A non$-$dimensional velocity field in cylindrical coordinates is given by:

$V^{}=-(\frac{1}{r})i_r,+4r{r}_i$

Determine

a$)$ An expression for the acceleration of a particle anywhere within the flow field.

b$)$ The equation for a streamline passing through the point $(x,y)=(3,0).$

c$)$ The components of the rate$-$of$-$strain tensor; sketch a differential element in cylindrical coordinates and show $($as vector arrows$),$ the direction of the rate$-$of$-$strain components.

d$)$ The vorticity of a particle at $(3,0).$