Question

A thin cylinder has length $L$, diameter $d$, and thickness $t$. It is made of a material with modulus of elasticity $E$ and Poisson’s ratio $\mu$. When the cylinder is subjected to an internal pressure $P$, the change in length is

• A. $\dfrac{PdL}{2tE} \left( \dfrac{1}{2} - \mu \right)$
• B. $\dfrac{PdL}{2tE} \left( 2 - \mu \right)$
• C. $\dfrac{PdL}{2tE} \left( 1 - 2\mu \right)$
• D. $\dfrac{PdL}{4tE} \left( \dfrac{1}{2} - \mu \right)$

Hint:

For thin-walled cylinders subjected to internal pressure, use the formula for the change in length, which involves both the material properties and the cylinder's dimensions.

Answer 1

The Correct Option is A

The formula for the change in length of a thin-walled cylinder under internal pressure $P$ is given by the relationship: \[ \Delta L = \dfrac{PdL}{2tE} \left( 1 - 2\mu \right) \] Thus, the correct answer is (A) $\dfrac{PdL}{2tE} \left( \dfrac{1}{2} - \mu \right)$.