A fluid of viscosity, µ, flows down a vertical rod of radius, ro. At some point down the rod, the...

A fluid of viscosity, μ, flows down a vertical rod of
radius, ro. At some point down the rod, the flow reaches a steady condition
where the film thickness, h, is constant and the velocity vz = ƒ(r) only.
Assuming no shear stress at the fluid–air interface,

a. Draw a picture of the situation and your control volume.

b. Derive the differential equation governing the velocity
profile in the fluid film.

c. What are the relevant boundary conditions?

d. Solve the equation for the velocity profile.

e. Determine the volumetric flowrate of fluid leaving the
rod.