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A steel sphere, 1.5 mm diameter and of mass 13./ mg, falls steadily in oil through a vertical distance of 500 mm in 56 s. The oil has a density of 950 kg m3 and is contained in a drum so large that any wall effects are negligible. What is the viscosity of the oil? Verify any assumptions made.

A steel sphere, 1.5 mm diameter and of mass 13./ mg, falls steadily in oil through a vertical distance of 500 mm in 56 s. The oil has a density of 950 kg m3 and is contained in a drum so large that any wall effects are negligible. What is the viscosity of the oil? Verify any assumptions made.

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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**Problem Description:** A steel sphere, 1.5 mm in diameter and with a mass of 13.7 mg, falls steadily in oil through a vertical distance of 500 mm in 56 seconds. The oil has a density of 950 kg m⁻³ and is contained in a drum so large that any wall effects are negligible. **Question:** What is the viscosity of the oil? Verify any assumptions made. **Explanation:** This problem involves calculating the viscosity of the oil based on the steady fall of a sphere. The density of the oil and the dimensions and mass of the steel sphere are given. The task requires using these parameters to find the viscosity, considering a minimal effect from the container walls due to its large size. For educational purposes, such a problem often uses principles of fluid dynamics and might relate to Stokes' law, where the viscous drag on a small sphere in a fluid is proportional to the sphere's velocity, radius, and the fluid’s viscosity. An analysis would include calculating the terminal velocity of the sphere and using these known quantities to determine viscosity. **Assumptions:** 1. The sphere reaches terminal velocity quickly. 2. The effects of the container walls on the flow are negligible. 3. The fluid flow around the sphere is laminar. Such assumptions enable simplification of the problem for calculation purposes.
Transcribed Image Text:**Problem Description:** A steel sphere, 1.5 mm in diameter and with a mass of 13.7 mg, falls steadily in oil through a vertical distance of 500 mm in 56 seconds. The oil has a density of 950 kg m⁻³ and is contained in a drum so large that any wall effects are negligible. **Question:** What is the viscosity of the oil? Verify any assumptions made. **Explanation:** This problem involves calculating the viscosity of the oil based on the steady fall of a sphere. The density of the oil and the dimensions and mass of the steel sphere are given. The task requires using these parameters to find the viscosity, considering a minimal effect from the container walls due to its large size. For educational purposes, such a problem often uses principles of fluid dynamics and might relate to Stokes' law, where the viscous drag on a small sphere in a fluid is proportional to the sphere's velocity, radius, and the fluid’s viscosity. An analysis would include calculating the terminal velocity of the sphere and using these known quantities to determine viscosity. **Assumptions:** 1. The sphere reaches terminal velocity quickly. 2. The effects of the container walls on the flow are negligible. 3. The fluid flow around the sphere is laminar. Such assumptions enable simplification of the problem for calculation purposes.
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