A thick cylinder of inner dia ‘D’, wall thickness t_{2} and length ‘L’ is sealed at its both ends with caps. The thickness of the cap is t_{1}. Allowable tensile yield stress = σ_{y} and allowable shear stress = τ_{y}. A gas is pumped into this cylinder at pressure ‘p’. The cap will yield in shear at circumference of diameter ‘D’ when the gas pressure applied is more than

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ISRO Scientist ME 2013 Paper

- \(\frac{{4{t_1}{\tau _y}}}{D}\)
- \(\frac{{8{t_1}{\tau _y}}}{D}\)
- \(\frac{{4{t_2}{\tau _y}}}{D}\)
- \(\frac{{2{t_1}{\tau _y}}}{D}\)

Option 1 : \(\frac{{4{t_1}{\tau _y}}}{D}\)

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ISRO Scientist ME 2020 Paper

1538

80 Questions
240 Marks
90 Mins

**Concept:**

At the end of the cylinder, a cap is fixed.

**For pressure:**

The pressure on the circumference of plate is equal to the shear stress on the plate, i.e. \(P \times \frac{\pi }{4}{D^2} = {\tau _y} \times \pi \times D \times {t_1}\)

Therefore, \(P = \frac{{4{t_1}{\tau _y}}}{D}\)

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