Submarines, Pressure, and Crushing
Name: Jeremy O.
I have a question regarding Water Pressure. All the
formulas I have seen relating to Water Pressure seem to show a linear
increase in atmospheric pressure the deeper one goes. (One
rationalization for this is that only the water 'above' you is
'pressing down' on you.) If this is the case, why are submarines and
other deep object damaged by the intense pressure as likely to be
crushed from side-to-side as top-to-bottom?
Because the water on either side of a submarine also has all the water
above it pressing down on it. If it could move
sideways to escape that pressure, it would. The only thing stopping it
from moving sideways is the submarine.
The pressure in a non-viscous fluid at any given point is the same in all
directions. The pressure must be sufficient to support the water above it.
For example if you are 10 feet under water in a salty ocean where the water
density is 64 lb/ft^3 (which means a cube of water one foot on a side weighs
64 pounds), the force pushing down on the top of a horizontal plate one foot
square is 640 pounds. The plate, however, feels no net force since the
water under it is pushing up with the same force.
Now if you turn the plate so it is vertical , there will be a force pushing
on each side of the plate of 640 pounds. In fact, no matter what the angle
of the plate is, there will be a force of 640 pounds on each side of the
plate. This should seem reasonable to you since I am sure you would agree
that water would rush into an evacuated pipe 10 feet under water regardless
of the orientation of the pipe. You might want to try that by sealing the
ends of a pipe with your hands and then putting it under water and taking
your hands away. It might be better to take a glass tube sealed at one end
and putting the open end under water. You will see that whether the tube is
vertical or almost horizontal (do not let any air out of the tube), the water
pressure compresses the air in the tube by the same amount. I am sure you
can think of other ways to check this physics.
Best, Dick Plano,
Professor of Physics emeritus, Rutgers University
You have got both basic concepts there, but it might be a little tricky
explaining how to put them together. The best way I can describe it right
now is that the water around the submarine is also under the same pressure
from the water above it. Since a fluid under pressure will go anyway it can
to relieve the pressure, it presses against the sides and bottom of the
submarine as well.
Perhaps it would be better to use an analogy of a crowded meeting hall.
Everyone inside is assumed to be pushing towards the front of the hall,
while trying to keep a little personal space to move around in. as you
approach the front of the hall, people begin getting closer to you from all
sides, not just from the direction of the entrance.
A good question, maybe a way to escape the idea of the weight of water from
above. Think about air pressure, climb to higher levels, When you are on
top of the mountain, is not the air pressure less? Does it not act from all
sides? At the bottom of the ocean, is not the air still above the
water? Would it not combine with the water? If the
ocean was made from Jell-O instead of water, would not the pressure at the
bottom be more, than at the surface? Materials are identified by their
specific gravity, weights measured relative to a standard of distilled water.
Inserting the word gravity gives a clue, all these pressures are related to
gravity. Each material because of its molecular structure behaving
differently, but all influenced by gravity.
The increase in pressure (water pressure) is very linear with depth. This
is indeed because the water above is pressing down.
At large depths, the water pressure on the side is almost the same as the
pressure on top or the bottom. The difference is minor.
The failure of a sub can come from any side. When under water, pressure
is applied equally from all sides, thus a hull collapse can occur from any
direction. The "direction" of the collapse is based on where the flaw is
and how it is oriented. Your comment about the water above you pressing
down on you is correct, but what is also pushing down on you from the top
is coming from the side and the bottom. Think of it this way: you have a
tall column of water that has a certain pounds per square inch near the
middle of the column. If this column starts to buckle and bend to the
side at this point, the column of water above the bend point is the weight
pushing towards the side of the column causing it to buckle. So when you
are down so many feet under water, the pressure above you is also being
pushed on you from the side and the bottom.
Hope this helped. Thanks for
Christopher Murphy, P.E.
Air Force Research Laboratory
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Update: June 2012