A simple viscometer measures the time t for a solid sphere to fall a distance L through
Chapter 1, Problem p1.50(choose chapter or problem)
A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fl uid of density . The fl uid viscosity is then given by < Wnett 3DL if t $ 2DL where D is the sphere diameter and Wnet is the sphere net weight in the fl uid. ( a ) Prove that both of these formulas are dimensionally homogeneous. ( b ) Suppose that a 2.5 mm diameter aluminum sphere (density 2700 kg/m 3 ) falls in an oil of density 875 kg/m 3 . If the time to fall 50 cm is 32 s, estimate the oil viscosity and verify that the inequality is valid.
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