Discussing the physical meaning of the Reynolds Transport Theorem and applying it to formulate the continuity equation. Part of the Advanced Fluid Mechanics course.
material volume ,material particle, system , fixed volume , etc , lots of concepts in the fluid mechanics and slightly different equations . Without your explanations i could ve fail fluid mechanics course. fixed in space was remaining i think for the control volume
In the derivation of continuity equation for incompressible fluid, The divergence of the velocity field is zero. I was confused since you take the gradient of velocity.
Here, the nabla operates on a vector field (velocity) and the result is a scalar, so it is indeed divergence. Gradient operates on a scalar field, and the result is a vector.
Thank you! I use the screen capture as write the notes on a tablet and then remove the background and overlay them on the main frame in Final Cut Pro (you could also do it in Premiere or other video editors).
Mass times volume is not equal to mass. Density times volume is equal to mass. Using "beta" = extensive property per unit mass would have reconciled your equations to be dimensionally correct and prevented confusion. Nicely presented otherwise.
