A fluid exits at the top of a solid cylinder of radius $kR$ and flows down around the exterior of the cylinder forming a film of constant thickness.

The vertical component of the velocity is the only non$-$zero component.

a$)$ Obtain the vertical linear momentum balance in terms of the non$-$zero molecular and convective momentum flux terms.

b$)$ What are the boundary conditions?

c$)$ Obtain an expression and draw the stress profile.

d$)$ Obtain an expression and draw the velocity profile.

e$)$ Determine the force exerted by the fluid over the cylinder.