Fluid Mechanics: Topic 10.2 - The material derivative

[@carlosmayorga2779]

Thank you professors!!! This explanation was simple the clearest I ever listened to. Incredibly clear!!!

[@CPPMechEngTutorials]

Hooray!!!

[@gavilin-u5k]

This was a perfect recap of the material derivative, thank you.

[@CPPMechEngTutorials]

Thanks

[@adhavankadhiravan4132]

An asset for anyone who wants to learn the fundamentals of Fluid Mechanics.

[@CPPMechEngTutorials]

Thanks!

[@mirkodibenedetto3155]

This is the best explanation of this topic I've ever found

[@CPPMechEngTutorials]

Thanks!

[@hamidfortab7769]

Very good video. However, I do not understand from 0:41 to 1:07. Why dV(A) is equal to dV? At t+dt there will be a new element in the control volume and may have completely new velocity at a completely different direction. Even based on your example the red arrows (velocity vectors of element and control volume) at t+dt is different. Considering the fact that the initial velocity at t is same for element and control volume, so how dV(A) is similar to the dV? Thank you

[@MrVitness]

They are equal as dt approaches zero, which means its basically the same point but in two different reference systems.

[@gzitterspiller]

I really liked the video, I am working on a sph simulator (very simple, 2d) and I want to get good intuition around fluid dynamics. One way to get it mathematically is to think it this way (P stands for property) P(x,y,z,t) in eulerian, then attach the vector field which would stand for the particle position in terms of time g(t)=(posx(t),posy(t),posz(t),t) Let D(t)=P(g(t)) and then just apply the chain rule.

[@fernandojimenezmotte2024]

beautiful explained , very didactic and neat even for professionals that are not from mechanical engineering !

[@alexanderpetsopoulos715]

Phenomenally concise and helpful video, great job.

[@mohammadhomsee8640]

There is point that I didn't understand, Why you are putting plus between derivatives at 01:28, Some people say this is chain rule, but i didn't understand how this could be chain rule. Thank you professor for your time

[@florianarbes]

Finally I understood that, thank you! I wish i had seen that video a long time ago...

[@beoptimistic5853]

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[@math3mantic]

Very clear explanation. Really helpful, thank you! I really appreciate your work.

[@CPPMechEngTutorials]

Our pleasure.

[@AppVolution]

Amazing video! Thank you so much!

[@saddamgillani7608]

whats the meaning of velocity at the previously occupied location also changes ... what i can understand out of this correct me if i,m wrong is that if the fluid element after moving through space comes to the same location it was at some other time , the velocity isn,t going to the same for the same fluid element

[@vusvis]

Awesome video, just a question on notation: why is the convective term written as "(V dot Nabla)alpha" instead of "V dot Nabla dot alpha"

[@CPPMechEngTutorials]

The dot product is an operation performed between two vectors (V and nabla). Alpha is not a vector.

[@vusvis]

@@CPPMechEngTutorials Ah that makes sense, thank you for the quick reply!

[@waqaskhandev]

would you explain me a little bit of what is Convective term . I didn't full understand it.

[@beoptimistic5853]

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[@muhammadajmal7363]

Great Job Sir... But we can take grad only of scalar Quantities, like del(T). Then how we take del(V) i,e, V. Del(V)?

[@wiskeypint4514]

We took del.v n not delv, which would be the divergence and not the gradient

[@ramazanoruc34]

Very good explanation really appreciate to your work.

[@HMotam-dn6by]

Thank you very much for this fantastic video!

[@nikan4now]

One question. In the Eulerian description x, y , z are not functions of time are they? So why is dv(eulerian)=dv/dxdxdt and so forth?

[@CPPMechEngTutorials]

V is a function of space and time in the Eulerian point of view, leading to the full derivative expression at 1:10. Then we simply divide by dt. dx/dt refers to how fast a particle would move in the x direction at a given location in the flow field, which we call u.

[@nikan4now]

Thanks, but my question is "x" in the Eulerian description is not a function of "t", is it? So are we differentiating x with respect to t or not? If we did that would be the Lagrangian description, wouldn't it?

[@dariodiaz2695]

@@nikan4now In the Eulerian description you can always write the coordinates as functions of their initial values instead of time, therefore you can write the velocity field in function of space only.

[@nikan4now]

Not sure what you mean by writing coordinates as function of their initial values. What initial values?

[@MrAmgadHasan]

The temperature differs from one location to another. The fluid picks up the temperatures of the locations it passes by. To calculate the change in temperature of the fluid, we calculate the change in temperatures between the locations which the fluid passes by. To determine the rate of change of the temperature, we multiply by the rate with which the fluid passes by these location, which is the velocity. You can first think about it in 1D. dT(change in fluid temperature)=dx(the change of location) *dT/dx( how much the temperature changes from location to another). dT=dx*dT/dx dT/dt (how fast the temperature of the fluid changes) = dT/dx*dx/dt (how fast the fluid changes location, also called velocity). Hope this helps.

[@biaoli7405]

very excellent explanation!

[@MrAmgadHasan]

Isn't the convective term simply the directional derivative along the velocity?

[@beoptimistic5853]

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[@TheCaptainCombo]

I think now I am starting to understand this topic. Thanks...

[@beoptimistic5853]

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[@pro.navalarchitect]

Very good explanation, much appreciated.

[@ivankolodko937]

Could you please explain why doesn't dx, dy, dz equal 0 while the point where the velocity is measured is fixed?

[@ajayjadaun100]

For time dt which tends to zero we imagine that we moved to next fixed point which has x+dx position but as dx is also very small the new point is approximately the same point.

[@iam.cristiano007]

awesome video very easy to understand.informative gud work.

[@davidbarreto6180]

Amazing explanation

[@CPPMechEngTutorials]

Thanks

[@hawraaraheem2449]

You describe 3 derivatives with material derivative can you write it here because my native language is Arabic and need to translate these details derivatives please

[@OlafvanBuul]

Thank you! Very concise and clear

[@seayellow5834]

Damn, finally understand DV/Dt!

[@mohammadmohagheghfaghih8313]

Well done!

[@beoptimistic5853]

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[@annothree7881]

very clear, helped me a lot, thanks :)

[@beoptimistic5853]

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[@Felipx2812]

Thank you SO much !!!

[@CPPMechEngTutorials]

You are welcome SO much. :)

[@AdiRadoniqi]

godbless u guys

[@CPPMechEngTutorials]

Awww... thanks.

[@second_lieutenant]

thank you!

[@beoptimistic5853]

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[@xamoralx]

охуенное объяснение, большое спасибо!

[@krishnasai928]

thanks a lot dude

[@CPPMechEngTutorials]

No problem.

[@josiahbray6870]

Thanks man!

[@CPPMechEngTutorials]

No problem man!

[@Pompowernobs]

perfect

[@int16_t]

Another known name is "The big D"

[@muhammadmubashir2956]

Video quality is poor

[@focusonbasics3066]

Great explanation