$(7$ points$)$ Fig. E$3\mathrm{.}3$b copied below from the textbook shows a flow field with circular streamlines. The velocity distribution for case $($b$)$ is

$V=\frac{V_0{r}_0}{r}$

where $V_0$ is the velocity at $r=r_0.$

$(5$ points$)$ Determine the pressure distributions, $p=p(r),$ for case $b)$ if pressure along the circle $r=r_0$ is $p_0.$

$(2$ points$)$ Calculate this pressure at $r=\frac{r_0}{2}$ assuming that $r_0=3m,V_0=0\mathrm{.}5\frac{m}{s}.$