Description and Derivation of the Navier-Stokes Equations

Рет қаралды 312,140

6 жыл бұрын

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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Пікірлер: 167

@mertgunes9854 4 жыл бұрын

so this is what it feels like to be TAUGHT something *gratitude*

@erickgomez7775 Жыл бұрын

There should be an organization that gives awards for best educational youtube videos each year. This one deserves an award.

@AravindUkrd 3 жыл бұрын

That's among the most meaningful 11 minutes I have ever spent

@ArpitAnand-yd7tr Жыл бұрын

The amount of intuition conveyed by the instructor to the audience is absolutely unbelievable Thank you

@guilhermehambrusch7064 5 жыл бұрын

Oh my god, what an incredible explanation. Congratulations.

@adamchelchowski 3 жыл бұрын

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.

@fabiovezzari2895 Жыл бұрын

Most professors should start this way, before obtaining the formulas from the model and using them...make the overall concept clear and simple

@sayyedahmadkhadem3321 7 ай бұрын

Truly enjoyed the way the instructor explained this phenomenal PDE! This shows how deep he understands the concept!

@GaiaKnight11 4 жыл бұрын

OH MY GOD. Sir, you have just OPENED MY EYES. Thank you!

@diliprockz24 6 жыл бұрын

That was really simple and easy to understand. Thank you!

@smitkapadia8080 2 жыл бұрын

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 :))

@kacelamal4257 3 жыл бұрын

the best explanation I have ever seen. You really made it easier to understand for us. Thanks a lot

@fslurrehman Жыл бұрын

The best explanation of what Navier Stokes Equation is and how to derive it. Also a good correlation with a venturimeter.

@Junhyun-Park 5 жыл бұрын

thank you so much!! It was the most beautiful explanation that I ever heard.

@MathsatBondiBeach 5 жыл бұрын

Not bad for 11:17 mins. Euler's original work on fluids (in French - see the Euler Archive) follows this approach in substance.

@thathsaranidiliniherathher2364 4 жыл бұрын

Thank you so much for the wonderful explanations. Finally found a channel worth subscribing.

@durbhaganapati7227 4 жыл бұрын

This channel has got surprisingly less number of subscribers The way of making things easier... just felt awesome

@Eta_Carinae__ 5 жыл бұрын

Jesus, this was good. Been meaning to get into this for a while.

@ahmedhamadto8756 4 жыл бұрын

Amazingly done, I have to say, I look forward to exploring your channel

@marcelohurtadocastillo3982 4 жыл бұрын

The best explanation of the Navier Stokes's ecuation that I have seen until now

@tayyabrazashah2924 6 ай бұрын

same for me

@arianaaraujofalcon7474 3 жыл бұрын

Just beautiful, thank you so much! Perfect explanation!

@marc627 4 жыл бұрын

One more comment of gratitude and praise for your teaching skills :)

@yihe2806 4 жыл бұрын

so cool, bro, it's a good method to show the explanation of these complicate functions

@tivnator 2 жыл бұрын

Could you please explain how the constitutive equations for newtonian fluid are built? Please. You made an amazing explanation!!!

@AbDulRaHMaN-ox2yq 3 жыл бұрын

Dude you just covered a whole unit withing 11 minutes, 😍 thanks man,,

@joshuachang4564 5 жыл бұрын

beautiful explanation. thank you so much!

@joaopedrobarbosacoelho455 Жыл бұрын

Simple, clear, well done!

@kanakaraju1825 Жыл бұрын

thank you for this wonderful easy explanation this sure saves me for my final exam

@anirudhsingh1729 4 жыл бұрын

Really Sir, thankyou for such a good concise explanation!

@ProfeARios 4 жыл бұрын

Great explanation!!! Thank you so much for sharing!

@JamesVestal-dz5qm 10 ай бұрын

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.

@cipaisone 10 ай бұрын

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!

@melvingeorgechittilappilly1625 Жыл бұрын

Amazing video!!! You taught what college profs couldnt in an hour at least

@manuabasto6325 3 жыл бұрын

This is the best explanation ever

@akshatjhawer9155 3 жыл бұрын

you really have a very nice way of teaching compared to my professors 😊😊

@teachingengineering4205 5 жыл бұрын

Very well done! Bravo!

@pawankhanal8472 3 жыл бұрын

very nice explanation!!

@chenjane4814 2 жыл бұрын

really good explanation and everything! THX a lot !!!

@KanishkRajput-cm5lg Жыл бұрын

really awesome explanation!

@tayyabrazashah2924 6 ай бұрын

WOW, an amazing way to teach.

@nicolaswiles3236 4 жыл бұрын

You do a great job of explaining it, thanks!

@AdityaMotla-yt 3 ай бұрын

very well explained!

@noelgomariz3038 4 жыл бұрын

This was great, now i challenge you to make a video on how to find a general solution 😂😂

@adamfattal468 3 жыл бұрын

Lol

@siddharthkumar9349 3 жыл бұрын

😂😂

@sagarpatel3043 2 жыл бұрын

😂😂😂

@NUPUR-t3e 2 жыл бұрын

Even original founders of these equations was unable to find a general solution. 😂

@marcusrosales3344 2 жыл бұрын

@@NUPUR-t3e It's a Millennium prize problem so yeah.

@aidanschulze9799 9 ай бұрын

bless your soul for this video

@SeppyDawg 5 жыл бұрын

Beautiful, thank you

@007aha1 4 жыл бұрын

WOOOOOOOW THIS WAS TOO GOOD!

@guidedmissile4154 4 жыл бұрын

thank you for the explanation

@magicm8ball558 2 жыл бұрын

Guys this looks really easy I’ll solve it and keep you guys updated!

@AJ-et3vf 2 жыл бұрын

Great video! Thank you!

@JamesVestal-dz5qm 10 ай бұрын

I was always in the top 3 percent of standardized math testing growing up in minnesota.

@MoonOutCloudBack Жыл бұрын

It helps! Thank you!

@oliversadek2016 4 жыл бұрын

Thank you so much. it is simply illustrated

@arslansadiqe6615 2 жыл бұрын

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?

@m.nahidulislam2498 5 жыл бұрын

Thanks a lot .

@JamesVestal-dz5qm 10 ай бұрын

You could memorize shear stress and substript definitions by linking them with dot and cross product from physics right hand rule.

@iitian123 10 ай бұрын

Very nyc saved a much time

@AnindyaMahajan 4 жыл бұрын

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.

@allandavis6116 3 жыл бұрын

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.

@atillaus9168 4 жыл бұрын

great explenation

@dipsomania0 5 жыл бұрын

I like this video!

@wyattb3138 4 жыл бұрын

I’m in high school and you helped me understand this. Thank you.

@noobstudios7707 3 жыл бұрын

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?

@poisonpotato1 4 жыл бұрын

Does this account for summing the moments on the element?

@beshoyemad6587 4 жыл бұрын

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?

@Gealamusic Жыл бұрын

Thank you so much :)

@ALIRaza-MCE- 3 жыл бұрын

Thank you Sir ❣️💖❤️❤️❤️❤️

@erfuniti3570 8 ай бұрын

Thank You. How could I learn about derive Navier-Stokes equation in cylindrical coordinates from Cartesian ? Is there any book explained it?

@pradyumnchiwhane846 3 жыл бұрын

Amazing

@user-yd7rc3cc9n 5 ай бұрын

Thank you

@mikethe1wheelnut 10 ай бұрын

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.. 🙂

@__h.a.r.s.h.a__ Жыл бұрын

Wonderfull tq very much

@gustavocortico1681 11 ай бұрын

Please please please talk about the constitutive relations!

@rinzan 4 жыл бұрын

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.

@atmonotes 11 ай бұрын

if you didn't apply the mass continuity, would the equation directly become the compressible navier stokes?

@nidalal-sayed4019 3 жыл бұрын

The beeeeest explanation

@hanafieuwais3110 3 жыл бұрын

Anyone knows any video for the derivation of the last part?

@pstark4 4 жыл бұрын

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.

@vedhaswalke4406 4 жыл бұрын

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).

@brilliant1863 4 жыл бұрын

you're a LEGEND!

@deborahgardner6786 3 жыл бұрын

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

@hendemad8757 2 жыл бұрын

please can you explain how to slove problems

@sabarirajansingaravelu886 5 жыл бұрын

how did we get that expression for sigma xx = -p + 2(u)(du/dx) ?

@trik3002 5 жыл бұрын

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

@MSuriyaPrakaashJL 3 жыл бұрын

Good explanation sir but I couldn't understand those equation for Newtonisn fluids which came out of nowhere and helped us to prove it

@siddharth_20 Жыл бұрын

Notations for shear forces are a bit confusing... Does the subscrits following the pattern τyx meaning y face & along x direction...

@RumOwnesT 4 жыл бұрын

4:50 I didn't understand the low, how did you get that?? Please replay, how can be m*gx = ro(dxdydz)*gx

@mrcannotfindaname 4 жыл бұрын

(dxdydz) is simply the volume of this infinitesimally small cube of length dx by dy by dz. So density times volume equals mass.

@marianodeanquin 6 жыл бұрын

estaria bueno que pusieran esto en cilindrica y polar...gracias colorado

@ShadowZZZ 4 жыл бұрын

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.

@TufanKirmaci 3 жыл бұрын

@muhammadsaid4654 3 жыл бұрын

Newtons law of viscosity

@jordifrias8829 4 жыл бұрын

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?

@holmessherlock5106 4 жыл бұрын

hello, did you find any reference for your question? it happens that i have the same remark, thank's

@jordifrias8829 4 жыл бұрын

@@holmessherlock5106 No, Sorry. It was not very important for me and I did not made the effort.

@holmessherlock5106 4 жыл бұрын

@@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"....

@bh-rf9dd 4 жыл бұрын

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.

@sri78hari 10 ай бұрын

These UCB videos r better than MIT in my opinion.

@ethanmartin2781 5 жыл бұрын

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)?

@patrickamstad5091 5 жыл бұрын

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

@benjaminsmus8553 4 жыл бұрын

@@patrickamstad5091 Thank you

@gergodenes6360 4 жыл бұрын

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.

@veritythomas5682 3 жыл бұрын

Anyone got a derivation or link to one in the y and z direction please?

@deborahgardner6786 3 жыл бұрын

He provided general expressions for each. It's the same process.

@67-abdulrehmanshahzad20 5 жыл бұрын

Solve this in terms of cylindrical coordinate system

@bahaulfahmialhaq4948 Жыл бұрын

the 2, whare does he go?

@trisnrik2245 2 жыл бұрын

doesn't gravity only affect the Z axis tho?

@aleenalaique6618 4 жыл бұрын

Is this the Conservative form or non-Conservative form of Navier stokes equation?

@ntorres1152 2 жыл бұрын

goated video

@theInternet633 5 жыл бұрын

I think that the equations look a lot nicer and more concise in vector notation but otherwise solid video

@Ottmar555 5 жыл бұрын

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.

@moonman239 3 жыл бұрын

Why does the function u depend on 3 coordinates, and not just one?

@alexandertownsend3291 3 жыл бұрын

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.

@JamesVestal-dz5qm 10 ай бұрын

I drew Cartesian x y planes over and over again in middle school.

@rahulmenon4003 3 жыл бұрын

I have only one thing to say... Thank You

@kylenemeth6252 5 жыл бұрын

Well f*@%#%! done, thank you.

@LouisLiuMusic 5 жыл бұрын

still don't get it. why is g on the x direction?

@gabrieldigiuseppe3106 5 жыл бұрын

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.

@pranavsateesh3002 5 жыл бұрын

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.

@itswhoppertime 5 жыл бұрын

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.

@honkhonk8009 2 жыл бұрын

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.