Question

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?

Answer 1

Answer:

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