Question

A research submarine has a 30-cm-diameter window that is 8.6cm thick. The manufacturer says the window can withstand forces up to 1.2×10^6 N . What is the submarine's maximum safe depth in salt water?

The pressure inside the submarine is maintained at 1.0 atm.

Answer 1

What is missing is the density of salt water. Let's denote it ρ.
The pressure at depth d then is:
p = p0 + ρ g d
, where p0 is the atmospheric pressure at the surface of the sea. We assume it is equal to the 1 atm inside the sub.

Hence the pressure difference between inside and outside of the window is:

Δp = ρ g d

The force on the window is this pressure difference, multiplied by the area of the circular window of diameter D. The latter equals
A = ¼ π D².

So
F = p A = ¼ π D ²ρ g d.
This should be less than Fmax.

Hence d < Fmax / (¼ π D ²ρ g ).