Fluid Mechanics 12.4 - Gravity Driven Liquid Film on an Inclined Surface

In this segment, we apply the conservation of mass and Navier Stokes equations to obtain the velocity distribution in a liquid film sliding down an inclined surface.
Module 12: Navier Stokes Equations:
In module 9, we covered the differential form of the conservation of momentum. We also made an assumption that fluid is inviscid and ended up with the Euler's equations. In this module, we relax the inviscid restriction and obtain the Navier Stokes equations, which are a very important equation for establishing the foundation for further studies in fluid dynamics.
Student Learning Outcomes:
After completing this module, you should be able to use the Navier Stokes equations to determine viscous flow characteristics between parallel plates and circular tubes. This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

[@Shiptoast0]

clear concise to the point and appeal to simple reason, perfect

[@kaleishamiller1585]

Very clear and helpful video!

[@CollegeFluidMechanics]

Glad you think so!

[@chivo2468]

Good day and thank you so much for the explaination. You made it extremely clear! Would you be so kind as to point me in the right direction for cases in which the flow is not steady ( ∂u/∂x ≠ 0 ). I mean I think the initial crossing out of the NS-Equation would be easy but what should I do after that? I'm designing an inclined channel to set up a thin film of thickness h. The velocity of the thin film will be measured with a pitot tube that I will somehow install at a selected height y (according to your nomenclature), therefore the value I will be calculating is the thickness h mentioned above, and then I will confirm it with a measurement device. I am a bit confused however since, even though I differentiate now between steady and non-steady (h not constant throughout x) flows, I can't seem to find which one of the two occur naturally when a body of water flows in an inclined surface (and therefore I don't know which initial assumptions I should consider for my set-up. I would be extremely thankful if you could shine some light on my issue! :)

[@SuhasSathyakiran]

Thank you very much sir😃 Explanation is very clear and Precise.

[@CollegeFluidMechanics]

You are most welcome. Thanks, Suhas.

[@TianqiZeng]

Thank you sooooo much for the explanation. It helped a lot.

[@CollegeFluidMechanics]

Glad it helped!

[@143mathematics]

very good.

[@devashishthakkar6723]

Lovely 😍

[@carolinagervacio9595]

I love how u explain. Sorry, which Is the app yo use for your keyboard?

[@CollegeFluidMechanics]

Hi Carolina, I use the Notability app on Ipad.

[@moses2061]

What reference book can you recommend?

[@fredrickedafe4782]

Just want to be much clearer in this, is the pressure P1 same as P2?
I see there's a difference in height between P1 and P2. Doesn't that make a difference in pressure? I need to be corrected Sir,
Thanks

[@CollegeFluidMechanics]

I responded to your other comment, but yes P1=P2

[@abanobjoseph4222]

Excuse me sir, from which text book you got the problem?

[@CollegeFluidMechanics]

Hello Abanob, I am not taking the questions from books. I am preparing them myself.

[@ElgaymeproTorshock]

nahhhh

[@fredrickedafe4782]

Just want to be much clearer in this, is the pressure P1 same as P2?
I see there's a difference in height between P1 and P2. Doesn't that make a difference in pressure? I need to be corrected Sir,
Thanks

[@CollegeFluidMechanics]

That is correct. P1 must be equal to P2. Both points are exposed to the atmosphere which has a constant pressure value at a given elevation.