Material derivative [Fluid Mechanics

[@inezm9051]

im in the 9th week of my fluid mechanics graduate course and have been lost since week 1. just started binging your series and things are making so much more sense!!!! thank you so much for putting this absolute gold into the universe.

[@prof.vanburen]

Thanks for the kind words and good luck with grad studies!

[@Sophie_Ludgate]

I feel like this has been the missing link that is never found in the literature. Its really helped me to begin understanding the equations of motion for fluids. Much appreciated!! Thank you :) I'll be checking out your other videos now

[@prof.vanburen]

Thank you so much! Hope you enjoy them.

[@kiranpawar6490]

Nicely explained. It is treat to watch.

[@prof.vanburen]

Thanks!!

[@ashfaqahmed9574]

Beautifully explained Thank you so much professor.

[@prof.vanburen]

Thanks!!

[@thinkingpi]

Very nicely explained. Thank you

[@prof.vanburen]

Thank you!

[@rudraksh5840]

This really explained the stuff. Thanks a lot.

[@prof.vanburen]

You're welcome! Glad you liked it

[@saugatojha9870]

@ 4:37 , how the change in velocity with respect to time was constant ?

[@prof.vanburen]

In this case, it is taking the Eulerian perspective so that the balls passing through the window always have the same velocity, no matter what time you view through that window. This is not the same as the balls individually accelerating, which they are. In the Eulerian perspective, you are constantly observing a new particle. Does this help?

[@frahman1963]

@@prof.vanburenFor the Eulerian perspective, if du is always 0, then how can you get a value for acceleration using the material derivative?

[@prof.vanburen]

Technically, in the window you are observing you can only say that velocity is not changing in time, so du/dt = 0. However, the velocity of the ball before and after the window might be different, so du/dx might not be zero. These lead to non-zero terms in the material derivative. @@frahman1963

[@frahman1963]

@@prof.vanburen thank you!