Question

The top of a submersible diving vehicle is 2.58 m deep in the ocean (the specific gravity of seawater is 1.03) when it experiences a short circuit, which cuts off all power. To escape before it sinks, the crew must open a circular hatch (radius 0.445 m) in the top. If the pressure inside the submersible is 1 atm: find F, the magnitude of the force the crew must exert on the hatch to open it, in N.

Answer 1

Depth of the top of submersible vehicle, h = 2.58 m

Specific gravity of sea water, ds = 1.03

Density of sea water, d = 1.03 x 1000 = 1030 kg/m3

Radius of circular hatch, r = 0.445 m

Area of circular hatch, A = πr2 = 3.14 x 0.445 x 0.445 = 0.622 m2

Pressure inside the submersible, P1 = 1 atm

Pressure on the top of the hatch, P2 = P1 + dgh

Pressure = force/area = F/A

Force, F = (P2 – P1)A= (P1 + dgh – P1) a = dgh A = 1030 x 9.8 x 2.58 x 0.622 = 16198.4 N

Force required to open the hatch, F = 16198.4 N