Hydraulic analogy
[2] The analogy may also be reversed to explain or model hydraulic systems in terms of electronic circuits, as in expositions of the Windkessel effect.
This is reminiscent of electrical diagrams with an up arrow pointing to +V, grounded pins that otherwise are not shown connecting to anything, and so on.
The pressure and volume flow variables are treated as phasors in this definition, so possess a phase as well as magnitude.
A hole (or long tube) is analogous to an inductor that stores kinetic energy associated with the flow of air.
A relatively wide hose completely filled with water is equivalent to a conducting wire.
When comparing to a trace or wire, the hose or pipe should be thought of as having semi-permanent caps on the ends.
A resistor is equivalent to a constriction in the bore of a pipe which requires more pressure to pass the same amount of water.
The mass of the rotor and the surface area of its vanes are analogous to inductance, and friction between its axle and the axle bearings corresponds to the resistance that accompanies any non-superconducting inductor.An alternative inductor model is simply a long pipe, perhaps coiled into a spiral for convenience.
To create the analog of an ideal current source, use a positive displacement pump: A current meter (little paddle wheel) shows that when this kind of pump is driven at a constant speed, it maintains a constant speed of the little paddle wheel.
On the basis of this analogy Johan van Veen developed around 1937[8] a method to compute tidal currents with an electric analogue.
Higher-frequency AC and transmission lines is somewhat equivalent to sound being transmitted through the water pipes, though this does not properly mirror the cyclical reversal of alternating electric current.
A better concept (if sound waves are to be the phenomenon) is that of direct current with high-frequency "ripple" superimposed.
Any deviations from the assumptions (e.g. pipe or wire is not straight, flow or current is changing over time, other factors are influencing potential) can make the relationship fail to hold.
For this reason, waves in water travel at the speed of sound, but waves in a sea of charge will travel much faster as the forces from one electron are applied to many distant electrons and not to only the neighbors in direct contact.
This is formalized in Kirchhoff's current law, which does not have an analogy to hydraulic systems, where the amount of the liquid is not usually constant.
For this reason, continuing electric currents require closed loops rather than hydraulics' open source/sink resembling spigots and buckets.
Also, typical velocity of charge carriers within a conductor is less than centimeters per minute, and the "electrical friction" is extremely high.
Quantum mechanics: Solid conductors and insulators contain charges at more than one discrete level of atomic orbit energy, while the water in one region of a pipe can only have a single value of pressure.
For this reason there is no hydraulic explanation for such things as a battery's charge pumping ability, a diode's depletion layer and voltage drop, solar cell functions, Peltier effect, etc., however equivalent devices can be designed which exhibit similar responses, although some of the mechanisms would only serve to regulate the flow curves rather than to contribute to the component's primary function.
Hydraulic systems are deceptively simple: the phenomenon of pump cavitation is a known, complex problem that few people outside of the fluid power or irrigation industries would understand.
The hydraulic analogy can give a mistaken sense of understanding that will be exposed once a detailed description of electrical circuit theory is required.
The above "electrical friction" example, where the hydraulic analog is a pipe filled with sponge material, illustrates the problem: the model must be increased in complexity beyond any realistic scenario.
