A flow has a velocity field $V=\frac{A}{r^2}{e}_r+\frac{B}{r}{e}_{}+$Csin$(t)e_z$ expressed using cylindrical coordinates $($as

defined in our Vector Algebra class slides$).$ The symbols $A,B,C$ and $$ denote dimensional constants

and $t$ is time. Find, as explicit functions of position, expressions for

$($a$)$ the time rate of change of velocity seen at a fixed point in space,

$($b$)$ the acceleration of the fluid material,

$($c$)$ the time rate of change of volume of a fluid particle as a fraction of its volume,

$($d$)$ the average angular velocity of the fluid particles.