Column Pressure and conservation of energy

[genergy]

Mwater g(H+h)

If you have a column of water 100 meters tall (10 atm) and you insert an object in at the bottom of the column you have to use enough energy to displace the volume of the object.
The pressure times the volume is your energy requirement: correct?

But suppose you were able to put a solid barrier between the top of the water at a height of only 10 meters (1 atm). None of the pressure of the upper 9 atm is allowed to transfer into the bottom 1 atm environment.
Would the energy requirement to insert the object be the volume times 10 atm or 1 atm?

Are you violating the Law of Conservation of Energy if you say 1 atm?
Why or why not?

 

[Simon Bridge]

There have been perpetual motion machines based on the idea you just showed.
The idea is, usually, that you close off the column with a valve, insert a buoyant object at the bottom, open the valve, the object shoots to the top with such force it pops out of the surface and falls back to the ground... where it uses it's momentum from falling to reinsert into the bottom.

Lynchpin: When you insert the object you also have to displace the water you are pushing it into.

When you insert into the unbroken column you have to get the displaced volume of water to the top. When you put the barrier in, you only have to get the displaced water to the top of the lower part ... as described, and if your seals were perfect, then you would not be able to insert it ... otherwise the displaced water will have to exit around the seals.

It's more fun if you are using a heavy, but compressible, gas.

To answer your question: you have not described anything that violate conservation of momentum - but it cannot be turned into a loop.

http://www.lhup.edu/~dsimanek/museum/unwork.htm
... scroll down to "Buoyancy motor #4".
The page on buoyancy misconceptions is also useful.

 

[genergy]

Would you be violating conservation of momentum if you displaced the water into an empty tank? Obviously, at some point the tank will fill up!
But, until the tank fills would there be any problem with conservation of momentum?

 

[Simon Bridge]

Nope. No problem. Having to do this is what makes the ppm's fail.
What is this in aid of?