$(30$ points$)$ For a irrotational flow, the potential function is given

by $\frac{O}{?}=U_{}rcos+\frac{B}{r}cos$

$($a$)$ Find the velocity components $v_r$ and $v_{}$

$($b$)$ If the flow filed describes the uniform flow of velocity $100\frac{m}{s}$

past the cylinder with radius of $5$ m $,$ determine the value of $\frac{?}{\text{b}\text{a}\text{r}}(B).$

$($c$)$ With the parameters given in $($b$),$ calculate the velocity

distribution on the cylinder surface.

$($d$)$ Calculate the pressure coefficient on the cylinder surface.

Please write out each step clearly