Fluid Mechanics Lesson 04A: The Material Derivative

[@DeethAlAkir]

Thank you. Wish I had paid more attention in calculus. I think trying to understand fluid mechanics without strong fundamentals of calculus makes it way more difficult than it needs to be.

[@johncimbala]

Thank you for your kind comment. Please tell your friends and colleagues about my KZbin channel where there are hundreds of free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

[@VicenteAlvarado-l6x]

You are a blessing to this world!!!!

[@johncimbala]

Thank you for your kind comment. Please tell your friends and colleagues about my KZbin channel where there are almost 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

[@xinghuahan610]

This video helps me a lot, with very clear explanation and examples. Thank you!

[@johncimbala]

Thank you for your comment. Please tell your friends and colleagues about my KZbin channel where there are more than 400 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

[@ejimadam2022]

I'm not sure what u,v and w are? At 7:00 what happens to u,v, and w in the operator, also i'm not sure of this combined operator and why it's not just del dotted into v. It seems wrong to me.

[@johncimbala]

u, v, and w are the velocity components of V, the velocity vector. Del dot V would become a scalar equal to delu/delx +delv/dely + delw/delz, whereas V dot Del is still an operator that can be applied to any scalar, vector, or even tensor. Thank you for your comment. Please tell your friends and colleagues about my KZbin channel where there are more than 460 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

[@gelomelo3426]

Great explanation 👏👏👏👏 thank you so much🌹🌹🌹🌹🌹

[@bariskirmizigul3160]

Hi sir thank a lot. I have a question. How can we take the material derivative of velocity in cylindrical coordinates? Can you make an example of it. I couldnt find any on the internet

[@johncimbala]

The left-hand side of the Navier-Stokes equation is essentially the material derivative of velocity, which is acceleration of a fluid particle following the fluid particle. So... look at the equation sheet in cylindrical coordinates and the left-hand side is the material derivative in cylindrical coordinates! Thank you for your comment. Please tell your friends and colleagues about my KZbin channel where there are more than 400 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

[@commentingonly4402]

Nice video but I dont understand what would be the answer if in the example problem V=3xy*i-3y*j? So the first component of the vector field also depends on y for example.

[@johncimbala]

That is why you take PARTIAL derivatives instead of total derivatives. delV/dely = 3x*i - 3j in your example. And delV/delx = 3y*i since there is no x in the second term of your example. When all is said and done, collect all the i terms and all the j terms separately. Hope this helps. Thank you for your comment. Please tell your friends and colleagues about my KZbin channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.