Please answer in a step by step format using concepts from Materials Science. Thank you in advance!

The torpedo tube of on a submarine consists of a cylinder recessed into the body of the submarine as shown in the image below.

When the tube hatch opens, the tube fills with sea water and the stress in the unit is given by the hoop stress of a cylinder:

${}_{\text{h}\text{o}\text{o}\text{p}}=\frac{pr}{t}$

where $p$ is the difference between the water pressure and the pressure inside the submarine $($can be assumed to be zero as it will be much less than the water pressure$),r$ is the tube radius $(0\mathrm{.}25$ m $),$ and $t$ is the wall thickness. The density of water is $1000k\frac{g}{m^3}.$

Before being released for duty, the submarine is inspected for flaws. The minimum detection limit of the inspection method is known to be a crack of $0\mathrm{.}5$ mm $.$ If the submarine descends to a depth of $5000$ m $,$ what is the minimum torpedo tube thickness required?

Note the water pressure is approximately equal to:

$P=gh$

where $$ is the density of water