and it can cause things like water hammers: https://en.wikipedia.org/wiki/Water_hammer which are analogous to inductor sparks: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/...
Water analogies only go so far. You would do well to pick up a book on basic electrical networks to learn this material further. Don't shy away from the math; it's really the only way to build the understanding that leads to intuition.
The biggest difference is in mechanical effects: in hydraulics, physical force is primarily a function of the system pressure and velocity of the flow rate. For electromagnetics, those are reversed: voltage controls the speed of a motor and current controls the force, for example.
They also deviate from the linear regime in different ways, which means the more interesting components have to be built completely differently to perform the same job. A one-way check valve and a diode are both governed by similar equations on a macro scale, but you’ll never be able to understand the internal structure of the valve by an electronic analogy or the design of the diode by a hydraulic one.
Part of that is getting comfortable with the maths, and the way that’s visualised is just equations, graphs and sometimes things like diagrams of fields or heatmaps. I work in RF so we do antenna simulations and things like that, and the software generates radiation pattern diagrams in 2D, or in 3D heatmaps showing the energy density. It just doesn’t work to, say, try and think of what would happen if an antenna was spraying water out or something.
It's then equally straightforward to see how the same explanation applies to the more contrived case of two capacitors.
Once you include that, you'll see your LC resonator is perfectly undamped and oscillates the charges back and forth forever, breaking the assumption that a "steady state" would equalize the charge on both capacitors.
The equations will also reveal the problem to you when you try to calculate the current that flows from one capacitor to another, with no inductance or resistance in between. You might try putting in an inductor and looking at the circuit behaviour in the limit as the inductance goes to zero -- you'd see the frequency of oscillation climbs to infinity; the full charge essentially teleports back and forth from one capacitor to the other, but still never settles into a steady state of equal charge on both capacitors.
Once you see this, it's like having a problem set up with a frictionless ball on a hilltop beside a valley, saying "in the steady state, the ball has rolled down and settled in the valley. But there was no friction! Where did the energy go?", and the answer is just that the ball doesn't settle in the valley, but rather continues back up the other side, carried along by the kinetic energy that had been neglected in the problem statement.
(Before the well-actualies point out that an LC circuit will damp itself via radiation, let's just say it's also perfectly shielded).
A full model is complicated by the fact that your capacitors have an internal series resistance and leakage resistance, and that the leads and circuit board traces have resistance and inductance. Just like the pipes and valve has some resistance to flow, and some water might leak out or evaporate, and the water has inertia and nonzero viscosity, and turbulence will turn some of the motion to heat, and depending on the phase of the moon, the time of day, and the compass orientation of the barrels, the water may be pulled into a picometers-higher tide in one barrel. When you say "they equalize with half the water in each" you don't typically mention that the phase of the moon may be a factor.
We do store energy in water towers for example, so it is pretty surprising and unintuitive that if you put two large water tanks, one full and one empty, right next to each other, open a valve between them allowing their levels to equalize, then assuming there is no distance and you used teflon coated valves you lose... half of the energy as they equalize!
I certainly wouldn't have thought so. I'd have thought you keep 70%-95+% of the energy.
Actually the oscillation explanation didn't match my intuition at all, because I would have thought the water flows from high to low until the point of equalization and then stops flowing, without oscillation.
I get that this doesn't happen, but I would have thought it would!
It might very well do that. You will just have lost half the energy already to heat from friction with the piping and due to water's viscosity.
> it is pretty surprising and unintuitive that if you put two large water tanks, one full and one empty, right next to each other, open a valve between them allowing their levels to equalize, then assuming there is no distance and you used teflon coated valves you lose... half of the energy as they equalize!
If you did that, they would equalize - very briefly - and then the second tank would fill higher and higher, until it's (nearly) full. Then the reverse begins.
This is very similar to a pendulum. Just that our intuition about pendulums is better than for near-frictionless transfer of fluids in connected systems.
> I'd have thought you keep 70%-95+% of the energy.
Well, the potential energy being zero at the bottom of each tank is arbitrary. If both tanks are inside a water tower, you might keep 99% of the "useful" energy even if you let them equalize, because the height above ground is greater than the height above "tank bottom". Maybe this is the source of some confusion here?
The oscillation bit happens, but it doesn't dominate. Water analogies can be misleading because water has intrinsic properties (eg turbulence ~= resistance) which aren't always significant in an electronic circuit. To make the equivalent of an LC-dominant circuit with (open) water tanks, you'd need something like a high-momentum turbine in the transfer pipe.
The demonstration is called Pascal's vases.
https://www.physics.purdue.edu/demos/display_page.php?item=2...
So is it not accurate to say that water does this by oscillating and throwing away energy as parasitic losses, until it equalizes?
Are you saying in general does a system of connected tubes NOT throw off lots of energy as it gets into the equalized state shown?
If it does, I think this fact should also be mentioned when teaching the "water seeks its own level" demonstrated above. (Called Pascal's vases.)
In this case, the equations not matching up proved that our initial assumption (steady state) was itself wrong.
But obviously, even with this 1/2, your relation after dividing between two tanks still holds. :)
Now I want to try the water barrel thing myself and see how many times the water goes back and forth before it finally stops...
At the first engineering firm I worked for, we had a very good heat transfer solver but no electrical solver since it was an infrequent need in our field.
One of old timers was an expert at reframing the electrical problems into heat transfer, solving in the available tools, then converting back. As he said "it's all unit conversions". I never picked it up beyond simple resistance networks, but it was a cool way to abuse the tools.
https://lpsa.swarthmore.edu/Systems/Thermal/SysThermalElem.h...
Radiation could be the sound produced by the rushing water?
Well, but maybe... if you equalize two water tanks with a very fat pipe it will swap forth and back, causing the whole assembly, table, and room to rock?
Is there some underlying physical explanation of this? Something that says that "in a dynamical system the maximum efficiency can be at most 50%".
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.
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
The initial energy is mgh and the final energy is 2 * (m/2 * g * h/2) = mgh/2 so half of then energy has disappeared. It is clear that work could have been done by the water moving between the two barrels (like in a hydro-electric power station).