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This question already has an answer here:

Lets assume that the red ball is more dense than the white fluid and less dense than the blue fluid. The fluids are of very low viscosity and the machine can be of any height. The flaps open when pushed from the bottom and after the ball goes through then they close hermetically(some magnets perhaps).

My understanding is as follows:

The ball needs a finite velocity to open the flaps. Since H1, H2, can be of any height that is not a problem.

The ball needs a finite velocity to jump off the water high enough. That is not a problem since H3 can be of any height.

The ball needs a finite velocity to get into the water. That is not a problem since H1+H2+H3 can be of any height.

If it worked it would be a perpetuum mobile. Please help me find out why it won't work.

Perpetual motion machine

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marked as duplicate by Community Aug 27 '15 at 21:13

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First, remove the flaps and replace them a single flap (or valve) where the balls enter the water on the bottom right which prevents the water to flow out. In order to get the red ball into the water, you'll then have to overcome the excess pressure corresponding to the water column, which will cost an energy exactly equal to the energy gained by the balls rising to the top in water. Thus, the overall process is energy neutral.

By inserting extra flaps, you just split this extra work into several slices. (You can see this by inserting very thin layers of vacuum at each flap.)

This is a random illustration I found on the internet: enter image description here

BTW, it seems buoyancy is a favorite tool for perpetuum mobiles, see e.g.
https://www.lhup.edu/~dsimanek/museum/themes/buoyant.htm
or
http://www.hp-gramatke.net/perpetuum/english/page0220.htm
(which essentially has your device in the section Hydraulic Perpetua Mobilia).

And that's just the first two google hits for "perpetuum mobile buoyancy". The third hit is a similar question here on physics.se: Why this is not a perpetuum mobile.

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