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Description and Derivation of the Navier-Stokes Equations
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- Опубликовано: 21 окт 2017
- The equations of motion and Navier-Stokes equations are derived and explained conceptually using Newton's Second Law (F = ma).
Made by faculty at the University of Colorado Boulder, College of Engineering & Applied Science.
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![[CFD] Conservative, Advective & Material Derivative forms of the Navier-Stokes Equations](http://i.ytimg.com/vi/ljdv4T2U464/mqdefault.jpg)
so this is what it feels like to be TAUGHT something
*gratitude*
There should be an organization that gives awards for best educational youtube videos each year. This one deserves an award.
That's among the most meaningful 11 minutes I have ever spent
The amount of intuition conveyed by the instructor to the audience is absolutely unbelievable
Thank you
Oh my god, what an incredible explanation. Congratulations.
If you can explain someone the idea of something, it means you really do understand the matter of that topic. This video is a true example of how a really difficult topic may be presented to students and others in an extremely accessible way. Thank you for those 11 minutes.
Most professors should start this way, before obtaining the formulas from the model and using them...make the overall concept clear and simple
Truly enjoyed the way the instructor explained this phenomenal PDE! This shows how deep he understands the concept!
Thank you for this amazing easy-to-understand breakdown of the Navier-Stokes Equations! Been trying to understand them since a while and this makes matters so simple :))
OH MY GOD. Sir, you have just OPENED MY EYES. Thank you!
That was really simple and easy to understand. Thank you!
the best explanation I have ever seen. You really made it easier to understand for us. Thanks a lot
thank you so much!! It was the most beautiful explanation that I ever heard.
The best explanation of what Navier Stokes Equation is and how to derive it. Also a good correlation with a venturimeter.
This was great, now i challenge you to make a video on how to find a general solution 😂😂
Lol
😂😂
😂😂😂
Even original founders of these equations was unable to find a general solution. 😂
@@NUPUR-t3e It's a Millennium prize problem so yeah.
Thank you so much for the wonderful explanations. Finally found a channel worth subscribing.
Jesus, this was good. Been meaning to get into this for a while.
The best explanation of the Navier Stokes's ecuation that I have seen until now
same for me
Not bad for 11:17 mins. Euler's original work on fluids (in French - see the Euler Archive) follows this approach in substance.
This channel has got surprisingly less number of subscribers
The way of making things easier... just felt awesome
Amazingly done, I have to say, I look forward to exploring your channel
One more comment of gratitude and praise for your teaching skills :)
Could you please explain how the constitutive equations for newtonian fluid are built? Please. You made an amazing explanation!!!
so cool, bro, it's a good method to show the explanation of these complicate functions
Just beautiful, thank you so much! Perfect explanation!
Dude you just covered a whole unit withing 11 minutes, 😍 thanks man,,
thank you for this wonderful easy explanation this sure saves me for my final exam
Excellent. I went through a couple of books trying to get what that all meant, beaver able to get it. You just explained so simple even the donkey I am could understand it!
Great explanation!!! Thank you so much for sharing!
Amazing video!!! You taught what college profs couldnt in an hour at least
beautiful explanation. thank you so much!
WOW, an amazing way to teach.
Really Sir, thankyou for such a good concise explanation!
you really have a very nice way of teaching compared to my professors 😊😊
very well explained!
Simple, clear, well done!
really good explanation and everything! THX a lot !!!
Guys this looks really easy I’ll solve it and keep you guys updated!
bless your soul for this video
This is the best explanation ever
very nice explanation!!
Very well done! Bravo!
really awesome explanation!
It helps! Thank you!
You do a great job of explaining it, thanks!
thank you for the explanation
WOOOOOOOW THIS WAS TOO GOOD!
Great video! Thank you!
Beautiful, thank you
Neat explanation, but I think you should have went into the derivation for the relationship between stress and velocity profile as well. Just for the sake of completeness.
That's the hard part. It follows from Newton's Law of Viscosity but it's a mess. That is, you have an expression for shear stress, and the fact that the fluid is isotrophic, and you have to 'derive' the expressions for the normal stresses from that alone.
when putting the value of sigma_xx into the equation we got for density time acceleration in x direction,there is a factor of 2 with (mu*del^2u/del_x^2). In the next step that factor if gone. Can you please explain, how did you factor that out?
Very nyc saved a much time
Thank you so much. it is simply illustrated
Thanks a lot .
Wonderfull tq very much
Does this account for summing the moments on the element?
Thank you
great explenation
I like this video!
Please please please talk about the constitutive relations!
I’m in high school and you helped me understand this. Thank you.
Am also a high school student. To be honest I'm a tad confused by a few concepts since I never took physics (self-studied), but hey. That's why we're here, eh?
Thank You. How could I learn about derive Navier-Stokes equation in cylindrical coordinates from Cartesian ? Is there any book explained it?
Amazing
Thank you so much :)
please can you explain how to slove problems
estaria bueno que pusieran esto en cilindrica y polar...gracias colorado
Anyone knows any video for the derivation of the last part?
Good job tho for such explanation in dat short time and i loved that skip in writing btw Which software are u using for such work?
if you didn't apply the mass continuity, would the equation directly become the compressible navier stokes?
Thank you Sir ❣️💖❤️❤️❤️❤️
The beeeeest explanation
You could memorize shear stress and substript definitions by linking them with dot and cross product from physics right hand rule.
That's why I taught me freshman to lable axes and units, because the more graphs you know the easier it is to learn new graphs.
I was always in the top 3 percent of standardized math testing growing up in minnesota.
Nice explanation! Shouldn't the velocity at steady state at the middle of constriction reaches its maximum. I mean points 1 and 3 have the same velocity and point 2 have the maximum with left and right of it being the acceleration and deceleration respectively. I may be incorrect.
Thank you for showing the stresses on all 6 faces, usually descriptions of tensors only have three faces(9 terms, 3 faces), which has confused me. Do you have a link to derivation of stress equations for a newtonian fluid at 9:22? Question: my understanding is that we use the material derivative as an equation between Lagrangian and Eulerian descriptions. If so, does the volume element move, do we follow it through the narrow part, or does it remain in a fixed place? sorry if the question isn't well stated.
The material derivative portion is the right hand side of this equation(excluding rho). It describes the total acceleration of a fluid particle(Lagrangian description) using the velocity field(Eulerian description).
Important to note: This only works under the assumption that density fluctuates very little or not at all ( rho = rho_0 + rho' with rho'/rho_0
Solve this in terms of cylindrical coordinate system
the 2, whare does he go?
Notations for shear forces are a bit confusing... Does the subscrits following the pattern τyx meaning y face & along x direction...
4:50 I didn't understand the low, how did you get that?? Please replay, how can be m*gx = ro(dxdydz)*gx
(dxdydz) is simply the volume of this infinitesimally small cube of length dx by dy by dz. So density times volume equals mass.
doesn't gravity only affect the Z axis tho?
you're a LEGEND!
how did we get that expression for sigma xx = -p + 2(u)(du/dx) ?
Taught in adv fluid mech in m tech. Theres a porf R J Garde I guess, u can read his books of afm for explaination.
This is a very long derivation, we used to get this for at least 10 marks to derivd in our exams
Good explanation sir but I couldn't understand those equation for Newtonisn fluids which came out of nowhere and helped us to prove it
Great explanation but I have 2 questions:
1. How exactly is the chain rule at 2:14 applied at u(x,y,z,t,)/dt in order to get that differentiative term?
2. Where do these terms at 9:15 come from? I know you said you won't cover it in this video, but I'm still curious because I want to understand every aspect of it.
+1
Newtons law of viscosity
2:10 I thought you use the chain rule not just because velocity is also a function of x y z, but because velocity is a function of x(t), y(t), z(t), namely, u(x(t), y(t), z(t), t)?
Yes that is true, because remember, we are describing here how the momentum changes of fluid particle that travels with the flow; therefore the coordinates x, y and z of the fluid particle are functions of the time t; and that is the reason why we have to take the chain rule.
What he said in the video is incorrect
@@patrickamstad5091 Thank you
For differentiating multivariable functions, it's useful to always expand everything out.
Assume there was some other variable h in there, that we don't even know if it depends on time or not. If we use the chain rule, and it turns out that h is independent of time, dh/dt will just be 0 and we're good to go, we're at the same conclusion.
So really, he's right: It has multiple variables, so we use the chain rule.
Is this the Conservative form or non-Conservative form of Navier stokes equation?
this is interesting. I can't quite tell whether it's narrated by an ai or not. I think it is because it's just too perfect. I have trouble believing a human could be that perfect.. perfection, in this particular case, is a good thing.. 🙂
Amazing work. I am glad I found this. But I have a remaining question: Do you have any reference on how to get the sigmas and taus in 9:24?
hello, did you find any reference for your question? it happens that i have the same remark, thank's
@@holmessherlock5106 No, Sorry. It was not very important for me and I did not made the effort.
@@jordifrias8829 thank you for your answer, I've just found a lot of references. For info, all we need to do is to search in google using the key words: "constitutive relation for a newtonian fluid"....
You guys should definitely look up the derivations for the constitutive relations to stresses. The derivation is quite complex but is also quite beautiful. It deals with tensors up to the fourth order I believe.
I think that the equations look a lot nicer and more concise in vector notation but otherwise solid video
Yeah. Besides this is the incompressible and constant physical properties version, which wasn't specified in the video. But to really get there, you usually need to get into tensor calculus, which I think may be outside the scope of this video.
Anyone got a derivation or link to one in the y and z direction please?
He provided general expressions for each. It's the same process.
Why does the function u depend on 3 coordinates, and not just one?
It is because the Navier Stokes equations describe the flow of fluids like water or honey in 3 dimensional space. There is one coordinate for each of the 3 coordinates of space.
Do the pressure solution.. COme on its soooo Simple..
I have only one thing to say... Thank You
goated video
Well f*@%#%! done, thank you.
still don't get it. why is g on the x direction?
It´s just a generalization, you don´t actually have a gravity force in that direction, so when you do the math, you consider it to be 0.
Take a case when the control volume is at an angle to the x axis, then there would be a component of g acting on the x axis.
Imagine you had fluid flowing down an inclined plane, and you chose your coordinate system to that the x-axis coincides with the incline and the y-axis is normal to the incline, then there will be components of gravity in the x and y directions.
Can you explain everything in math and physics to me?
how those equations were derived where you related normal and shear stresses with viscosity.... 9:19
I hope I get to the point in life where I actually get to understand this shit lol.
Im rn in highschool, but about to head off to college. My grades were basically fucked by the pandemic, so im gonna hopefully be able to transfer off community college if possible.