Navier-Stokes Equation Final Exam Question

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Күн бұрын

MEC516/BME516 Fluid Mechanics I: A Fluid Mechanics Final Exam question on solving the Navier-Stokes equations (Chapter 4). Calculation of the fully-developed velocity field between two parallel plates, with a pressure gradient and one plate moving. (This is a classical exact solution that dates back 100+ years: Couette flow with a pressure gradient.)
All the videos for this course and a copy (pdf) of this fluid mechanics presentation can be downloaded at: www.drdavidnaylor.net
This website also includes an exam bank and solved problem sets.
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluiddynamics #Navier-Stokes

Пікірлер: 112

@FluidMatters Жыл бұрын

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

@badejosamuel-qk5ud 9 ай бұрын

I need the PDF Sir

@FluidMatters 9 ай бұрын

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

@ryadryad4692 9 ай бұрын

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

@ishitavardhan7697 11 күн бұрын

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

@user-pu3po6zg6b 7 ай бұрын

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

@FluidMatters 7 ай бұрын

Glad to hear it was helpful.

@adamprechtl9987 3 жыл бұрын

15 minutes of pure gold, thank you so much!

@woodysworkshop7123 3 жыл бұрын

Good luck at 8am. See you on zoom.

@piyusholivkar7281 3 жыл бұрын

Best video for navier stokes example in the whole youtube

@spectra5029 2 жыл бұрын

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

@charithjeewantha 2 жыл бұрын

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

@Juuki8 3 жыл бұрын

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 2 жыл бұрын

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?

@tunahandegirmencioglu6450 3 жыл бұрын

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

@zaynbashtash 2 жыл бұрын

The Simplest, mlst understandable explanation. Thank you !

@thembelanimiya8964 3 жыл бұрын

Nice clarification in approaching N-S equation problems!

@sanatandas6007 Жыл бұрын

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

@mushimushinomi 3 жыл бұрын

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

@hrkalita159 2 жыл бұрын

Where was this channel 😭,how nicely he explained 🙏

@estebantapia-penas8206 3 жыл бұрын

Best video on navier stokes for sure

@sambenkamel 2 жыл бұрын

thank you so much for the simplicity

@alexklaver9936 2 жыл бұрын

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

@moonloop6 3 жыл бұрын

Very well presented example. Thanks!

@alvareztube7208 3 жыл бұрын

the best explanation on KZfaq 😍

@diegoguatemala1520 3 жыл бұрын

Right to the point, thanks!!

@veyselcankaradeniz4945 3 жыл бұрын

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

@maheshsoftware4742 Жыл бұрын

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

@FluidMatters Жыл бұрын

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

@alperenokur1272 3 жыл бұрын

after this video, I got Navier stokes equetions. thanks

@yellow5997 4 ай бұрын

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

@FluidMatters 4 ай бұрын

Glad it helped!

@iuyvhulioionkbjun3040 2 жыл бұрын

I really enjoyed this exercise thank you

@antoniamillaraylizanaraban9380 Ай бұрын

THIS VIDEO IS SO GOOD

@hongkyulee9724 Жыл бұрын

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

@FluidMatters Жыл бұрын

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

@howididthatpodcast 3 жыл бұрын

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

@FluidMatters 3 жыл бұрын

Thanks. Glad I could help.

@TheColdBloodedGamerS 2 жыл бұрын

Wow, thank you Sir!

@AmeerHamza-bc4fh 2 жыл бұрын

Excellent!

@parkerwarneke1145 3 жыл бұрын

Very helpful!

@jayavardhan0760 Жыл бұрын

Its perfect, right from the start to the very end

@FluidMatters Жыл бұрын

Thanks. Glad to hear it was helpful.

@praticksinha1248 2 жыл бұрын

Very helpful video sir thanks

@andrewmerafuentes6683 2 ай бұрын

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

@FluidMatters 2 ай бұрын

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

@jeggarmcjensen3034 3 жыл бұрын

Vielen dank, sehr sehr hilfreich

@Hussain-px3fc Жыл бұрын

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

@FluidMatters Жыл бұрын

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

@abstract2807 Жыл бұрын

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 Жыл бұрын

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

@gbs2473 8 ай бұрын

thank you so much.i needed this🌹

@FluidMatters 8 ай бұрын

Glad you found it helpful.

@user-lb8qx8yl8k Жыл бұрын

Excellent video!!

@FluidMatters Жыл бұрын

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

@ProfeARios 9 ай бұрын

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

@FluidMatters 9 ай бұрын

Glad to hear it was helpful.

@JohnnyBravo58 Жыл бұрын

This was my quiz question

@amarifatima961 3 жыл бұрын

Thanks a lot

@shershah9406 6 ай бұрын

Thank you sir

@zeynepbecermen5187 3 жыл бұрын

thanks a lot

@chouaibsadki2942 3 жыл бұрын

thank you

@haiderhameed5966 Жыл бұрын

Thanks So much, Sr. good lecture.

@FluidMatters Жыл бұрын

Thanks for the kind words.

@pidgeonengineer7060 3 жыл бұрын

invaluable

@manasagrawal3630 Жыл бұрын

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 Жыл бұрын

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

@atillaus9168 3 жыл бұрын

cristal clear lecture

@user-kd5ql5ot7s 3 жыл бұрын

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

@saddamhecine9024 Жыл бұрын

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

@FluidMatters Жыл бұрын

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

@quickscoppedzombie Жыл бұрын

LEGENDDDDDDDDDD

@FluidMatters Жыл бұрын

Thanks!

@craftanddiywithbak7006 2 жыл бұрын

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

@FluidMatters 2 жыл бұрын

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).

@elvina105 Жыл бұрын

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

@FluidMatters Жыл бұрын

Thanks! Glad that it helped.

@tammammohammed4442 2 жыл бұрын

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 2 жыл бұрын

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

@tammammohammed4442 2 жыл бұрын

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

@FluidMatters 2 жыл бұрын

@@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 2 жыл бұрын

@@FluidMatters Thanks a lot!

@cheechyba 2 жыл бұрын

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

@shudumansindile5891 3 жыл бұрын

what happens when the plates are moving in the same direction

@FluidMatters 3 жыл бұрын

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).

@alisoltani7581 3 ай бұрын

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

@FluidMatters 3 ай бұрын

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 3 ай бұрын

@@FluidMatters Ok,thank you very much🙏🙏

@luketodd8634 2 жыл бұрын

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

@TheColdBloodedGamerS 2 жыл бұрын

Same…

@TerminallyOnline92 Ай бұрын

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 Ай бұрын

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 Ай бұрын

@@FluidMattersThanks! I didn’t see that

@unusualgaming8629 2 жыл бұрын

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

@FluidMatters 2 жыл бұрын

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

@unusualgaming8629 2 жыл бұрын

@@FluidMatters thanks

@Mohamed_zyd 2 жыл бұрын

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

@venkateswarareddy007 9 ай бұрын

What will happen if the flow is unsteady

@FluidMatters 9 ай бұрын

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 Жыл бұрын

😍

@rishabhkumar2931 3 жыл бұрын

🙏🙏

@MarwanMahdy Жыл бұрын

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

@FluidMatters Жыл бұрын

Thanks for the kind words.

@bonks4395 Жыл бұрын

@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 Жыл бұрын

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 KZfaq. Best of luck.

@cheechyba 2 жыл бұрын

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 2 жыл бұрын

btw. this was helpful

@cheechyba 2 жыл бұрын

btw. this was helpful