Question

A vertical off-shore structure is built to withstand a maximum stress of ${10}^9$ Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

Answer 1

The maximum allowable stress for the structure, $P={10}^{9}Pa$
Depth of the ocean, d = 3 km = $3\times {10}^{3}m$
Density of water, $\rho ={10}^{3}kg/m^3$
Acceleration due to gravity, $g=9.8m/s^2$
The pressure exerted because of the sea water at depth, $d=\rho dg$
$=3\times {10}^3\times {10}^3\times 9.8=2.94\times {10}^{7}Pa$
The maximum allowable stress for the structure $\left({10}^{9}Pa\right)$ is greater than the pressure of the sea water $(2.94\times {10}^{7}Pa)$. The pressure exerted by the ocean is less than the pressure that the structure can withstand. Hence, the structure is suitable for putting up on top of an oil well in the ocean.