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This is just a thought experiment considering an unlikely system:
1) The tube is six inches diameter (constant) and 132 feet long.
2) You generate gas into a balloon at the bottom until it reaches a six-inch diameter, so as it rises it displaces ALL of the water above it as it moves upward.
3) You would have the buoyancy of 6" sphere (0.49 Gallons) against all the water in the column (194 Gallons). The balloon will rise VERY slowly at first (for argument sake, assume no friction). Near the top it will have expanded to 5 times its original volume and now looks like a sausage in the tube. It has accelerated steadily as it rose because it displaced an increasing amount of water (2.45 gallons at the top).
Please check this assumption: If the tube in the system described above were 264 ft long instead of 132 ft, the balloon would move twice as much water (398 Gallons) Right? Meaning it would produce twice as many turns of a turbine? Create twice as much energy, twice as much hydrogen? A balloon rising through a 6-inch tube 1,320 ft long would move 10 times as much water (1,940 Gallons). True?
4) Now, imagine putting such a balloon in the bottom of the 132 ft tube, and when it has risen 10 feet, put another one in the bottom. Do this 13 times and you will have a balloon in the tube every ten feet for a total of 19.07 Gallons! That's a LOT of buoyancy! Almost 10% of the volume of the tube.
Question?: How much energy does such a balloon represent? How do you measure it? It would be easy to calculate the energy in a 6" water balloon dropped through air 100 ft. right? ~2lb x 32/ft/sec/sec for 100ft (something like that)
Limited knowledge of bubbles: Borrowed from: http://www.scubacourse.com/scmain/articles/bubblemech.asp The misconception is that if you follow your smallest exhaust bubbles you will not exceed an ascent rate of 60 feet per minute (the maximum ascent rate for recreational diving). This assumes that all bubbles ascend at less than 60 feet per minute. When a diver exhales bubbles into the water, the bubbles begin to expand as they rise. As they expand they increase their buoyancy and therefore travel to the surface with increasing speed which causes them to expand faster and travel even faster towards the surface.
So it sounds like the size of the bubble is a MAJOR factor in the calculation. Balloons are just for argument, but accumulating small bubbles into larger bubbles prior to releasing them may indeed change the dynamics of the system.