(Solution) - A simple viscometer measures -(2025 Original AI-Free Solution)

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A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fluid of density ?. The fluid viscosity ? is then given by ? ? WnetI /3? DL if t ?2pDL /? 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.