I've had a chance to revisit the proposal while I'm less tired ... see next post.
CWatters said:
I believe you can look at it two ways. Either..
1) A volume of water equal to the volume of the bubble has been raised the full depth of the water or
2) The whole water column has been raised by the height of the bubble.
That would work the same if you lifted the volume in option 1 above the surface of the water.
However, we are talking about the air bubble going up requiring a corresponding bubble of water going
down.
I can't see how the volume (column) of air displaced by the hydrogen is not entirely lifted.
If you introduced a pebble into the bottom of a tank of water surely the water level rises slightly.
If you introduced the pebble from
outside the tank sure. If you started with the pebble inside the tank, and lowered it the water level remains the same. If the pebble started on a platform floating on the water in the tank, then the water level goes down.
It is easier to think about bubbles rising through water.
The situation I was talking about, the bubble is already at the bottom of the tank and rises to another level, still under water. The height of the water in the tank dos not change.
You do have to do work to introduce the bubble into the bottom of the tank in the first place though. There's an example of this on Simanek's buoyancy page linked earlier, and it is why I have pointed out the energy needed to inflate a balloon ... even without the balloon the released gas must displace (and mix with) the surrounding air somewhat.
As the others point out, it is trickier with hydrogen in air.
=== [edit] ================
After writing it occurs to me there is a risk of the thread going astray by discussing the "ways of getting water to the top of a hill" ... that is not the intention: I
know they are seductive. I wanted them as examples of the seductive nature of these things.
I've deleted the exampes ... apologies to those who received them.
Please, anyone who wants to know more, refer to the Museum of Unworkable Devices.