A solid cylinder of diameter D, length L, density s falls due to gravity inside a tube of diameter Do The clearance, (Do D) D, is filled with a film of viscous fluid (,) Derive a formula for terminal fall velocity and apply to SAE 30 oil at 20C for a steel cylinder with D 2 cm, Do 2 04 cm, and L 15...

The geometry is similar to Prob 147 only vertical instead of hori ...

A solid cylinder of diameter D, length L, density s falls due to gravity inside a tube

Question:

A solid cylinder of diameter D, length L, density ρ s falls due to gravity inside a tube of diameter Do. The clearance, (Do −D) << D, is filled with a film of viscous fluid (ρ,μ). Derive a formula for terminal fall velocity and apply to SAE 30 oil at 20°C for a steel cylinder with D = 2 cm, Do = 2.04 cm, and L = 15 cm. Neglect the effect of any air in the tube.