take a closer look on the stress tensor: ruclips.net/video/Ds3PdJz14HE/видео.html
That's how viscosity is defined
I have doubt in the terms you derived for shear stress xz and yz shouldn't stress xz =ų(dw/dx + du/dz) and stress yz = ų( dw/dy + dv/dz). watched another video and confirmed it.
Thank you! It was useful.
You're welcome!
Thank you. It helps a lot.
Glad to hear that!
Thank You so much, sir.
I have a question regarding its application, like how do we apply this equation?
Excellet explanation!!
Glad it was helpful!
Nice explanation,i've a question how tau=mu*neblavelocity? how we can derive it?
It's a constitutive equation, derived from physical experiments for Newtonian fluids. You can't derive it mathematically.
@@engineer_leo can you give me link how to derive it?
Sir make a video on fracture mechanics of HSC
Hello! Can you please explain, why in wikipedia the viscosity term is called "diffusion"? As well as the transportation of the velocity itself term is called "divergence"? en.wikipedia.org/wiki/Navier-Stokes_equations#Incompressible_flow
In your explanation everything is so clear. However in wikipedia it is a mess...
Great! keep up the good work.
Thanks!
It rouines my life atm in my master career
sir can u provide the difrential equation solution of momentum equation
congrats bro
Excellent work!
Thanks again!
I'm trying to program a fluid, and I ran into a problem. can you tell me the input and output of the naiver stokes equations. also is there an version of the navier stokes equation with one unknown?
thanks
Sorry, could you elaborate more on your problem?
Thanks dude
very informative video
Part 2 is avaiable! Check it out!
Can you provide the document from which you are explaining the link in the description if possible
@@abdulraqeeb4942 yes, I'll provide as soon as possible.
Thank you so much, it is very helpful video
Thanks!
Obrigado cara. Ótimo vídeo
Obrigado!
Pressure and viscosity forces aren't volumetric forces
Yes they are, as written in this form for the NS equations.
The nature of the forces doesn't change with the form you use to express the force balance.
No, they don't change. To be clear, I wasn't talking about the nature of the forces itself, that's another discussion. On this video I talk about how the forces appear and behave in the context on the Navier-Stokes equation.
Regarding your statement about the nature of the forces, I believe only the gravitational force can be considered a volumetric force, which acts on the whole of a small volume of fluid. When deducing the stress tensor, the pressure and viscous stresses act on the surfaces of the control volume.
Well see ruclips.net/video/vxJrb7JKigQ/видео.html you're naming pressure and viscous forces as volumetric forces. Again, even when you are doing a volumetric balance, the nature of the forces doesn't change. Maybe you can say that these are volumetric terms coming from surface forces.
Good point. I'll clarify this on another video, probably the part 3 of this series.
Thank you! :)
Muito produtivo e been explicativo! Ja quero ver os próximos! (Apenas indicaria um cuidado com o Ingles, pronuncias erradas e muito sotaque, mas isso melhora com a prática (: )
Bem*
Obrigado!
Grava em português também! Vamos impulsionar nosso povo.
Hey bro, I got exams coming up, do u kind helping me abit
Yes. You can contact me via Facebook, Twitter and LinkedIn
Errata: missed the unit vectors in the nabla operator.
Another Errata: The tensor expansion (using Newton's viscosity formula) was interchanged for txz and tyz.
On this video ruclips.net/video/Ds3PdJz14HE/видео.html I highlight this error and provide some more details on the stress tensor.
Do nada tava entendo o inglês tão bem até reparar que é brasileiro
very helpful!
Thanks!
.
👍👍👍👍👍
Such a good explanation, good job!