Archimerged has been thinking about why he believes the TrombePump should efficiently convert hot compressed air into an equal volume and a greater number of moles of cold compressed air. He assumes that the countercurrent heat exchanger can be made to operate efficiently so that not much heat flows from the hot source to the cold sink without heating expanding air, and that turbulence can be reduced to tolerable levels. The question is about how bubbles that don’t even look like they can push water ahead of them should raise water.
Well, the bubbles don’t push water up. The water is moving and will tend to continue to move. In the steady state, the volume of air in the bubble pump equals the volume in the trompe and the hydrostatic forces exactly balance. Adding a little air to the bubble pump will reduce the weight of water above and cause an imbalance of forces so that water in the bubble pump moves a little faster. And adding more air to the trompe will similarly reduce the weight of water in the trompe and reduce the downward force, slowing the watter a little.
From another viewpoint, the water which goes down the trompe has nowhere to go but back up the bubble pump, and vice-versa. We aren’t raising any more water than we let down. The mass of water balances.
If too much compressed air is released into the bubble pump, the excess energy goes into accelerating the water. If too much air goes into the trompe, excess energy to compress it comes from the kinetic energy of the flowing water, which must slow down because there is more hydrostatic pressure coming down the bubble pump than down the trompe and the net force is backwards, slowing the water.
So, Archimerged concludes that the apparent ability of water to flow around the bubbles is not a problem. The bubbles don’t push the water. Gravity pulls the water downward as far as it can go, as usual.
Revised: Archimerged has thought about this some more, and realized that he was wrong. Gravity pulls water down in both tubes, with the flow in the trompe and against the flow in the bubble pump. Bubbles will tend to rise due to water flowing from along side to underneath them. This slows the descent in the trompe and speeds the ascent in the pump. Thus, to keep the same average density in both tubes, more gas flow by volume is required in the pump than in the trompe.
So Archimerged is now looking for more information about how bubbles behave. Do tiny bubbles move more slowly? What is the effect of detergent in the water? Does fast moving water reduce the effect or leave it alone?
Archimedes Submerged 
2006-07-01 at 19:45 |
Assuming we are anticipating a pressure of 100 psi for the high pressure cold air the height of water in the towers will have to be approximately 231 feet high/deep.
The only forces acting to move water in the vertical directions are the boyant forces of the air bubbles present, and differences in density due to the difference(s) in temperature in the columns of water.
The temperature of the air in the bubbles will be essentially the same as the water surrounding each bubble. Any bubble is bouyed up, or rises, due to the difference in density between air and water, i.e. according to the Ancient Archimedes a bubble is bouyed up by the equivalent weight of the water it displaces! Very small bubbles rise slowly, larger ones faster, and consequently the larger the bubble the greater the bouyant force and hence the faster it rises. The size of a specific bubble is dependent on the depth it is below the surface or in other words the pressure in the bubble is the pressure of the water surrounding it.
As in the case of the Ragged Chutes hydraulic air compressor air is introduced in the the fast downward flow by means of tubes so as to introduce large quantities of small bubbles which can be swept downward by the rapid flow. In it pristine natural state it was possibly a whirlpool effect which entrained some air but not as much as was later by man’s intervention.
The addition of detergent, unless if in a very small amount, would cause foaming in both the high pressure accumulator and at the top of the bubble pump affecting the intake of atmospheric air.