Question

A research submarine can withstand an external pressure of 62 megapascals (million pascals) all the while maintaining a comfortable internal pressure of 101 kilopascals. How deep can it dive in the ocean before it would risk collapsing from the pressure

Answer 1

The depth will be equal to 6141.96 m

Step-by-step explanation:

pressure on the submarine
`P_(sea)` = 62 MPa = 62 x 10^6 Pa

we also know that
`P_(sea)` = ρgh

where

ρ is the density of sea water = 1029 kg/m^3

g is acceleration due to gravity = 9.81 m/s^2

h is the depth below the water that this pressure acts

substituting values, we have

`P_(sea)` = 1029 x 9.81 x h = 10094.49h

The gauge pressure within the submarine
`P_(g)` = 101 kPa = 101000 Pa

this gauge pressure is balanced by the atmospheric pressure (proportional to 101325 Pa) that acts on the surface of the sea, so it cancels out.

Equating the pressure
`P_(sea)`, we have

62 x 10^6 = 10094.49h

depth h = 6141.96 m