An ocean-going research submarine has a 10-cmcm-diameter window 8.6 cmcm thick. The manufacturer says the window can withstand forces up to 1.2*106 NN. What is the submarine's maximum safe depth?

15144.268 m

Explanation:

Pressure: This can be defined as the ratio of force to the surface area in contact. T²he S. I unit of pressure is N/m²

P = F/A ... Equation 1

Where P = pressure, F = Force, A = Area of the submarine.

The pressure in water is

P = ρgh ... Equation 2

Where ρ = density of the water, g = acceleration due to gravity, h = depth.

Therefore,

ρgh = F/A

F = Aρgh ... Equation 3

Making h the subject of the equation,

h = F / (Aρg) ... Equation 4

Given: F = 1.2*10⁶ N, A = πd²/4 where d = diameter = 10 cm = 0.1 m

A = 3.14 (0.1) ²/4 = 0.00785 m².

Constant: g = 9.8 m/s². ρ = 1030 kg/m³

Substitute into equation 4,

h = 1.2*10⁶ / (1030*9.8*0.00785)

h = 15144.268 m.

Hence the submarine's maximum safe depth = 15144.268 m