Question

You are designing a manned submersible to withstand the pressure of seawater at the bottom of the Mariana Trench, which is one of the deepest parts of the earth’s oceans. The bottom of the trench is at a depth of 10,900 m. (1) What is the inward force on a circular glass window 6.0 cm in diameter due to the water outside? (2) If the internal pressure is 1 atm, what outward force does this produce on the window? (You may ignore the small variation in pressure over the surface of the window). Express answer in Newtons.

Answer 1

Answer :

Pressure = Force / Area

Pressure exerted underwater depends on the depth and the density (and gravity of course).

So, Pressure also equals density * depth * g

P = ρgh

density of water = 1025 kg/m³ g

acceleration of gravity 9.8 m/s²

Ptotal = Patmosphere + Pfluid Patmos = 1.01e5 N/m² or 101 kPa

assuming the vehicle has 1 atmosphere of air pressure inside.

P = 1025 * 10900 * 9.8 = 1.09E8 pascal or 109 Mpa

Pressure = Force / area

so Force = Pressure * Area
Area of window is πr²
Area = π x (0.06)²

Force =106 Mpa x 0.0113 = 1.23 MN