How does the stability of a submarine’s buoyancy vary with depth?
http://en.wikipedia.org/wiki/Buoyancy#Submarines states “Submarines rise and dive by filling large tanks with seawater. To dive, the tanks are opened to allow air to exhaust out the top of the tanks, while the water flows in from the bottom. Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth.”
To illustrate my question, consider a five metre high submarine at the surface in calm shallow water. Assume the water is five metres deep at low tide, and that the sub is at rest on the bottom, and then will float one metre above the floor with a one metre tide, so the top of the sub is always exactly at the water surface. Now, consider if the sub is connected to a plastic bag containing liquid underneath it and equal to it in size. This bag is also fastened to the sea floor, and has inlet and outlet valves and pipes, and is able to expand and contract like a bellows. So when the sub is resting on the floor the bag beneath it is squeezed empty, and when the tide rises, the submarine will rise, and the connected bag below it will therefore expand like a bellows, sucking in additional liquid through the inlet valve and pipe, say from a fresh water bag at the surface. As the tide falls, the submarine will also fall, expelling liquid from the bag beneath it, forming a tidal pump powered by the weight of the submarine on top of it. Assume the outlet pipe is wide enough to fully empty the bag over the 6.5 hour period of a falling tide.
If we then shift this scenario to an ocean location of depth one hundred metres, and balance the submarine flotation tanks so that it is again sitting on the floor at low tide and floating one metre above the floor at high tide, how will the power of pumping be affected? If the same plastic bag of liquid with inlet and outlet valves is fastened both to the ocean floor and to the underside of the sub, will it have the same pumping power as in the shallow water situation? If less by how much?
If we extend this to depths of one or two kilometres (using a sealed bag of brackish water in place of the manned submarine) will the forces at that depth reduce this tidal pumping power further, and by how much?
Many thanks for any information on how to understand this problem.