Tesla Gravity Tower


One of the things I like about reading "The Problem of Increasing Human Energy" was the concept of the evacuated chamber in a lake.  Water is allowed to pour into this chamber, where it undergoes electrolysis using the energy generated by the water passing through the turbine.  I think it would be a noble thought experiment to take this thought out and perform the math to see how tall this tower would need to be before 'free energy' is generated.  That is, more energy output than input.




In the book, The Problem of Increasing Human Energy, This is probably not the tower you have come to picture when thinking about Tesla, but it is certainly one of the many fascinating ideas in his book, "The ..." . Nikoa Tesla talks about a hypothetical situation where a void is created in a lake, and water is allowed to flow in. As this water flows in, it performs mechanical work, and the mechanical work is turned into electricity. This electricity electrolyzes water into hydrogen and oxygen gases which float out of the vessel due to their buoyancy.
This thought was so inspiring to me that I used it for the cover art seen below. These towers are located at the poles of the planet and provide support for the space based solar array that is always orientated towards the sun.



Today, I want to explore the mathematics behind this system. en below. These towers are located at the poles of the planet and provide support for the space based solar array that is always orientated towards the sun.

Assumptions:
We will use water as our working fluid
ρ Water Density is 1000 kilograms per cubic meter kg/m^3
Gravity 9.8 meters per second^2 m/s^2 Obviously this will change with height, hence using 9.8 instead of 9.81.
Height - This is the variable that we are solving for.
Friction - estimated forces of impedence in Force per unit length Newtons/meter or N/m Water is 18.01528 grams/mol so 55.508435062 moles per kilogram
ηturbine exothermic
ηturbine endothermic
ηelectrolysis
ηfriction
Friction obviously will depend strongly on the velocity of the fluid being moved. We will assume that if such a structure was capable of being produced, it would be produced to make friction negligible.

Today, As noted above, the equation is solving for the required height of the system. Height is the dependent variable.
Today, The Tesla Tower system comprises 4 subsystems. These are Hydroelectric Power Generation, Electrolysis of the Water into Hydrogen and Oxygen gases, frictional losses from the rising gases and falling water, and the reconstitution of the water at the top through a thermal combustion process
Electrolysis is very inefficient, can lead to the formation of caustic gases, and the consumption of the electrodes. Because of these factors, using this gravity engine might be more advantageous in applications that vaporize and create steam instead of electrolysizing the water. Probably the best place to look for this information would be towards geothermal wells, where the working fluid falls down into the ground. In our system we would use this mechanical work in order to add more vaporization heat at the bottom. This would allow for a higher fluid flow rate, and greater efficiency of the system. Obviously this is not without additional capital costs, and these costs should be considered, but thinking along these lines, we might imagine a traditional rankine cycle steam power plant using this to some advantage. Today, The advantage of this system is that it eliminates pumps, and takes advantage of a created hydrostatic head. What this system avoids is pumping water back "uphill". By converting the water to a gas or possibly a steam, we are lowering the density and allowing the water to float back up to the top. It would be interesting to build a small scale version of this system, maybe more on the powerplant level using steam instead of electrolysis One creative use of this system would be to place a conventional power plant next to a mountain. The boiler and the turbine would be placed at the bottom of the mountain, and the cooling tower at the top. As the steam rises towards the cooling tower accomadations would be needed for the condensation created as the steam cooled, but the steam that did reach the top could be converted into water and reduce the amount of horsepower needed to pump the water up to pressure prior to entering the boiler. Obviously this is not without costs, and the capital needed for the plumbing would probably offset efficiency gains in the overall plant Another theoretical example would be a thermal process that releases water vapor. Rather than releasing the water vapor to the atmosphere, this water vapor could instead be channeled into a storage location at a higher elevation. Because we have already increased the energy of the fluid vapor, we can allow this fluid to float up and later release this stored potential energy in the form of mechanical work when we release it down the hill later. This would have some obvious draw backs as well. You would need a use a pretty clean fluid in order to avoid scaling, and the height that the fluid could summit would vary with heat transfer losses which would change transiently as the lines are brought up to temperature, and seasonally at the ambient conditions change.
Today, Here is a drawing of earth with the tower drawn to scale:


Include pictures from dams out in Washington, and Niagara Falls power project. H2+12O2H2+12O2⟶H2O(l)⟶H2O(g)ΔH∘fΔH∘f=−285.8 kJ/mol=−241.8 kJ/mo




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