I was so confused when my prof just randomly brought up strain rate tensor out of no where and boom, derived the Navier-Stokes equation. This really helped a lot and gave me a good direction to work with, thank you so much!
Wow amzing videos! These concepts are so hard to understand from the textbook (perhaps because of not knowing the correct math). Thanks a lot for sharing!
Nice video! Only one note. At 4:42 you say "It deforms in proportion with viscocity mu", but I think the correct should be "It deforms in proportion to the pressure τ" depending on the material, it has a different constant mu. The graphics are awesome!
Thanks, you are right that μ is material dependent. However, the deformation (represented by the strain rate tensor τ) is related to the viscous stress, in proportion with this mu. So you could both say that the deformation is in proportion with μ and with the stress. (Furthermore, remember that viscous stress is not only pressure (perpendicular to the surface), but also stress parallel to the surface.)
Can you please explain how you rewrite the last three terms of the equation at 1:22 as the dotproduct between the vector dx and the matrix grad(v)? If I multiply the row vector dx with components (dx, dy, dz) with the 3×3 matrix grad(v), then I do not get the equation from 1:22
Yes, so the terms in white are of the vector dx, the terms in red are of the gradient. Now in a dot product, you multiply the first component of the first vector with the first component of the second vector, then you add the second component of the second vector multiplied by the second component of the second vector and the same for the third components. That is what happens here as well. Then, since the dot product is commutative, you can see that I switched around the components (white and red, left to right and vice versa).
Thank you for your visually aided explanations. I wish to kindly bring your attention to two things: the velocity gradient tensor matrix (should not have been transposed) and your simulation of the 3D dilation (dilation was only along the x-axis).
How did you learn Manim by yourself? I mean I want to learn it too but where should I start learning it.I mean in which folder can I find the predefined methods,shapes,classes that can be used
Very beautifully explained. Please keep up the good work. This visual way of unravelling the mechanics is truly amazing. Thank you.
Thanks!
I was so confused when my prof just randomly brought up strain rate tensor out of no where and boom, derived the Navier-Stokes equation.
This really helped a lot and gave me a good direction to work with, thank you so much!
Somehow my professor derived it without using strain rate tensor
Thank you so much!!! I had been reading this stuff for months and couldn't understand it deeply. You made it so simple. Thank you Thank you Thank you!
Es muy bueno saber eso! Gracias!
Very intuitive and clear explanation. Congratulations
The best Visual explanation of such a deep concept
Share more videos like this.
I hope I saw this earlier.
it helps me alot. thanks
very helpful ! Thanks for this video, the visualization of the tensor is excellent
Wow amzing videos! These concepts are so hard to understand from the textbook (perhaps because of not knowing the correct math). Thanks a lot for sharing!
Dear Sir, thank you very much for your explanation video. It helped me very much in getting the big picture of velocity gradient
Thank you so much , this was so helpful!! I'm finally able to visualize what the tensor mathematics means
Super nice visuals!!
Awesome explanation
These are awesome!
Nice video! Only one note. At 4:42 you say "It deforms in proportion with viscocity mu", but I think the correct should be "It deforms in proportion to the pressure τ" depending on the material, it has a different constant mu. The graphics are awesome!
Thanks, you are right that μ is material dependent. However, the deformation (represented by the strain rate tensor τ) is related to the viscous stress, in proportion with this mu. So you could both say that the deformation is in proportion with μ and with the stress. (Furthermore, remember that viscous stress is not only pressure (perpendicular to the surface), but also stress parallel to the surface.)
Underrated video
Amazing! Thank you very much!!
Thank you so much!!!
Divergence is scalar, right? Why do you represent it with a column matrix?
Can you please explain how you rewrite the last three terms of the equation at 1:22 as the dotproduct between the vector dx and the matrix grad(v)? If I multiply the row vector dx with components (dx, dy, dz) with the 3×3 matrix grad(v), then I do not get the equation from 1:22
Yes, so the terms in white are of the vector dx, the terms in red are of the gradient. Now in a dot product, you multiply the first component of the first vector with the first component of the second vector, then you add the second component of the second vector multiplied by the second component of the second vector and the same for the third components. That is what happens here as well. Then, since the dot product is commutative, you can see that I switched around the components (white and red, left to right and vice versa).
Thank you for your visually aided explanations. I wish to kindly bring your attention to two things: the velocity gradient tensor matrix (should not have been transposed) and your simulation of the 3D dilation (dilation was only along the x-axis).
Awesome!!
Very nice video
Why do we can the velocity gradient tensor to be grad v^t and not grad v only
How did you learn Manim by yourself? I mean I want to learn it too but where should I start learning it.I mean in which folder can I find the predefined methods,shapes,classes that can be used
Watch the videos by Theorem of Beethoven, they explain it very intuitively!
Good. Amazing
thank you sir
Excelente.
Manim
Please make more videos