$4)$ A cylindrical solid rod of length $3$ m with a diameter of $0\mathrm{.}75$ m is carried in still water at a uniform and steady speed of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Determine disregarding viscous$-$frictional effects by treating motion as incompressible and potential

a$)$ Stream function of water flow relative to rod

b$)$ Static pressure difference between point $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ on the rod surface

If surface friction of the rod is taken into account

c$)$ Drag force

d$)$ The magnitude of rod speed producing potential flow $($with surface friction$)$ Hint: Take water viscosity as $\backslash (1\mathrm{.}5\backslash$times $10^\{6\}\backslash$mathrm$\{$~m$\}^\{2\}/\backslash$mathrm$\{$s$\}\backslash )$ and density as $\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}3\backslash ).$ Neglect the weight of solid.