The successor to Alvin, the submersible that was used to locate the Titanic, is being built. The goal is to be able to reach the deepest depths in the Atlantic and Pacific oceans, about $11,000 \mathrm{~m}$. Assuming water density is unchanged with depth,

a. What is the pressure at the $11,000 \mathrm{~m}$ mark?

b. If the submersible is to be nominally $3 \mathrm{~m}$ in diameter, what force does the water exert on the craft?c. How thick would the hull of the submersible have to be? The design equation for thickwalled spherical shells can be expressed as:

\[t_{h} \cong r_{i}\left[\left(\frac{2 S_{d}+2 P}{2 S_{d}-P}\right)^{1 / 3}-1\right]\]

where $t_{h}$ is the wall thickness, $r_{i}$ is the inner radius of the shell $(3 \mathrm{~m}), S_{d}$ is the design stress for the wall material, and $P$ is the pressure the vessel is exposed to. For this example, the hull material is a titanium-molybdenum alloy whose design stress in approximately $275 \mathrm{MPa}$.