Fluid Mechanics Lesson 11D: More Solutions of the Navier-Stokes Equation
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- เผยแพร่เมื่อ 10 ก.พ. 2025
- Fluid Mechanics Lesson Series - Lesson 11D: More Solutions of the Navier-Stokes Equation.
In this 14-minute video, Professor Cimbala shows the detailed step-by-step procedure for solving the continuity and Navier-Stokes equations for two more example problems: (1) Oil falling as a thin film on a vertical wall, using Cartesian coordinates, and (2) Flow in the gap between two concentric cylinders where the inner cylinder rotates and the outer cylinder is stationary, using cylindrical coordinates. In both cases, exact analytical solutions are obtained for laminar flow.
This video incorporates material from Section 9-6 of the Fluid Mechanics textbook by Cengel and Cimbala, edition 4.
An Excel file listing of all the videos in this series, along with the annotated notes generated during filming of the videos, can be found at
www.me.psu.edu... .
If you liked this video, please subscribe to Dr. Cimbala's TH-cam channel at / @johncimbala to be informed when new videos are posted.
You can also watch all related short videos with one click by going to one of Dr. Cimbala's playlists:
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Dr. John M. Cimbala is Professor of Mechanical Engineering at Penn State. He is an educator, textbook author, Christian author, husband, father, and grandfather. He also created and maintains a website for helping people grow in their faith called Christian Faith Grower at www.christianf... His TH-cam channel is at / @johncimbala
You explained things in this video better than anything I heard in class. Much love John!
Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are hundreds of free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.
It's two 2:50 in the morning and u just helped to solve this problem, very thankful may Allah Leads u to the wright way, thank u vr
Thank you for your comment. I am glad that my videos were helpful to you. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.
It is the man himself! Keep up the good work. It is a matter of time until students find this channel
Please tell them about it!
@@johncimbalahow and where to get solutions to cengel book.... It doesn't even have answers..... How do you suppose that indian students get solutions for the book whereas USA has homehelp and solutions websites..... Please help this message from India....
@@varunkumarvb The Solutions Manual is available only to instructors officially, in the USA and everywhere else. Some of the instructors choose to post portions of the manual online. Seek and you will find.
Best video on youtube on the topic, thank you so much sir.
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OMG the legend himself! 🤩
Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are hundreds of free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.
What if there is the constant differential pressure in the z-direction? Thanks
I assume you are talking about the second example. In that case, there would be flow in the z direction, kind of like pipe flow (we call it annular pipe flow). That flow would also have swirl as in my example problem. The two solutions would co-exist.
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What happens if you don't have inner cylinder and only outer cylinder is rotating?
The flow would eventually become solid body rotation as the effect of spinning outer wall works its influence into the center
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@@johncimbala can solid body rotation formula be used in this case?
@@bonvoyage2514 Yes, but only if the system has been rotating for a long time so that steady solid-body rotation is established.
@@johncimbala could you please provide me a link for it?