complete answer

Carry out a "microscopic" mass balance of a flow system with v=vrr+v+vzz in cylindrical coordinates (i.e., deriving the equation of continuity in cylindrical coordinates). You can compare your answer with Eq. B.4-2 in the Appendix of the textbook. Please do not use Gauss's divergence theorem but to consider fluxes crossing each surface of a cylindrical control domain (the one I briefly mentioned in class)