Pressure vessels are verycommon in many industries. The purpose of this exercise is to examine how stresses evolvewithin the walls of a pressure vessel as a function of position within the wall and wall thickness.Recall the thick-walled cylinder solution developed in class. Re-write the solution to the caseof a thick-walled cylinder with inner radius a, outer radius b, internal pressure p₁, and externalpressure, p2.Orr =000 =+a²p₁-b²p2 (P2₂ - P₁)a²b² 1(b²-a²) (6²-a²) ²¹a²p₁b²p2(b²-a²)1axis(P2 - P₁)a²b² 1(b²-a²) r²(a) Draw a diagram showing the evolution of orr and σ00 from a to b when a/b=0.5 andP2 = 0.(b) Make the assumption that p₂ = 0, a + b ≈ 2r, ba≈t, and a b≈r to derive theexpression for orr and one for a thin-walled pressure vessel. For a sanity check, yoursolution should be arr 0 and σ00 = pir/t.=(c) Now consider the classical strength of materials approach to pressure vessels. Imaginethe pressure vessel shown in Fig. 2 (note, the radius of the thin-walled cylinder is r).Taking a section cut through the cylinder parallel to its axis and examining the balance offorces acting per unit length, L, in one direction that is balanced by the force generatedby eacting through a section of length L and thickness t, verify your calculation from(b). Repeat this for to balance forces through a cut made perpendicular to the cylinderaxis to find the axial stress in the thin-walled pressure vessel, a = (p₁r)/(2t).(d) Consider the combination of conditions that are possible in the axi-symmetric thick-walled cylinder problem: imposed displacements at r = a and/or r = b and imposedtractions at r = a and/or r = b. List (in words) all combinations of boundary conditionsthat are possible and the general equations you would use to solve for constants. You donot need to solve for the constants. You may assume plane strain or plane stress. Hint:there are four possible combinations.HLEt000Cut parallel to cylinder axis000Cut perpendicular to cylinder axisFigure 2: Diagram of thin-walled cylinder / pressure vessel.

Given: σrr=a2p1-b2p2b2-a2+p2-p1a2b2r2b2-a2σθθ=a2p1-b2p2b2-a2-p2-p1a2b2r2b2-a2 To find: Evolution of…

. Pressure vessels are very common in many industries. The purpose of this exercise is to examine how stresses evolve within the walls of a pressure vessel as a function of position within the wall and wall thickness. Recall the thick-walled cylinder solution developed in class. Re-write the solution to the case of a thick-walled cylinder with inner radius a, outer radius b, internal pressure p₁, and external pressure, p2.

. Pressure vessels are very common in many industries. The purpose of this exercise is to examine how stresses evolve within the walls of a pressure vessel as a function of position within the wall and wall thickness. Recall the thick-walled cylinder solution developed in class. Re-write the solution to the case of a thick-walled cylinder with inner radius a, outer radius b, internal pressure p₁, and external pressure, p2.

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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