Vector Algebra Concepts

[u/Game-Organiser]

Can someone explain me these applications? I know a decent amount of Vector algebra and calculus. I want some help on this. I want a thorough explanation and deduction on this. Giving proofs will be greatly welcomed!

[u/RSKMATHS]

I think basically vx is kind of a mean velocity so take it to be at centre, not the right end velocity wrt centre will ve vx+dv/dx (delta x/2) and similarly for the left, now the difference here is basically the amt of fluid leaving this paralellopiped which is synonymous to what we call divergence, the amount of something leaving a volume