The Material Derivative | Fluid Mechanics
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- เผยแพร่เมื่อ 6 ก.ย. 2024
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This video introduces the #MaterialDerivative and provides some intuition with derived examples using temperature and velocity. Essentially, the material derivative of a quantity carried by the particle in a substance in which that quantity varies is the combination of the intrinsic time variation of the system and the movement of the particle across the spatial gradient of the quantity.
Questions/requests? Let me know in the comments!
Pre-reqs: Basic understanding of ordinary and partial derivatives.
Lecture Notes: drive.google.c...
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EDIT: at 9:40, I made a mistake with the derivative and forgot that there was an additional factor of 3 out front! Thanks to Astrid below for pointing it out!
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Nice explanation. 9:49 I suggest you to take a look at derivative again. It should be multiplied by 3
Great explanation, so surprised I haven't heard of this term before during all my studies of vector calculus.
However, I believe there is a mistake at 9:40 when you take the derivative of the velocity profile term of 1/x^3 as -1/x^4, when it should be -3/x^4.
That's what i got too.
After 5 years in mechanical engineering it finally fully clicked! I had "kind of" the intuition but it was not 100%. It is so straight-forward now, thank you good sir.
I'm taking convective heat transfer this semester and this video helps out a LOT! Thank you guys at Khan!!
This video is brilliant! I felt I needed more intuition / visualisation of the material derivative. Now everything seems so simple. Thanks a lot sir!
Great explanation! Thanks a lot! You just solved my problem!
Title should be "why a physicists should care about the exterior derivative" ;)
Absolutely fantastic video! And this is coming from someone with no basis in fluid dynamics- helped me a lot with an online course I'm doing.
I like the fact that you talk fast, no time for my mind to wander off :)) Great channel!
thanks a lot for the great video and explanation ! but what happens if the particle P stays at the left side where the temperature doesn't change neither, but the right side's temperature goes from 300K to 350K ? DT/Dt also equals to 0 as for the first scenario ?
Very helpful, thanks.
Thank you so much for the video!!!!
Can you tell me please which writing software you are using?
Hi, what software and hardware do you use handwriting? Thank you!
Thanks for your work. Helps alot. Something I don't understand is how in the material derivative, sometimes the temporal term is equal to 0, because it seems to me that a particle can travel through space without moving in time, given that the space coordinates are function of it.
Good question! The temporal term being zero (I assume you're referring to the partial v/partial t term) just means that the velocity profile is not a direct function of time. That is, if you look at a specific point in the velocity profile of the fluid, the velocity at that specific point does not change with time.
However, if you drop a random particle into the fluid, then of course it will move around and accelerate depending on where it is in the fluid space. The material derivative is meant to capture the change in velocity of the particle as it whizzes through different parts of the fluid (i.e. the velocity will indirectly be a function of time as the position of the particle will change with time as it moves throughout the fluid). However, the partial v/partial t can still be zero if at each point in the fluid, the velocity at that point does not change with time directly.
@@FacultyofKhan thanks so much for your reply :)
Dear Khan,
What university are you currently studying at and what are you going there for?
I am really interested, but respect you if you don't wish to respond.
Best,
Ken
I always liked the name substancial derivative. It made me think of something juicy. Another good name is convective derivative.
Question: is the material derivative comprised of a particle-independent term and a particle-dependent term? If yes, then why did you solely use the velocity profile of the fluid in your DV/Dt example. Thanks!
In the sense that the particle-independent term is the rate of change of temperature partial T/partial t and that the particle-dependent term is the u dot grad T, then yes, your first statement is correct. I'm not sure what you mean by solely using the velocity profile of the fluid: our goal is to find the rate of change of the temperature of a specific particle in that fluid, which would involve using the fluid's velocity profile to track that particle.
You sound like hank green. But no words just math
I thought the same!
The explanation was just too good
fantastic video! Thank you!
Perfect explanation!
Glad it was helpful!
Is it different between
“(v dot del)v” and “v dot (del v)” ?
I am your fan dude.... Very interesting video :D
I don't understand why you assume that the moving particle should immediately get the same temperature as the background. I think that the convection is a transfer of heat due to the fluid particles carrying thermal energy along with them, so maintaining for a while a different temperature than the temperature of other particles that were already in that area.
@@beoptimistic5853 stop spamming
Here we are not considering fluid particle as a molecule, but as a clump of infinite number of molecules called fluid parcels( also known as fluid particle, don't know why🙄). And a fluid parcel always behaves same as the fluid flow. So ,when flow deforms, fluid parcel deforms; when flow accelerates, parcel accelerates; and when flow changes temperature unevenly, the parcel also changes its temperature in the same way.
@@aniketsingh810 yes, the fact is that fluid parcel is most appropriate because we are describing indeed an abstract point sensing🌡️ the temperature of the fluid at that coordinates and nothing physically moving and carrying on its own temperature. However yes, long time has past, I understood it myself eventually.
Yup! Kind of along the lines of what you and Aniket said; it's more of an abstract point used to describe a concept that simplifies the notation in equations like Navier-Stokes. I do agree that in reality, there would be a (slight) delay in the particle acquiring the temperature of the surrounding fluid, but again, this is an abstract concept.
Hope that helps and apologies for the late reply!
Holy crap you are FLYING
Can you make a vedio about Lyra's Geometry ?
In every physics course using the material derivative none of them mentioned that it is the derivative with a moving particle xD luckily I already knew about it, but everytime students were confused necessarily... maybe it is something that researchers assume everyone knows lol
(Like waves, I hate waves. I do not understand them lmao... like wtf is a k vector and how can I tune it using a machine? I understand I can e.g. choose the frecuency of the laser, but what is k? I cant picture it clearly, which is disturbing since it is such a basic topic compared to other stuff I study)
Yea I hear you lol. It's frustrating not just in lectures but while reading textbooks; they go from an equation on one line to a different equation on the next line without any explanation (and it turns out there's like 50 algebra steps needed to move from one line to another).
Material derivative of velocity is acceleration. Shouldn’t there be second order derivative?
OMG NICE
🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
Why is no-one talking about the fact that he did the derivative wrong?
So that wasn't just me that noticed that. I had: (V)[(-3)(R^3/X^4)]
My mistake! I forgot the additional factor of 3. Thanks for pointing it out: I'll make an edit in the description!
That notation DT/Dt is heresy