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.

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Solution

Depth of sea $h = 3 \times 10^{3} m$
Maximum stress $= 10^{9} P a$
Density of water $ρ = 10^{3} k g / m^{3}$
Pressure exerted by a water column of depth 3 km
$P = h ρ g$
$= 3 \times 10^{3} \times 10^{3} \times 9.8$
$= 2.94 \times 10^{7} P a$
This pressure is less than the maximum stress of $10^{9} P a$ ; so the structure is suitable.

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A vertical off-shore structure is built to withstand a maximum stress of 109 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.

Depth of sea h=3×103mMaximum stress =109PaDensity of water ρ=103kg/m3Pressure exerted by a water column of depth 3 kmP=hρg =3×103×103×9.8 =2.94×107PaThis pressure is less than the maximum stress of 109Pa; so the structure is suitable.

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.