A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fluid of density p. The fluid viscosity u is then given by 2PDL if t2 3TDL where D is the sphere diameter and Wnet is the sphere net weight in the fluid. (a) Prove 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.
A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fluid of density p. The fluid viscosity u is then given by 2PDL if t2 3TDL where D is the sphere diameter and Wnet is the sphere net weight in the fluid. (a) Prove 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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A simple viscometer measures the time t for a solid sphere
to fall a distance L through a test fluid of density p. The
fluid viscosity u is then given by
2PDL
if t2
3TDL
where D is the sphere diameter and Wnet is the sphere net
weight in the fluid. (a) Prove 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.
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