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Q3 A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius ro = 0.3m and internal radius of ri = 0.1m. (a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferential stresses at the internal and external surface may be expressed by the following equations. at ri σ₁ = 0 and σ = -2Pok² k² - 1 - = -2.25P at ro: Or = -Po and σ = -Po(k² + 1) k² - 1 = -1.25Po (b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm‍³ and g = 9.81ms²². (c) In an effort to reduce the stresses at the inner surface, the operators decide to increase the internal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change in length when submerged in the sea to a depth of 7000 metres, with this internal pressure applied. Consider Young's modulus of silicon is 106 GPa and Poisson's ratio is 0.33. Answers (a) Proof (b) or =0, σ0=-158.4 MPa, oz = -79.2 MPa (c) -0.371 mm

Q3 A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius ro = 0.3m and internal radius of ri = 0.1m. (a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferential stresses at the internal and external surface may be expressed by the following equations. at ri σ₁ = 0 and σ = -2Pok² k² - 1 - = -2.25P at ro: Or = -Po and σ = -Po(k² + 1) k² - 1 = -1.25Po (b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm‍³ and g = 9.81ms²². (c) In an effort to reduce the stresses at the inner surface, the operators decide to increase the internal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change in length when submerged in the sea to a depth of 7000 metres, with this internal pressure applied. Consider Young's modulus of silicon is 106 GPa and Poisson's ratio is 0.33. Answers (a) Proof (b) or =0, σ0=-158.4 MPa, oz = -79.2 MPa (c) -0.371 mm

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Q3 A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius ro = 0.3m and internal radius of ri = 0.1m. (a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferential stresses at the internal and external surface may be expressed by the following equations. at ri σ₁ = 0 and σ = -2Pok² k² - 1 - = -2.25P at ro: Or = -Po and σ = -Po(k² + 1) k² - 1 = -1.25Po (b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm‍³ and g = 9.81ms²². (c) In an effort to reduce the stresses at the inner surface, the operators decide to increase the internal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change in length when submerged in the sea to a depth of 7000 metres, with this internal pressure applied. Consider Young's modulus of silicon is 106 GPa and Poisson's ratio is 0.33. Answers (a) Proof (b) or =0, σ0=-158.4 MPa, oz = -79.2 MPa (c) -0.371 mm
Transcribed Image Text:Q3 A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius ro = 0.3m and internal radius of ri = 0.1m. (a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferential stresses at the internal and external surface may be expressed by the following equations. at ri σ₁ = 0 and σ = -2Pok² k² - 1 - = -2.25P at ro: Or = -Po and σ = -Po(k² + 1) k² - 1 = -1.25Po (b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm‍³ and g = 9.81ms²². (c) In an effort to reduce the stresses at the inner surface, the operators decide to increase the internal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change in length when submerged in the sea to a depth of 7000 metres, with this internal pressure applied. Consider Young's modulus of silicon is 106 GPa and Poisson's ratio is 0.33. Answers (a) Proof (b) or =0, σ0=-158.4 MPa, oz = -79.2 MPa (c) -0.371 mm
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