A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.The material of the cylinder has Young’s modulus E. Poisson’s ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere?

Question

TuteeHUB · Accepted Answer

${\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}$

TuteeHUB · Answer

${\rm{\Delta }}T = \frac{{3vpr}}{{2\alpha tE}}$

TuteeHUB · Answer

${\rm{\Delta }}T = \left( {v - \frac{1}{4}} \right)\frac{{pr}}{{\alpha tE}}$

TuteeHUB · Answer

${\rm{\Delta }}T = \frac{{vpr}}{{\alpha tE}}$

1.	A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.The material of the cylinder has Young’s modulus E. Poisson’s ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere?
A.	\({\rm{\Delta }}T = \frac{{3vpr}}{{2\alpha tE}}\)
B.	\({\rm{\Delta }}T = \left( {v - \frac{1}{4}} \right)\frac{{pr}}{{\alpha tE}}\)
C.	\({\rm{\Delta }}T = \frac{{vpr}}{{\alpha tE}}\)
D.	\({\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}\)
Answer» D. \({\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}\)

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