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Mechanical Properties of Fluids

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Question : 7 of 31
Marks: +1, -0
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.
Solution:  
Here, depth of water column,
h=3km=3×103mh = 3\,\text{km} = 3 \times 10^{3}\,\text{m}
density of water,ρ=103kgm3\rho = 10^{3}\,\text{kg}\,\text{m}^{-3}
If P be the pressure exerted by this water column at this depth, then
P=hρg=3×103×103×9.8P = h \rho g = 3 \times 10^{3} \times 10^{3} \times 9.8
=29.4×106Pa= 29.4 \times 10^{6}\,\text{Pa}
=30×106Pa=3×107Pa= 30 \times 10^{6}\,\text{Pa} = 3 \times 10^{7}\,\text{Pa}
As the structure is put on the sea, sea water will exert upward thrust of 3×107Pa.3 \times 10^{7}\,\text{Pa}.
Maximum stress which the vertical off-shore structure can withstand =109Pa.= 10^{9}\,\text{Pa}. (Given)
Then 3×107Pa<109Pa3 \times 10^{7}\,\text{Pa} < 10^{9}\,\text{Pa}
Thus we conclude that the structure is suitable as the stress applied by it is much lesser than the maximum stress it can withstand.
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