Q3A closed ended, thick-walled cylinder, manufactured from silicon material is designed to containinstrumentation for underwater research. It has an outer radius r = 0.3m and internal radius ofr¡ = 0.1m.(a) The cylinder is subjected to an external pressure Po. Show that the radial and circumferentialstresses at the internal and external surface may be expressed by the following equations.at ri:at ro:0₁ = 0 and 60Or = -P and o==-2Pok²k² 1-2.25P−P(k² + 1)k²-1=-1.25Po(b) Calculate the radial, circumferential, and axial stresses at r₁, when the cylinder is submergedto a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm-³and g9.81ms-².(c) In an effort to reduce the stresses at the inner surface, the operators decide to increase theinternal pressure in the cylinder to 20 MPa. If the cylinder is 1.5m long, calculate its change inlength when submerged in the sea to a depth of 7000 metres, with this internal pressureapplied. Consider Young's modulus of silicon is 106 GPa and Poisson's ratio is 0.33.

Given data, Outer radius of the cylinder, ro = 0.3 m Inner radius of the cylinder, ri = 0.1 m…

A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius r = 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: at ro: and g 0₁ = 0 and o = = Or-Po and og = -2Pok² k²-1 = -2.25Po -Po(k² + 1) k²-1 (b) Calculate the radial, circumferential, and axial stresses at ri, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm-³ 9.81ms 2. = -1.25Po (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.

A closed ended, thick-walled cylinder, manufactured from silicon material is designed to contain instrumentation for underwater research. It has an outer radius r = 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: at ro: and g 0₁ = 0 and o = = Or-Po and og = -2Pok² k²-1 = -2.25Po -Po(k² + 1) k²-1 (b) Calculate the radial, circumferential, and axial stresses at ri, when the cylinder is submerged to a depth of 7000 meters under seawater. Consider the density of seawater as 1025kgm-³ 9.81ms 2. = -1.25Po (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.

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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Concept explainers

Pressure Vessels

The term pressure vessel refers to a closed container that contains gas or liquid at a different pressure than environment pressure. The pressure vessels have a wide scale of applications in our day-to-day lives and other industrial places. Some common examples of pressure vessels are gas cylinders, autoclaves, compressor vessels, etc.

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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 r = 0.3m and internal radius of
r¡ = 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:
at ro:
0₁ = 0 and 60
Or = -P and o
=
=
-2Pok²
k² 1
-2.25P
−P(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 1025kgm-³
and g
9.81ms-².
(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.

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