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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 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.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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 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.
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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