A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snuglybetween 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 \alpha. What is the minimum rise in temperature \Delta {T} 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

A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snuglybetween 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 \alpha. What is the minimum rise in temperature \Delta  {T} 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?

Examsnet · Accepted Answer

Correct Answer is :  ∆T=‌vprαtE

GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper