I know what they can do for climate control and every aspect of how the planet can benefit from them just from regulation of sea surface temperatures (SSTs) and the enormous amount of electrical power they can produce from the kinetic energy in the gulf stream current. I understand how and why they work physically in the real world but I really can't figure out the math behind them. Is there a mathematical formula that can prove how and why they work? I built a test scale model (1/650) out of PVC pipe and used red food coloring to show how water is forced uphill from the kinetic energy and made videos of it on youtube.

How do those things work?

In its simple form F1>F2 but I will explain where F1 and F2 come from and try to piece it together.

If the whole tunnel structure is submerged and anchored to the sea floor and the Tunnel inlet at depth is faced into the 6mph gulf stream current opposing its flow a certain amount of pressure at the tunnel inlet will exist depending on the depth it is. That pressure at the tunnel inlet I call force 1. The Tunnel outlet near the surface also has a certain amount of pressure depending on how deep it is. This force I call force 2.

Two very important people discovered long ago what will happen at both ends of the tunnel. One was Pascal and the other Was Bernoulli. What I did was combine these principles to do work. At tunnel inlet at depth Force 1 exists as the gulf stream flow impinges against the mouth of the tunnel inlet. That force is transferred to the inside walls of the tunnel and the pressure decreases with altitude. Pascal discovered the theory of hydraulics where if you apply a force to a cylinder that force is transferred everywhere within that cylinder including the walls of the cylinder. So tunnel inlet where force 1 exist I credit Pascal.

Now for the other end of the submerged tunnel near the surface where force two exists at the outlet. As the 6mph gulf stream flows past the tunnel exit a more negative pressure is created like on a airplanes wing where lift is created as the air flows over the wing or like in perfume bottle when you squeeze the bulb creating a more negative pressure in the mixing chamber drawing the fluid upwards. I credit this application to Bernoulli.

So if you combine both forces Pascal at the opening at depth and Bernoulli at the opening near the surface you can see there is a pressure differential set up across the whole tunnel structure throughout its height. Pascal states where ever there is a differential of pressure flow will occur. Hopefully, I explained it good.

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