$2.$ Consider a catheter inserted into a blood vessel. For this problem, make the $($silly$)$ assumption that there is no blood flow $($i$.$e$.$ the blood is stationary$),$ but the catheter is being withdrawn from the blood vessel at a constant velocity $\backslash ($ U $\backslash )($see figure below$).$ Thus, the flow of blood in the annulus between the catheter and blood vessel is driven by shear. You can also assume that the flow is unidirectional in the axial direction. The radius of the blood vessel, $\backslash ($ R$\_\{$b$\}\backslash )$ is $3$ times the radius of the catheter, $\backslash ($ R$\_\{$c$\}\backslash ).$

a$.)$ Starting with the appropriate Navier$-$Stokes equations, write an appropriate equation for the motion of fluid in the annulus between the catheter and in the blood vessel. In order to get full credit, justify ALL the assumptions you make to simplify the equation.

b$.)$ Solve the differential equation from part a to obtain the general solution.

c$.)$ Write appropriate boundary conditions $(2)$ for the flow in the annulus

d$.)$ Using the boundary conditions you specified in part c$,$ solve to obtain the particular solution to the differential equation.

$*$Please wrote it out instead of typing it out. I understand there is AI$,$ but I looked at other solution and it's really confusing. Thank you. $*$