Let vec$(v)=($:$x^{2}z,4-4xyz,x{z}^2$:$)$ be the velocity field of a fluid. Compute the flux of vec$(v)$ across the surface $16x^2+9z^2=(y-12{)}^2$ where $0$ and the surface $is$ oriented away from the origin.

Hint: Use the Divergence Theorem.