Comment by mitthrowaway2
3 days ago
Wait, the electrical pipe water analogy is actually a very good one and it's quite difficult to find edge cases where it breaks down in a way that would confuse a student. There are some (for example, there's no electrical equivalent of Reynold's number or turbulence, and flow resistance varies differently with pipe diameter than wire diameter, and no good equivalent for Faraday's law) but I don't think these are likely to cause confusion. It even captures nuance like inductance, capacitance, and transmission line behaviour.
As I recall, my systems dynamics textbook even explicitly drew parallels between different domains like electricity and hydrodynamics. You're right that the counterparts aren't generally perfect especially at the edges but the analogies are often pretty good.
Intuitively it fails in making an equivalence to area which is an unrelated dimensional unit, as two lengths multiplied together equaling resistance, as well as the skin-effect related to Intensity/Current which is why insulation/isolation of wires are incredibly important.
The classical approach used charge diffusion iirc, and you can find classical examples of this in Oliver Heaviside's published works (archive.org iirc). He's the one that simplified Maxwell's 20+ equations down to the small number we use today.