$(30$ points$)$ The Navier$-$Stokes Equations represent the conservation of momentum used to

mathematically model fluid flow phenomena. Can you derive the following form of the Navier$-$

Stokes Theorem $($known as Cauchy's equation$)$ for the control volume $($CV$)$ below?

$\frac{D(vec(V))}{Dt}=.+vec(f{)}_b$

where

$=$ density

$=$ stress.tensor

vec$(f{)}_b=$ bodyforce