When I need to explain voltage+current to my inlaws, the analogy is good enough. Perfect is the enemy of done.

Wouldn't it be easier to just say "current is how many electrons flow through a specific section of the wire in a second" and "voltage is the force that makes the electrons move"?

It's just as easy to understand without need for analogies.

Those two sentences that you wrote are precisely the hydraulic analogy. If it weren't, instead of electrons it would be charge (that can be positive or negative), or field strength (if you explain the transitory period of a capacitor or non-DC), and voltage would become not the force, but a number that applies to conservative fields that allows to calculate the capacity to do work relative to another such number...

Absolutely not. You can't just throw out axioms and expect people to catch on. The utility of analogies is that you can anchor an idea in something people are familiar with.

I would say that, in general, this is a tool most useful to help people that are completely new to the concept gain an intuition about the behavior.

Based on what you've described, where would you develop the intuition about the difference in speed between the electrons and the electromotive force they are relaying? Or why you need both voltage and current to do work, or the behavior of an LCR circuit? Or an open circuit? Etc etc.

Same, by the time you need to explain how transformers use electromagnetism, they probably understand the basics of V=IR which is really as far as the analogy goes.

Could a turbo-pump can be thought of as a very bad transformer? able to transform a flow mv1 at a pressure P1 to mv2 P2 where their product, power is constant (except its way more lossy).

Still, I think the water analogy is over used

That’s probably a good description of the main usefulness of the analogy - explaining to people who won’t actually need to apply the concepts. My conclusion (after years of doing electronics design professionally, including RF) is that to do much useful in electronics, you need to get into the habit of thinking natively in terms of voltage and current and resistance etc. so soon that the hydraulic analogy is basically not worth learning at all, since the missing things just get confusing and it becomes a distraction or blocker to advancement until you “unlearn” many of the concepts.

I mean, it’s probably worth mentioning current and voltage are “kind of” like flow, pressure etc., in a first lecture to start to get the basic idea, but then warning not to think of it as being the exactly same because that will just be confusing later.

You can do 99.999% of practical applications of electricity with the liquid analogy, up to and including most industrial electrical stuff (remember, check valves, accumulators and whatnot are a thing).

What you can't do is design a bottom dollar power supply that uses some trick circuitry to not emit enough RF noise to matter.

I'm specifically talking electronics, where the usefulness runs out very quickly... As soon as you get to EMI/EMC there is no real liquid analogy (so that rules out basically any reasonably complex custom electronic design you're going to get certified to sell as a product). Parasitic effects of traces, ESR, characteristic impedance, etc. are similarly problematic (people try to come up with stuff like springs or flexible tubes for characteristic impedance but again it's just more confusing in practice). So that rules out anything decently high speed digital (like, say, routing DDR3/4). That's of course not to mention RF, antennas, transmission lines etc. where all bets are off.

>> 99.999% of practical applications of electricity

All radio/wifi and everything involving fiber optics or magnets. That's probably slightly more than 00.001% of applications.

Not still a good analogy, but radiation can be seen as a consequence of vacuum not being empty from the perspective of an electric field (it has a very low permittivity, but it is not zero, so it is not empty of that property) even though it is empty of mass. If your water pipes are a bit porous and the medium on which your water pipes are was not air, but a very dense fluid, radiation emanating from the porous pipes would travel at the speed of sound through the medium, and could be detected without particles of water actually travelling through the dense fluid that constitutes the medium where your hydraulic circuit is submerged.

There's a large difference between "applying the concepts" and "doing useful things in electronics". The vast majority of people barely find utility in repairing what they already own, to say nothing of tinkering or creating something new.

The water analogy, is, in my opinion, the sweet spot for people who will never own a multimeter or fire up a SPICE program. It's the level that ought to be the expectation for citizens of a technic civilization.

> Water only ever remains inside the pipes that carry it.

If only! My apartment was recently destroyed by water that refused to do exactly that...

Electricity also doesn't freeze solid, expand, and break open its insulation; it doesn't evaporate and condense on cold surfaces and cling there under surface tension, it doesn't drip down.

But the analogy is still a pretty useful one for people who have lots of hands-on experience with water and not much with electricity, or vise-versa.

>> cling there under surface tension = Static charges. When a walk in wool socks on a wet carpet my socks pick up water. When I walk on a dry carpet my socks pick up electrons.

>> expand, and break open its insulation = an arc causes by too much electricity in too thin a pipe.

>> it doesn't evaporate and condense on cold surfaces = electro vapor deposition aka physical vapor deposition

The 2nd one would be less like an arc and more like the wire/conductor getting too hot and melting/failing.

Arcing (or shorting in general) would probably be more akin to water's tendency to find the lowest point.

Also not advised to drink electricity.

No analogy is perfect. They are intended to help illustrate a concept to gain insight. Ideally when using an analogy its limits should also be described. Luckily the very first link after the analogy is explained does just that: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir3.....

Hydraulic intensifiers can act as an analog of an electrical transformer. An intensifier is a hydraulic device where a large area piston is coupled to a small area piston. They are often used in water jet cutters to produce high pressures. A jet pump[0] is another device which acts sort of like a transformer and exchanges high pressure for high flow. 'Inertance' of the water in the pipe can act in a manner similar to inductors.

[0]https://en.wikipedia.org/wiki/Injector#/media/File:Ejector_o...

> Anything involving the electrical energy not inside wires has no water analogue (ie the electromagnetic waves inside a transformer)

You don't even need fancy things like transformers for energy not in the wires to be important. Even a simple DC circuit consisting of a battery in series with a light bulb mostly involves an electromagnetic field to transfer energy from the battery to the light bulb, which mostly takes place outside the wires.

The function of the wires when it comes to energy transfer is to carry moving charge which creates the magnetic part of the electromagnetic field that actually carries the transferred energy.

Here's a pretty good explanation [1]. That video was from January 2019, and not controversial. Veritasium did a video on the topic in late 2021 that didn't really present things as well and ended up being quite controversial [2]. Other well-known YouTube channels such as EEVblog [3] and ElectroBOOM [4] responded.

There was also someone who bought a bunch of wire and did the experiment as described in the Veritasium video (although scaled down). That was discussed on HN and that discussion contains some very interesting links [5].

In particular the link to a talk by Rick Hartley in this subthread is very informative [6]. He talks about how most EMI problems in PCB designs are due to people not taking into account the the energy is not in the wires.

[1] https://www.youtube.com/watch?v=C7tQJ42nGno

[2] https://www.youtube.com/watch?v=bHIhgxav9LY

[3] https://www.youtube.com/watch?v=VQsoG45Y_00

[4] https://www.youtube.com/watch?v=iph500cPK28

[5] https://news.ycombinator.com/item?id=29598860

[6] https://news.ycombinator.com/item?id=29601273

The thing is that KVL and KCL hold, and KVL and KCL hold for both electrons and water. You just have to not think too deeply about what motivates the electrons to move. Current is indeed the mean velocity of carriers through some area, and voltage is mmm... well it's related to the electric field. It's just not exactly fluid pressure even though it behaves as such.

The right way to think about this if you _really_ care is a bit like the way that RF engineers think about dielectric resonators. The metal motivates the fields to be guided along pairs of conductors by the motion of charge carriers within. A metal will respond in a particular way to fields, which results in new fields, and so on and so forth in a way that results in the fields propagating along in a particular way.

A propagating pulse is a bit hard to think about but you can imagine some field configuration that results in the electrons in the metal slipping a bit, and those electrons move in a way that results in new fields which contain the new wavefront of the pulse. The electrons don't keep moving -- they move on average the distance of the mean free path and give their energy to the lattice as heat. This is why the drift velocity is just a meaningless number. The fields propagate at around c and the conductors guide them.

> Water only ever remains inside the pipes that carry it

If that were the case I wouldn't be paying twelve hundred bucks and counting to fix the plumbing in my mom's house.

> For anyone desperate enough to want to find an analogy to a light-emitting diode (LED), consider the fountain-emitting one-way value shown in Figure 2.

Transformers can be represented by paddle wheels and gearboxes and such. They come free with inductance (inertia.)

The pedagogical failure of this analogy is how it suggests that the energy is stored in the potential and kinetic energy of the fluid (the electron density) rather than in the fields. Then you end up with this drift velocity nonsense which is essentially a holdover from the Drude model which is only predictive by luck.