Question

When a submarine dives to a depth of 100m , to how large a total pressure is its exterior surface subjected? The density of the sea water is about 1030 kg/m3. The atmospheric pressure is standard at 1.013 x 105 N/m2.

Answer 1

To calculate the total pressure on the exterior surface of the submarine, we need to consider both the pressure due to the weight of the water above it (hydrostatic pressure) and the atmospheric pressure. The hydrostatic pressure can be calculated using the formula:

P = ρgh

where P is the pressure, ρ is the density of the sea water, g is the acceleration due to gravity (9.81 m/s2), and h is the depth.

So, at a depth of 100m, the hydrostatic pressure would be:

P = (1030 kg/m3)(9.81 m/s2)(100m) = 1.013 x 106 N/m2

This means that the submarine's exterior surface is already subjected to a pressure of 1.013 x 106 N/m2 due to the weight of the water above it.

In addition to this, we need to add the atmospheric pressure of 1.013 x 105 N/m2, giving a total pressure of:

Total pressure = hydrostatic pressure + atmospheric pressure
Total pressure = 1.013 x 106 N/m2 + 1.013 x 105 N/m2
Total pressure = 1.1143 x 106 N/m2

Therefore, when the submarine dives to a depth of 100m, its exterior surface is subjected to a total pressure of 1.1143 x 106 N/m2.