Mechanical Properties of Fluids
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Question : 7
Total: 31
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 = 3 k m = 3 × 10 3 m
density of water,ρ = 10 3 k g m – 3
If P be the pressure exerted by this water column at this depth, then
P = h ρ g = 3 × 10 3 × 10 3 × 9.8
= 29.4 × 10 6 P a
= 30 × 10 6 P a = 3 × 10 7 P a
As the structure is put on the sea, sea water will exert upward thrust of3 × 10 7 P a .
Maximum stress which the vertical off-shore structure can withstand= 10 9 P a .
Then3 × 10 7 P a < 10 9 P a
Thus we conclude that the structure is suitable as the stress applied by it is much lesser than the maximum stress it can withstand.
density of water,
If P be the pressure exerted by this water column at this depth, then
As the structure is put on the sea, sea water will exert upward thrust of
Maximum stress which the vertical off-shore structure can withstand
Then
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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