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Comment by adharmad | Hacker News Reader

The secondary question though is: Why does the energy always dissipate by 50% in both the electric and hydrodynamic models?

Is there some underlying physical explanation of this? Something that says that "in a dynamical system the maximum efficiency can be at most 50%".

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Because in the examples you have two capacitors/barrels, if you had three or four, you would be looking at 33% or 25%.

To say that the energy of the water is mgh is a simplification. It's really 1/2 * h^2 * A * mass density. The water at the top has more energy than the water on the bottom. The energy in the water is square to the water level, but the amount of water is linear. It's the same with a capacitor, the energy is square to the voltage, but the number of electrons is linear.

It works out to the same 50% because the analogy is just very good. Dividing over two barrels/capacitors means halving the potential level (amount of water/load doesn't change), which means 1/4 of the energy in each barrel.

This is wrong. The energy is proportional to the height, not its square. You would get wrong units otherwise.

The energy is proportional to both the height and the mass. The mass is proportional to the height itself. Hence the energy is proportional to the square of the height.

If the fill level is h, so the weighted average of the mass is at h/2,then

E = m * g * h / 2

m = V * r

V = A * h

E = A * r * g * h^2 / 2

m2 * kg/m3 * m/s2 * m2 = kg m2 / s2 = J

Yeah, I totally forgot that there is a height component in the mass as well.

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