Demystifying the Navier Stokes Equations: From Vector Fields to Chemical Reactions
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- เผยแพร่เมื่อ 31 ก.ค. 2024
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Welcome to a video all about the Navier-Stokes Equations, one of the most renowned mathematical equations that govern the dynamic motion of fluids. Join me as we embark on an enlightening journey, unravelling the essence of Navier-Stokes Equations, and showcasing captivating real-world applications and solution examples that will ignite your curiosity whether it be in Chemical Engineering, Nuclear Fusion or Computational Fluid Dynamics! Whether you're enthused by chemistry, technology, or simply eager to expand your knowledge, this video will hopefully give you some fascinating thoughts and insights. Please like, subscribe and share the video if you enjoyed it!
Video contents:
0:00 - A contextual journey!
1:25 - What are the Navier Stokes Equations?
3:36 - A closer look...
4:34 - Technological examples
6:11 - The essence of CFD
7:17 - The issue of turbulence
8:07 - Closing comments
Music by Vincent Rubinetti
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Great visualization and explanation! One thing to suggest as others have mentioned is to lower the audio of the background music. Otherwise, this is an excellent video and I hope you make more!
Thank you for the feedback :).
Great Video! One thing that pops to Mind is We need New Thinking and New Math Tools: We need to over come the difficulties in Working with Non-Linearities!!! Something as revolutionary as when Calculus was discovered and Developed!!!
Thanks, and yes spot on! AI coould very well be this given how apt it is for extracting hidden non linearities! :)
When people say underrated they normally mean they like your content but this is very very underrated, I hope that you will soon get the attention you deserve
Thank you :)!! More videos coming soon!
You might want to re-mix the sound on this video and set the music lower. It's hard to hear what you are saying in several places because of the music being too loud.
Would you consider leaving on a red cloth regular table lamp in the bedroom and a tubular vintage oval bulb desk lamp in the office, and seeing which type of bulb burns out first after a while, "doing an experiment" ?
I got the same response for my videos :) :) :)
@@MathPhysicsEngineering Would you consider leaving on a red cloth regular table lamp in the bedroom and a tubular vintage oval bulb desk lamp in the office, and seeing which type of bulb burns out first after a while, "doing an experiment" ?
Thank you for the feedback :) - noted, I will ensure this is balanced better for future videos. Didn't think it was too bad when posting, but on re-listening the background music could definitely do with toning down slightly in places.
I’m using my iphone speakers (not headphones or external speakers).
It wasn’t an issue for me personally.
Thank you for those amazing visualizations!
Glad you like them! :)
Excellent video! Chemical engineering PhD student here.
Thank you :) !! Hope the PhD is going well - I see you're doing it in photochemical nitrate processes from your vid? Sounds very fascinating!
Retired PE in Chemical Engineering with career focused now on fishing…always found these fascinating
You leave on 2 table lamps with 2 different kind of bulbs. You wait to see which type of bulb burns out first after a while and how long it takes for each one.
Would you consider this example to be a scientific experiment ?
@@javiercorreapr9977You leave on 2 table lamps with 2 different kind of bulbs. You wait to see which type of bulb burns out first after a while and how long it takes for each one.
Would you consider this example to be a scientific experiment ?
@@tacoexpressSEEDEEholeeveryones Hi. Sounds like reliability engineering testing but maybe not. Regards
One of the best video's on the topic! It's a shame it hasn't been seen more but this easily has a million views in its future!
Thank you :)!! Glad you enjoyed the video!
Interesting presentation! 😊
Thank you :)! Glad you enjoyed it!
Awesome and amazing. Great overview. Thanks. (I'm a subscriber now)
I'm very happy you found it useful, and thank you for subscribing - more videos coming soon!
the music is very loud, please turn it off or quieter in the next vids. Besides that, it's a very clear explanation thanks
Thank you, and yes I'll lower the music volume for future vids :).
Thanks for clearing the confusion
No problem, I'm happy the video has helped! :)
Great information:noisy, loud music makes what is said hard to hear.
I'm glad you found the video informative! Big thank you for your feedback, will defo bear this in mind going forward :).
Can you please redo the audio on this great visual explanation video.
Thanks for your comment and feedback on the quality. I didn't think the audio balancing was too big of an issue on uploading, but on re-listening there are several places in particular where the vocal audio gets partially overpowered. I don't plan on re-uploading the video as I allude to in my responses to similar comments - I will ensure no future video has this balancing issue though :).
@@ChemEfy
Thanks for the reply!
Keep up the great work.
I feel purpose of life is in understanding science but not in religion. So I have special respect science for content creators like you.
On a separate note… I had to quit this video in the middle and when I left I felt like storm passed away and felt very peaceful.
First, I think it's quite admirable of wanting to explain something as complicated as Navier-Stokes to the layman. However, I do think you do skip over important groundwork that prevent people from truly grasping what these equations say; yes, in essence, Navier-Stokes are just Newton's laws applied to fluids, but why certain terms are analogous is not at all obvious and requires one to understand what those operators really mean. You are already working with some pretty neat visualisations; perhaps build more on that and use it to explain what those expressions mean; nobody needs to understand how to calculate the divergence, curl, etc. in order to understand what ∇u represents. Finally, in order to talk about discrete solutions, I think it's important to lay down what differential equations are and how you'd go about solving them numerically; I don't think it's needed to talk about Eulerian (i.e. grid-based) solutions in order to show how we can still use Navier-Stokes despite having no exact solutions.
Thank you for your comment and feedback, both positive and negative. It was definitely a balancing act re. the content as to what to include and what not to include. Indeed some loose jumps on pre-requisite knowledge for full mathematical understanding are made for sake of keeping the video within a manageable length especially given the limited evening time after work to make them. The examples you give are very pertinent + clear so thank you for this 😊 - there is certainly a strong argument to be made for including what you mention. Just to mention my perspective when making, for me the link between operators and Navier Stokes was never easily explicit, with vorticity (via curl), and divergence (via flux/continuity equation) not having an explicit physically intuitive link into the final form of the simplified momentum balance. Perhaps I could’ve weaved this in though instead of leaving for another video. The grid-based approach was mentioned to link to a more typical solution method employed in CFD/intuitively demonstrate how a velocity profile can be built up in 2D/3D. I will definitely bear your suggestions in mind going forward though - thank you once again😊.
excellent, kindly tell me which software you use for your virtualization
Prolly manim
So it depends on what it is that's being animated but I use a mixture of different softwares - manim, powerpoint etc. Hope this helps :)
What do you use for edit?
I use Shotcut to edit at the moment :).
@@ChemEfy You think it could be done with PowerPoint?
@@ianthehunter3532 Hmm, I can't say I'm very familiar with Powerpoint's video editor so I think someone else could probably give you a better answer. Based on my experiences, which admittedly could be a lot broader, I think some of it could be edited on powerpoint - depends what you're trying to make. If in doubt, visualize what you're trying to make and give it a try would be my take :).
From where do you get the time derivative of the pressure? The time derivative of the pressure doesn't appear in Navier-Stokes equations.
You're absolutely right - there isn't a time derivative of pressure in Navier Stokes, and I don't believe there is one in the video either.
From where do you get the values of the pressure for different time values, when we don't have the time derivative?
@@jostpuur In a number of contexts typically the pressure field is something you measure with pressure sensors or predict/forecast. In other situations the pressure field is computed along with the velocity field too.
lower the music it's hard to hear your voice
Thanks for the feedback, I've responded to similar comments on this front. Will ensure balancing issues are not an issue for future videos :).
Why is the music so loud???
Thanks for your feedback :) - didn't think it was too bad when uploading, but on re-listening it does need toning down in places. Will ensure this is not a problem for future videos :).
I have solutions to all of the millennium prize problems I'm just waiting for them to raise the price
:D :D :D
Sounds like you're sitting on a jackpot! :)
Why the music...?
Thank you for the feedback! :)
Kinda thought that thumbnail was a block from Minecraft
:)
You might want to consider re-uploading the video with balanced audio. It has good quality, but as others have already pointed out, it’s unfortunately hard to hear you speaking.
Thanks for your comment and feedback on the quality. I didn't think the audio balancing was too big of an issue on uploading, but on re-listening there are several places in particular where the vocal audio gets partially overpowered. I don't plan on re-uploading the video as I allude to in my responses to similar comments - I will ensure no future video has this balancing issue though :).
I loved the video, next time have a purse and think moments, edgerunner
Thank you, I'm happy you enjoyed it! :) You make an excellent suggestion - will bear in mind for future videos - thank you!
The music is way louder than the voice, please lower it a bit, for the rest, great explanation
Thank you, and yes I'll lower the music volume for future vids :).
gravity and em fields are internal forces, not external forces.
Hi, thanks for your comment :). Gravity and electromagnetic fields are external forces in fluid dynamics because they act on the fluid from outside, unlike internal forces like viscosity that arise within the fluid itself. Hope this helps!
@@ChemEfy Hi! I don't think so. External forces are surface forces. Internal forces, also called body forces, act on the mass inside the enclosed volume, which in this case can be gravity or EM fields.
@@PedroCarvas Actually, in fluid dynamics, external forces can include both surface forces and body forces. Internal forces are the ones arising from interactions within the fluid, like viscous and pressure forces. Gravity and EM fields are considered externaly imposed forces manifesting themselves as body forces from the fluid's perspective because they originate from outside the fluid and act uniformly throughout it. Hope this clears things up!
Wait i thought Navier-Stokes equations model all fluids, not just newtonian-incompressible case? O_O
the most general form of navier stokes is all fluids, this video uses a simplfed version
To model non-newtonian fluids and compressible fluids, you have to keep viscosity and specific mass inside the vector operators, since they are functions of space and time. The only real limitation of Navier-Stokes lies in the continuum hypothesis, when this hypothesis fail, you have to use statistical mechanics.
Very pertinent comment :) - as others have already commented in reply, if I lift the incompressible, newtonian, isothermal assumptions you'll get a more general version of Navier Stokes which can apply to a wider range of fluids. I quote a common simplification of this general form in the video. In reality, the viscous term has the potential to house a more complex relation (e.g. a Non-Newtonian fluid like shear-thinning, shear thickening, Bingham plastic etc.); viscosity/density will not be constants and will vary with temperature/local concentration variations as the video mentions in the latter half, amongst other things which can complicate the equation set. Hope this helps :)
Can you lower the music please and re-upload? For a non native, it’s very difficult to hear what you’re saying. Thanks!
Thanks for your comment :). I don't plan on re-uploading the video as I allude to in my responses to similar comments - I will ensure no future video has this balancing issue with the music though :). Hope this is ok!
Lower the background music...
Thanks for the feedback, I've responded to similar comments on this front. Will ensure balancing issues are not an issue for future videos :).
Other wise great and helpful video@@ChemEfy
@@rostamr4096 Thank you! I'm glad you found it useful :)