A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fluid of density ρ. The fluid viscosity μ is then given by μ ≈ WnetI /3π DL if t ≥2pDL /μ Where D is the sphere diameter and Wnet is the sphere net weight in the fluid.
(a) Show that both of these formulas are dimensionally homogeneous.
(b) Suppose that a 2.5 mm diameter aluminum sphere (density 2700 kg/m3) falls in an oil of density 875 kg/m3. If the time to fall 50 cm is 32 s, estimate the oil viscosity and verify that the inequality is valid.