Consider the system shown below, which is used to coat wires with a polymer layer. A wire is pulled at a constant velocity $U$ through the center of a circular pipe filled with a polymeric solution. Additionally, there is a pressure difference $($i$.$e$.$ drop$)$ across the length $L$ of the wire. The coordinate system and geometry are defined below.

a$.$ List the relevant components of the total momentum flux and express them in terms of their non$-$zero molecular and convective momentum flux terms.

b$.$ What are the boundary conditions for the problem shown above?

c$.$ Obtain and expression for the relevant velocity components and sketch the velocity profile.

d$.$ Obtain an expression for the stress and shear force acting on the surface of the wire.