Exercise $9$

$*10-56.$ The thin$-$walled cylindrical pressure vessel of inner radius $r$ and thickness $t$ is subjected to an internal pressure $p.$ If the material constants are $E$ and

$u,$ determine the strains in the circumferential and longitudinal directions. Using these results, compute the increase in both the diameter and the length of a steel pressure vessel filled with air and having an internal gauge pressure of $15$ MPa $.$ The vessel is $3$ m long, and has an inner radius of $0\mathrm{.}5$ m and a thickness of $10mm.E_{st}=200$GPa,

$($