A thick cylindrical shell, closed at both ends using a flat disc, is used as a casing for a molten salt battery. The dimensions of the casing are as follows:

Inner diameter of shell $=r_1$

Outer diameter of shell and flat disc $=r_2$

Length of casing $=L$

A design review of this energy store determines that there is need to triple the capacity of the casing while maintaining the same storage pressure $P_0.$

If the maximum principle stress in the structure remains the same, determine the dimensions of the new casing.

Lames Equations:

${}_r=A-\frac{B}{r^2},$ and $,{}_h=A+\frac{B}{r^2}$

$P{R}_1^2$