You are designing a manned submersible to withstand the pressure of seawater at

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. What is the gauge pressure at this depth? (You can ignore the small changes in the density of the water with depth.) What is the inward force on a circular glass window 4.5 cm in diameter due to the water outside? 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.)

Explanation / Answer

here,

depth , d = 10900 m

gauge pressure = p * g * d

gauge pressure = 1000 * 9.8 * 10900

gauge pressure = 1.0682 *10^8 Pa

the gauge pressure at this location is 1.0682 *10^8 Pa

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for the inwards force on the window

inwards force on the window = (1.0682 *10^8 + 1.01 *10^5) * pi * (0.045/2)^2

inwards force on the window = 1.701 *10^5 N

the inwards force on the window is 1.701 *10^5 N
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for the outwards force on the window

outwards force on the window = (1.01 *10^5) * pi * (0.045/2)^2

outwards force on the window = 160.6 N

the outwards force on the window is 160.6 N

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