Question

A research submarine has a 20-cm-diameter window 8.0 cm thick. The manufacturer says the window can withstand forces up to 1.0 * 10⁶ N. What is the submarine’s maximum
safe depth? The pressure inside the submarine is maintained at 1.0 atm.

Short answer

Safe depth for submarine is 3158 m.

Step-by-step solution

Given information

Submarine has a 20-cm-diameter window 8.0 cm thick.

The window can withstand forces up to 1.0 * 10⁶ N.

The pressure inside the submarine is maintained at 1.0 atm.

Explanation

We can calculate pressure

P=hρg ........................(1)

We can calculate pressure using P = Force / Area

P = F/A ........................................(2)

From equation 1 and 2

$$\begin{gathered} \frac{F}{A}=h\rho g \\ \Rightarrow h=\frac{F}{A\rho g} \\ SubstitutevaluesA=\pi r^2 \end{gathered}$$

Substitute values given , we get

$$\begin{gathered} h=\frac{1.0\times {10}^{6}N}{(1029kg/m^3)\times (9.8m/s^2)\times 3.14\times (0.1m{)}^2} \\ h=3158\mathrm{m} \end{gathered}$$