Man, when I saw that stickman drawings I knew inmediately the explanation was going to be worthwhile. You made the best video explaining de total derivative, the best intuition Many thanks!
Many thanks for the video! Just one question... when you say dr/dt is the particle velocity, and then in the river example you say that u is the velocity field. I can see that would be the case for a water particle, but what would happen if the velocity of the particle is different from the velocity field? Would the equation be the same? Thanks again!
Ah. Good question and point to clarify. In the world of fluid mechanics we often talk about a "fluid particle" which in a sense doesn't really exist. For the case of deriving equations, we imagine a chunk of fluid that we can follow around a it goes with the flow so to speak. There is only one velocity since fluid and particle are one in the same. We could visualize what such a particle would do in an actual lab experiment, by putting an actual solid particle in and study it's movement. In the case of the solid particle, it is true that the particle velocity need not equal the fluid velocity. General a small neutrally buoyant particle will go with the flow. Larger particles, ones that are heavy or light relative to the fluid, will do something else. That is a complex problem but one that people have worked on.
Overall very good and well explained. To someone who has an okay math background but not much physics and engineering background the notation a little confusing. The C function for the stationary observer and the C function for the travelling observer (or fluid particle) may refer to the same physical quantity but mathematically they are different functions. So shouldn't they have different names? Please help/explain. Thank you a lot again.
Thanks a lot. I have one question, the definition of Material Derivate of C is partial(C)/partial(t) + u. nabla(C). The first term measures the rate of change of C at a fixed point in space with respect to t, this term makes me confused: how would it change by itself IF the fluid is not moving? meaning, if the u = 0, then what makes C changes in time, e.g. if C a red dye, what makes it change in time if the fluid is not moving? I "think" the only source of change is due to fluid motion, so if u = zero, then nothing should change?
Imagine the power plant runs clean, then suddenly dumps pollutant in the river. That will diffuse over time and cause a change in time, even if the flow is stationary
Yes. Imagine you are floating down a river in a raft I am sitting on the banks. If I compute D/Dt of any quantity at a point in space (in my fixed frame). The value I compute at that point, at some instant would be the rate of change YOU would sense as you pass through that point.
I am unable to get the concept why concentration is not a function of time in first case while in the second case it is a function of the same. Can you give a real world example so that I could relate to it?
In the chain rule you indeed use "*" instead of "+", and this is why there is multiplication in the second term, but note that having two terms here (with a "+" between them) is not due to the chain rule: It's because C is a function of two variables, so in order to calculate it's derivative over time, you have to sum both it's it's change rate due to the first term (r, which is itself a function of time, hence the chain rule) - *and* it's change rate due to the second term (t, which is simply the time itself, so no chain rule here)
You should ask yourself why the hell did you decide to use a pollution case study! You could use the flow a scent going out of the skin of a woman... This is why you're having problems find a good paying job! Think about this;)
The pollution probe flowing downstream was a really intuitive explanation, thanks!
Very good explanation! Thank you!
Brilliant. Best explanation for material time derivative.
Man, when I saw that stickman drawings I knew inmediately the explanation was going to be worthwhile. You made the best video explaining de total derivative, the best intuition Many thanks!
I swear! These old videos are hidden gems!
Excellent! Very intuitive explanation. Thank u so much!
such a nice explanation. I was looking for it. thanks a lot
wow, thank you for the explanation!
Instead of saying it's a "sick explanation", explain why it's a sick explanation and give your recommendation and advice if you have any.
Thank you sir for the explanation. The example you have given, have help it more.
Excellent explanation, thank you very much!
Thank you sir for explaining
Many thanks for the video! Just one question... when you say dr/dt is the particle velocity, and then in the river example you say that u is the velocity field. I can see that would be the case for a water particle, but what would happen if the velocity of the particle is different from the velocity field? Would the equation be the same? Thanks again!
Ah. Good question and point to clarify. In the world of fluid mechanics we often talk about a "fluid particle" which in a sense doesn't really exist. For the case of deriving equations, we imagine a chunk of fluid that we can follow around a it goes with the flow so to speak. There is only one velocity since fluid and particle are one in the same. We could visualize what such a particle would do in an actual lab experiment, by putting an actual solid particle in and study it's movement. In the case of the solid particle, it is true that the particle velocity need not equal the fluid velocity. General a small neutrally buoyant particle will go with the flow. Larger particles, ones that are heavy or light relative to the fluid, will do something else. That is a complex problem but one that people have worked on.
Overall very good and well explained. To someone who has an okay math background but not much physics and engineering background the notation a little confusing. The C function for the stationary observer and the C function for the travelling observer (or fluid particle) may refer to the same physical quantity but mathematically they are different functions. So shouldn't they have different names? Please help/explain. Thank you a lot again.
Kent is a wrestling coach whose shown me plenty of support at Armstrong chapel!
Great video from italy
Very helpful explanation!
excellent explanation
thanks a lot :)
very good. thanks
extremely clear
thnx man, that was brilliant!!!
Thanks a lot. I have one question, the definition of Material Derivate of C is partial(C)/partial(t) + u. nabla(C). The first term measures the rate of change of C at a fixed point in space with respect to t, this term makes me confused: how would it change by itself IF the fluid is not moving? meaning, if the u = 0, then what makes C changes in time, e.g. if C a red dye, what makes it change in time if the fluid is not moving? I "think" the only source of change is due to fluid motion, so if u = zero, then nothing should change?
Imagine the power plant runs clean, then suddenly dumps pollutant in the river. That will diffuse over time and cause a change in time, even if the flow is stationary
Thanks for the explanation and thanks for creating such informative tutorials :)
So Would I be right in saying that the material derivative is the time rate of change of a fluid particle expressed in a fixed reference frame?
Yes. Imagine you are floating down a river in a raft I am sitting on the banks. If I compute D/Dt of any quantity at a point in space (in my fixed frame). The value I compute at that point, at some instant would be the rate of change YOU would sense as you pass through that point.
I don't quite understand what you mean by equating C(r,t) = C(a,t) at around 4:10
It's a constant. Just a number. Not acceleration.
nice
sir, can you explain the convective and local part interpretation?
Amazing
Thank you!
Thank you sir!!!!!!!
That example is more describing the difference between Eulerian and Lagrangian rather than material derivative?
The material derivative actually gives the relationship between the Eulerian and the Lagrangian point of view
thank you so much!
I am unable to get the concept why concentration is not a function of time in first case while in the second case it is a function of the same. Can you give a real world example so that I could relate to it?
This morning we prayed for a friend who lost his life to alcoholism.
why at 6:14 you write "+" instead of "." or multuiply?
Aren't we supposed to multiply in a chain rule ????
In the chain rule you indeed use "*" instead of "+", and this is why there is multiplication in the second term, but note that having two terms here (with a "+" between them) is not due to the chain rule: It's because C is a function of two variables, so in order to calculate it's derivative over time, you have to sum both it's it's change rate due to the first term (r, which is itself a function of time, hence the chain rule) - *and* it's change rate due to the second term (t, which is simply the time itself, so no chain rule here)
머라카노이거
I would love to reply to your comment... but not even google could translate this for me!
This is what they're doing to the ohio river.
You should ask yourself why the hell did you decide to use a pollution case study! You could use the flow a scent going out of the skin of a woman... This is why you're having problems find a good paying job! Think about this;)
Got a problem? It's his way of teaching. You hate it? go away.
@@int16_t I was being ironic:)
I see... it is hard to detect tone in a text.