Derivation of the Mass Continuity Equation
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- Опубліковано 27 лип 2024
- 🌎 Website: jousefmurad.com
📈 APEX Consulting: theapexconsulting.com
In this video, we will derive the mass continuity equation by having a look at a simple Control Volume (CV). This derivation will then be used for a subsequent video to derive the Navier-Stokes Equations. Animations from Grant Sanderson (aka. 3Blue1Brown) are included.
► Part 2 - Derivation of the Navier-Stokes Equations: • Derivation of the Navi...
► Part 3 - Derivation of the Energy Equation: • Derivation of the Ener...
► PDF of the presentation: / derivation-of-33991149
► Grant's Channel: / @3blue1brown
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#NavierStokes
#MassConservation
#Mathematics
Time Stamps
----------------------
0:00 - 1:11 : Intro
1:12 - 3:32 : Reynold's Transport Theorem
3:33 - 4:25 : Differential Form
4:26 - 4:55 : Fundamental Equations of Fluid Mechanics
4:56 - 5:19 : Conservation of Mass
5:20 - 6:00 : Momentum Equation
6:01 - 6:08 : Recap Terminology
6:09 - 6:20 : Control Volume (CV)
6:21 - 6:33 : Conservation of Mass (in words)
6:34 - 10:55 : Derivation of the Mass Continuity Equation
10:56 - 14:58 : Explanation of the Divergence
14:59 - End : Outro
![[CFD] Conservative, Advective & Material Derivative forms of the Navier-Stokes Equations](http://i.ytimg.com/vi/ljdv4T2U464/mqdefault.jpg)
This equation serves as a foundation for many other important concepts in fluid dynamics, and it's intriguing to consider the potential applications of this knowledge in industries such as aerospace, automotive, and power generation. The video not only provides a deeper understanding of the subject matter but also makes one appreciate the elegance and simplicity of the mathematical formulas that govern the natural world.
As a mechanical engineer who has always been passionate about math and physics, I have always been intrigued by the math of fluid mechanics, and also by modern physics, despite neither relativity nor quantum mechanics were part of any course syllabus at my university. I studied these subjects on the side and found them really inspiring, I would go as far as to say that they gave me a novel perspective on life itself. That prompted me to create some online courses on Quantum Mechanics, Quantum Field Theory, special and General Relativity. It’s not my job of course, but I love talking about these topics and showing the "intution" behind the mathematics.
I have seen so many videos to understand CFD basics but didn't got the point.You explained it simply.Mainly the divergence and convergence point..Nice example.
Make more videos.GOD BLESS YOU BRO.
I'm an Electrical engineer, but I have lots of fascination towards fluid dynamics (and non linearity modelling in general). Thanks a lot for taking your time and effort to make these videos.
I love to see when people from other fields delve into topics that are not part of their day to day work :) Thank YOU for commenting and watching!
@@JousefM if you do face a situation where additional electrical/signal processing knowledge is needed, feel free to reach out 🥰.
@@manueljenkin95 I believe I can make use of that offer in the future :)
It’s been a while, hope you’re doing good. Currently learning turbulence modelling!
Dope! Which resources are you using 🙂
This Explanation was sooooo good. Sir!!!!
Thanks for watching! Feel free to share it with your nerdy friends 🙂
Thanks a lot for the great explanation, and especially the intuitive example for divergence 😊
What the heck.... I never thought my maths 3 is filled up with the equations of fluids nse, gauss & Stokes... Man 👨 u are really clearing up my fogs of my btech.
A loads of thanks brother... Keep un going.. It's really making a huge difference. ☺☺
Thanks for your feedback my friend! :) Stay tuned for the derivation of the Momentum Equation!
Thanks!❤
Your effort to make this video is just speechless..
BTW your voice is 🫰
Thank you so much. Made it pretty easy
Amazing!
Thank You!
wth....it makes sense! Such a good explanation mate. Keep up the good work.
Thanks Michael :)
Excellent Equation
Bro !!! this explanation is just perfect and amazing Plz continue .... lots of love and respect
Thanks brother :) Appreciate your nice comment!
Your explanation on the continuity equation is deep, convincing, and free of ambiguity. Thank you for this piece. Wish you could share me the video to the derivation of the energy equation. This is what the conventional mode of knowledge transfer lacked; visualization of the equations in real life is the key to understanding the physics of any equation and that's what you have been able to bring to the table. Thank once again.
Thanks my friend!!
Cool video 👌👍 good explanation about divergence. Expecting more videos from you😊
Thanks my friend! Make sure to share it with your friends who might benefit from it :)
great man. thanks
This is like a drug for me. I recently shifted from an engineering centric career to corporate strategy consulting. I need more of this in my life!
Glad you like it 🙂
It's a really great video 🤯🎉 thank you ✌
Thanks brother!
This is really very interesting. Many thanks
Thank you buddy!
Thank you very much man for the clarified explanations. I am a chemical Eng student n to be honest, you just made my life much easier. Thax a lot.
Thank you for watching! :)
Great work... Thanks a lot
Thanks for the feedback Dileep!!
Nice one!
Cheers!
Thanks😊
Thank you so much! Would really appreciate it if you could continue doing tutorials of CFD!
Planned for it ;-) What topics would you suggest?
@@JousefM I am exploring how CFD can help with spray drying :) I would appreciate any advice! Software we have is Matlab.
In the reynolds transport eqn, what is U? is is the amount of whatever is fluxing through the cross section?
I have used this explanation to help for my graduation project, thank you!
Anytime 🙂
Great video.
Thanks mate!
Good lecture ever I have seen
Thanks Friend :)
@Jousef Murad What books do you recommend to learn CFD by using the FEM instead of FVM (used by Ansys)?
Thank you and very nice video!!
Thanks for your feedback André!
Here some resources:
- amzn.to/2HkaXsn
- link.springer.com/chapter/10.1007/978-3-540-85056-4_10
- www.researchgate.net/publication/270588439_Finite_Element_Methods_for_Computational_Fluid_Dynamics_A_practical_Guide
- amzn.to/31XyYiw
Hope that helps :)
How is Flux negative in the Reynolds Transport Theorem?
Finally finally finalllyyyyyyyyy!
( ͡° ͜ʖ ͡°)
@@JousefM Ó_Ó
I really liked and enjoyed the video and the explanation is very crisp.
I had a doubt from the finishing part, where u mentioned for source, divergence will be positive and vice versa for sink.
for every control surface the area normal vector will be out of the surface and if any vector field is in the direction of normal vector, it is positive otherwise negative. For source as the velocity vector is out of the control surface (in the direction of normal vector its positive) and for sink velocity is coming towards the center, I mean its opposite to normal vector. so its negative.
bro, is this explanation is correct.....??
If not let me know the correct explanation.......
thanks for the informative video......
Sounds good and it's actually what I said in the video? :P
Maybe this helps to solidify your knowledge: ua-cam.com/video/XyiQ2dwJHXE/v-deo.html :)
And of course thanks for your kind feedback! :)
Great presentation, I really liked it. Just one note: the slide in which you introduce the incompressible fluid equation is wrong, you do not need constant density in time and space. Density can vary in time and space and the fluid can still be incompressible. And also the definition of steady state you gave is wrong.
That’s correct so my presentation would be another „special case“ - some books also put it that way but you’re right that I could have mentioned it that in my case it does not but in general tho can vary in time and space. For reference you can have a look in famous fluid mechanics from (I believe) Spurk
Yes
1:43 what is flux? or where sohuld I read to understand what it is?
I think the divergence at the source is still 0. The inflow from the tap minus the outflow to the rest of the sink is 0
Loved the derivation, straight forward and easy to follow.
Thanks! 🙂
I'm a research scholar. I just want to get the way of modelling turbulence from NS equation. Any lecture ??
Planned for the future 🙂
nice videos ! we come from the same school. ;)
Grüße gehen raus! :)
can you attach the presentation please ?
There you go: www.patreon.com/posts/derivation-of-33991149
thanks for good explanation
but I wonder where you are from ??
Originally from Germany and now living and running my business consultancy from the Netherlands!
Wait... I don't get.
The Mass Continuity equation you derived is different from the one you said is a part of the Navier Stokes equation.
How come?
I'm new to CFD. I would really like if you could explain.
How do you mean it’s different - if you specify I can help 🙂
@@JousefM the mass continuity equation you talked about in 5:08 is not what you derived in 10:33
This video finally showed the real tangible derivation ...
Cheers 🙂😉
Make lecture of fluid mechanics from basic to advance
Planned for my new course platform in the future. 🙂
Now why can’t my lecturer explain the material like this 🤦🏻♀️😂
🙂