Navier-Stokes Final Exam Question (Liquid Film)

MEC516/BME516 Fluid Mechanics I: A Fluid Mechanics Final Exam question on solving the Navier-Stokes equations (Chapter 4). The velocity and pressure fields are calculated for a gravity-driven liquid film on an inclined plate. This unique aspect of this problem is the no shear stress boundary condition at the top of the liquid film.
All the videos in this course and a copy (pdf) of this presentation can be downloaded at: www.drdavidnaylor.net
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
Chapters
0:00 Introduction
0:18 Problem statement
1:23 Discussion of the assumptions & boundary conditions
3:34 Solution for the velocity field u(y)
7:18 Application of the boundary conditions
9:45 Final Answer for the velocity field u(y)
9:59 Solution for the dp/dy
10:51 Final answer for dp/dy
11:42 Animation and discussion of DNS turbulence modelling
#fluidmechanics #fluiddynamics #mechanicalengineering

[@FluidMatters]

All the videos for this introductory Fluid Mechanics course are now available at: www.drdavidnaylor.net/

[@learjet55c]

Thanks Prof. Dr. Naylor, it helps me a lot! I have my exam in Germany in two weeks.

[@FluidMatters]

Glad it helped. Best of luck!

[@moqranmoqran]

I am a petroleum engineer from algeria but I always had something with fluid mechanics, Brought me back to my univetsity days

[@FluidMatters]

Glad to hear you liked fluid mechanics!

[@Nando-gc8kb]

Really great stuff!

[@FluidMatters]

Thanks for the kind words.

[@HUITXO]

I wish your channel had been available in the early 2000's, when I took Transport Phenomena in college (not even RUclips was available).

[@FluidMatters]

Thanks!

[@suleyman7478]

great stuff

[@marthamedina8839]

Thank you professor Naylor! It helped me a lot understanding the application of the N-S equation👏

[@FluidMatters]

Glad to heat it helped. Best of luck with your studies.

[@stefanvujic3102]

useful video!

[@mohammadfallahzade2110]

best instructor

[@FluidMatters]

Thanks for the kind words. Best of luck with your studies.

[@spideyguy1389]

Hi prof, I find your videos extremely helpful. Right now I'm struggling with Fluid Mechanics especially on Navier Stokes and Boundary Layer Theory. May I ask your kindness to upload more videos solving problems of Boundary Layer Theory and Navier Stokes?

[@FluidMatters]

Thanks. Glad to hear that you find the videos helpful. There is a least one more Navier-Stokes solution video on my website: ruclips.net/video/-kteMpRs69M/видео.html
My course in just intro and doesn't cover boundary layer theory, such as the Blasius solution. But I'll keep your suggestion in mind as an idea for a possible future video.

[@Szhihihihihihi]

Keep it up !

[@FluidMatters]

Glad the video was helpful.

[@amineattouchi6391]

thanks a lot

[@FluidMatters]

Happy to help

[@curimanvidaldiegoricardo8293]

I dont speak english but your videos are too god so I can understand everything

[@FluidMatters]

Thanks for the kind words. I guess math and physics is universal.

[@DrDerivative]

These videos are great. Your website is even better. Thank yout for this content.
Do you plan to add more topics to the website in the future? Pipe flow, sinks and sources, etc.?

[@FluidMatters]

Thanks! This course was developed (pre-pandemic) as a "Fluids 1" engineering course. After the pandemic, my department is not keen on having more online courses. So, I doubt this will get expanded to "Fluids 2" any time soon.

[@DrDerivative]

@@FluidMatters I wouldn't tell on you if you made these videos independently from your university/department. On your personal RUclips page?
Regardless, thank you for this.

[@FluidMatters]

@@DrDerivative I wish I had time....

[@muhammadsamiulhaq3883]

Hi, which book you are using? Please tell me. Thank you.

[@FluidMatters]

It's given in the video description: Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.

[@niels6186]

i have a question, does the order of integrating and applying boundary conditions matter? I mean if I integrate two times right away and then solve the constants I seem to get a different result than when I integrate, boundary, integrate and boundary do...

[@FluidMatters]

The result should be the same, regardless of the order.

[@niels6186]

@@FluidMatters thank you very much sir, excellent video 🙌

[@mairisberzins8677]

Is this something from an engineering course? Seems too applicable to be physics. If it is engineering, which year of study is it?

[@FluidMatters]

This is a required course for 3rd year mechanical and biomedical engineering students. I run the online version.

[@varunkumarvb]

Please solve cengel 4th SIE full it has 2000 problems ....😂😂😂you will get 2millions subscribers from India alone

[@anthonylorenzo1126]

Why isn't d^2u/dy^2 not 0?

[@FluidMatters]

d2u/dy2=0 means that the velocity profile must be linear i.e. no curvature. There is no basis for this requirement, as you can see from the solution.