Problem $8\mathrm{.}21$ Consider a ductile iron $(65-45-12,$ annealed$)$ to be used in a spherical pressure vessel. The stress in the vessel wall is given by

$=\frac{pr}{2t}$

where $p$ is the internal pressure, $r$ is the outer radius of the sphere, and $t$ is the wall thickness. Given a BHN of $200,$ an $r$ of $0\mathrm{.}3$ m $,$ and a wall thickness of $20$ mm $,$ use the information in Figure $6\mathrm{.}29$ to calculate the maximum operating pressure, p$,$ for this design..