Navier-Stokes Equation Final Exam Question

[@FluidMatters]

All the videos (and pdf downloads) for this introductory Fluid Mechanics course are available at: www.drdavidnaylor.net/

[@badejosamuel-qk5ud]

I need the PDF Sir

[@FluidMatters]

@@badejosamuel-qk5ud I've fixed the file error on my website. It is here: www.drdavidnaylor.net/exam-review-questions.html

[@ryadryad4692]

​@@FluidMatterscan u send more application to understund the low of navier ?

[@LenaHorowitz]

a full quarter of fluids and it only makes sense now after watching these videos!

[@FluidMatters]

Glad to hear it was helpful.

[@piyusholivkar7281]

Best video for navier stokes example in the whole youtube

[@spectra5029]

You are right, explaining all the simplified terms and the logic of solving the exercise.

[@adamprechtl9987]

15 minutes of pure gold, thank you so much!

[@woodysworkshop7123]

Good luck at 8am. See you on zoom.

[@Juuki8]

Thank you so much, I finally understand the individual terms of the N.S. equaitons. It has been hard to get a detailed answer on this, so I'm grateful for this video🙏

[@trisnrik2245]

i agree.. everyone just leaves it in 3 dimensions and never breaks it down. I do wish.. and am curious could he provided a value for U .. and b.. could we solve the velocity?

[@ishitavardhan7697]

This video is absolutely GOLD for someone like me struggling with fluid mechanics. Glad to find this on KZbin!!

[@sanatandas6007]

It's so easy to have the equation from your lecture sir ...Thanks a lot sir.

[@tunahandegirmencioglu6450]

A very nice example and explanation that can rarely be found on youtube.

[@maheshsoftware4742]

Wonderful explanation. He made an impossibly difficult problem into an easy one to understand and solve

[@FluidMatters]

Thanks so much for kind words! Best of luck with your studies.

[@hrkalita159]

Where was this channel 😭,how nicely he explained 🙏

[@estebantapia-penas8206]

Best video on navier stokes for sure

[@howididthatpodcast]

super helpful! explained more than I learned in an entire fluids class. awesome!

[@FluidMatters]

Thanks. Glad I could help.

[@jayavardhan0760]

Its perfect, right from the start to the very end

[@FluidMatters]

Thanks. Glad to hear it was helpful.

[@charithjeewantha]

I watched the entire play list of Navier Stokes equation. It was very helpful. Thank you so much!

[@zaynbashtash]

The Simplest, mlst understandable explanation. Thank you !

[@yellow5997]

Thank you really really much! This saved my life! I searched for something like this a week long. Thank you again!!

[@FluidMatters]

Glad it helped!

[@thembelanimiya8964]

Nice clarification in approaching N-S equation problems!

[@alvareztube7208]

the best explanation on KZbin 😍

[@manasagrawal3630]

Bro love you 3000....I watched this video 20 mins. Before my final exxam from IIT. I had the very same question in the exam for 20% marks.🎉

[@FluidMatters]

Glad it helped. Maybe your prof saw this video too! Ha Ha.

[@Hussain-px3fc]

Thank you so much sir for all the effort you put in this work❤, it really helped me with my studies 😊.

[@FluidMatters]

Glad to hear it was helpful. Good luck with your studies.

[@mushimushinomi]

You made me gain confidence in my knowledge thanks for your hard work

[@veyselcankaradeniz4945]

Very useful and well prepared example, it helped a lot. Thanks!

[@sambenkamel]

thank you so much for the simplicity

[@antoniamillaraylizanaraban9380]

THIS VIDEO IS SO GOOD

[@alperenokur1272]

after this video, I got Navier stokes equetions. thanks

[@ProfeARios]

Thank you so much for sharing. Best regards from Panama 🇵🇦

[@FluidMatters]

Glad to hear it was helpful.

[@alexklaver9936]

Thank you so much for making this video. You're a great teacher. Wish I went to Ryerson.

[@abstract2807]

That elimination of possiblity of u being a function of x(fully developed flow) using contuinity equation was sick. Now I always use Navier stokes and contuinity equation together. 😊

[@FluidMatters]

That's a good mathematical insight! You are really understanding the details. Sick! Ha Ha.

[@hongkyulee9724]

Thank you for the good explaining. This video was very helpful for me to understand the Navier-Stokes equation.

[@FluidMatters]

Glad to hear it was helpful. Thanks for the kind words. Best of luck with your studies.

[@diegoguatemala1520]

Right to the point, thanks!!

[@moonloop6]

Very well presented example. Thanks!

[@JohnnyBravo58]

This was my quiz question

[@iuyvhulioionkbjun3040]

I really enjoyed this exercise thank you

[@praticksinha1248]

Very helpful video sir thanks

[@thaddeebarge4023]

Amazing!

[@FluidMatters]

Thanks!

[@haiderhameed5966]

Thanks So much, Sr. good lecture.

[@FluidMatters]

Thanks for the kind words.

[@andrewmerafuentes6683]

I came just to check for a concept, then proceed to finish the whole series.

[@FluidMatters]

Glad to be able to help. Best of luck with your studies.

[@jeggarmcjensen3034]

Vielen dank, sehr sehr hilfreich

[@user-lb8qx8yl8k]

Excellent video!!

[@FluidMatters]

Thanks. Glad to hear it was helpful. Good luck with your studies!

[@gbs2473]

thank you so much.i needed this🌹

[@FluidMatters]

Glad you found it helpful.

[@shershah9406]

Thank you sir

[@AmeerHamza-bc4fh]

Excellent!

[@elvina105]

Thank you, I just clapped at the end of the video

[@FluidMatters]

Thanks! Glad that it helped.

[@omaraburashed3650]

I’m thankful for you Dr, actually I am done masters and I got module theoretical CFD and there’s something common with this course like the governing equations and I two questions were so beneficial to me so my question could you provide me with temperature questions , and how can I get some materials and questions for the rest of my CFD course such as finite volume

[@FluidMatters]

Sorry I don't think I can help with that. I'd suggest an intro cfd textbook.

[@TheColdBloodedGamerS]

Wow, thank you Sir!

[@cheechyba]

this seemed easy, but "under pressure" it is not. i feel like having a slightly over-tuned pressure gradient doing this in an exam again xD

[@luketodd8634]

Why can't my university professors be like this, instead of being so hard to understand

[@TheColdBloodedGamerS]

Same…

[@parkerwarneke1145]

Very helpful!

[@chouaibsadki2942]

thank you

[@alisoltani7581]

Hello , what about the unsteady case? how can we sole this problem for u(t,y)?

[@FluidMatters]

There are exact solutions for some simple unsteady problems, like an impulsively accelerated plane wall. This is beyond the undergrad level. See the classic book "Boundary-Layer Theory" by Schlichting, for example.

[@alisoltani7581]

@@FluidMatters Ok,thank you very much🙏🙏

[@quickscoppedzombie]

LEGENDDDDDDDDDD

[@FluidMatters]

Thanks!

[@saddamhecine9024]

Thank you so much ,do you have exam for boundary layer

[@FluidMatters]

The mathematics of viscous boundary layers are not part of this intro course. Sorry.

[@دانيةنعسان]

Could you please give me the references for these info in the video

[@atillaus9168]

cristal clear lecture

[@craftanddiywithbak7006]

thank you. but please how can we find the pressure gradient?

[@FluidMatters]

The pressure gradient (dp/dx) is supplied by the pump. In the final equation, the value of dp/dx is your choice (i.e. an input) and could be estimated from the pump head curve. The bigger the pump, the higher the flow rate, and a larger pressure loss per meter of channel length (dp/dx).

[@zeynepbecermen5187]

thanks a lot

[@pidgeonengineer7060]

invaluable

[@MarwanMahdy]

so it wasn't my fault, apparently my professors can't explain anything. Thank you so much.

[@FluidMatters]

Thanks for the kind words.

[@shudumansindile5891]

what happens when the plates are moving in the same direction

[@FluidMatters]

That's another possible exam variation. You can define U_1 for the bottom plate and U_2 for the upper plate. The solution is identical up to 12:44. The evaluation of C_1 (at 12:44) is different: u=U_2 at y=b. Results in a slightly different superposition of Poiseuille (pressure gradient-driven flow) and Couette flow (plate motion-driven flow).

[@tammammohammed4442]

Thanks for the video. I have a question about the pressure profile. Should we continue and solve for the pressure profile in x direction or it is enough to stop at the final form demonstrated by the video?

[@FluidMatters]

The questions asks "Derive and expression for the velocity profile", not the pressure gradient dp/dx. So, you can stop where I did.

[@tammammohammed4442]

@@FluidMatters Good. In case, we want to continue, what is needed to solve the pressure gradient term? Thanks.

[@FluidMatters]

@@tammammohammed4442 You would likely want dp/dx as a function of the volume flow rate, Q. To do this I would integrate the velocity profile across the channel to get the flow rate: Q=f(U,b, dp/dx). Then rearrange the expression to solve for dp/dx, which is a constant.

[@tammammohammed4442]

@@FluidMatters Thanks a lot!

[@TerminallyOnline92]

At 13:29, shouldn’t it be C1 = -1/(2*mu*b)*dp/dx - U/b and not C1 = -b/(2*mu)*dp/dx - U/b ? Doing the algebra, I feel the b should be in the bottom of the fraction and not the top. Can someone explain please?

[@FluidMatters]

Before simplification, we have b^2 in the numerator (from y^2 in the original expression applied at b). So, when you divide by b to isolate C1, you end up with b in the numerator. I hope that helps.

[@TerminallyOnline92]

@@FluidMattersThanks! I didn’t see that

[@unusualgaming8629]

How long roughly would students be expected to solve this in?

[@FluidMatters]

I recall this question was one of five on a three hour final exam. So, say, ~40 minutes.

[@unusualgaming8629]

@@FluidMatters thanks

[@Mohamed_zyd]

@@FluidMatters oh, we took a similar question for couette flow (N. S. E. ) in maximum 15 minutes in the midterm exam

[@venkateswarareddy007]

What will happen if the flow is unsteady

[@FluidMatters]

You'd need to specify initial conditions, like a still flow (u=v=0 everywhere) and perhaps an impulsively started plate at time zero. In this case you'd have the acceleration term du/dt (partials, of course) and it would be more difficult to solve, as u=u(x,t). These solutions are more advanced: See the classic book "Boundary Layer Theory by H. Schlichting", McGraw Hill.

[@elmarbouhjawad4259]

😍

[@rishabhkumar2931]

🙏🙏

[@bonks4395]

@fluidmatters Your mathematical equation is incorrect. It is impossible to have a "No Slip" situation for the lower plate boundary. The formula should instead show that the lower and upper plates are directly related to each other. Instead of making the upper plate move and the lower plate stationary...you should instead halve the velocities of both plates. This is both physically and mathematically the only way this equation can be properly solved and I can prove it. This is works the same for all fluids, whether it be water flowing through a fully contained pipe or the Pacific ocean flowing over bedrock.

[@FluidMatters]

I disagree. Couette flow with a pressure gradient is classical exact solution, dating back 100+ years. I will not debate it here. If you feel all the experts and dozens of textbooks are in error, you should submit your new idea to a refereed journal, rather than post an inadequately explained claim in the comments on KZbin. Best of luck.

[@amarifatima961]

Thanks a lot

[@cheechyba]

this seemed easy, but "under pressure" it is not. i feel like having a slightly over-tuned pressure gradient doing this in an exam again xD

[@cheechyba]

btw. this was helpful

[@cheechyba]

btw. this was helpful