The Material Derivative | Fluid Mechanics

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@FacultyofKhan 4 жыл бұрын

Thanks to Skillshare for graciously sponsoring this video! The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: skl.sh/facultyofkhan11201

@FactsSpeakerr Жыл бұрын

Nice explanation. 9:49 I suggest you to take a look at derivative again. It should be multiplied by 3

@MoeSalamaIbrahim 9 ай бұрын

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.

@brunohawkins5829 8 ай бұрын

That's what i got too.

@MCcraftersCZE 7 ай бұрын

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.

@erockromulan9329 2 жыл бұрын

I'm taking convective heat transfer this semester and this video helps out a LOT! Thank you guys at Khan!!

@ManUser77 2 жыл бұрын

This video is brilliant! I felt I needed more intuition / visualisation of the material derivative. Now everything seems so simple. Thanks a lot sir!

@shahryarhabibi7187 Жыл бұрын

Great explanation! Thanks a lot! You just solved my problem!

@knng2008 Жыл бұрын

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.

@sheknows9704 4 жыл бұрын

I like the fact that you talk fast, no time for my mind to wander off :)) Great channel!

@Rodolfoalvescarvalho 4 жыл бұрын

Hi, what software and hardware do you use handwriting? Thank you!

@brijeshmehra8182 4 жыл бұрын

Thank you so much for the video!!!! Can you tell me please which writing software you are using?

@oyugioyugi6018 4 жыл бұрын

Title should be "why a physicists should care about the exterior derivative" ;)

@tianyuzhang793 4 ай бұрын

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 ?

@AB-ts7gi 5 ай бұрын

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!

@FacultyofKhan 5 ай бұрын

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.

@BCarli1395 10 ай бұрын

Very helpful, thanks.

@demr04 2 жыл бұрын

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.

@FacultyofKhan Жыл бұрын

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.

@demr04 Жыл бұрын

@@FacultyofKhan thanks so much for your reply :)

@saylensya 2 жыл бұрын

Perfect explanation!

@FacultyofKhan Жыл бұрын

Glad it was helpful!

@commonwombat-h6r 2 жыл бұрын

fantastic video! Thank you!

@davidescobar7726 4 жыл бұрын

I am your fan dude.... Very interesting video :D

@VictorSarkarchb 3 жыл бұрын

The explanation was just too good

@josephtraverso2700 Ай бұрын

Thank you

@kennethdang4446 4 жыл бұрын

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

@Ottmar555 4 жыл бұрын

I always liked the name substancial derivative. It made me think of something juicy. Another good name is convective derivative.

@giuliocasa1304 4 жыл бұрын

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.

@giuliocasa1304 4 жыл бұрын

@@beoptimistic5853 stop spamming

@aniketsingh810 3 жыл бұрын

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.

@giuliocasa1304 3 жыл бұрын

@@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.

@FacultyofKhan 3 жыл бұрын

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!

@cau_drummer 8 ай бұрын

Is it different between “(v dot del)v” and “v dot (del v)” ?

@jgabb005 2 жыл бұрын

Holy crap you are FLYING

@هنا-ط9خ 4 жыл бұрын

Can you make a vedio about Lyra's Geometry ?

@RahulSharma-oc2qd 3 жыл бұрын

Material derivative of velocity is acceleration. Shouldn’t there be second order derivative?

@dwupus8661 2 жыл бұрын

You sound like hank green. But no words just math

@knng2008 Жыл бұрын

I thought the same!

@eulefranz944 4 жыл бұрын

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)

@FacultyofKhan 3 жыл бұрын

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).