I’m curious, how would you describe inductance in the context of the water analogy? I’m not very experienced in electronics so I’m hoping the “water version” of it might help me understand electric inductance better.

There's a property called "inertance" which is analogous to inductance in electrical circuits: https://en.wikipedia.org/wiki/Inertance

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/...

This video explains water hammer really well.

https://youtu.be/xoLmVFAFjn4

Yes it does! Watched, learned something, grateful.

It is the reason why domotica valves move so slow. If they were to move instantaneously then it would cause water-hammer to the point where it might even dislodge the valve from its connections if the run before it is long enough!

There is also a practical device which is basically a boost converter for water: https://en.wikipedia.org/wiki/Hydraulic_ram

It is the inertia of the water in the connecting pipes. In electrical systems, the inductance is that property of a component which tries to keep current constant. In both forms of the thought experiment, if you shut off the connection instantly, the voltage or pressure build to destroy the thing which stopped the connection.

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.

In electric circuits capacity and inductance make energy oscillate between the electric and the magnetic field. The closest analogy I can think of for water pipes would be the oscillation between the kinetic and the potential energy (or the flow and the pressure). As for better understanding of inductance and magnetic field, imho it's better to stick to Faraday, Gauss and Lenz laws than looking for analogies, as EM field has it's very specific properties.

Might be an unpopular opinion but my advice as an electronics engineer would be to try and move away from water analogies as quickly as possible. While they can be useful at the start for some basic concepts, I feel like trying to relate everything to hydraulic concepts (or springs) makes it harder to understand things in the long run when you start looking at concepts where the analogies don't work as well.

I have only a passing understanding of both, but enough to appreciate the (limited as you say) intuitive resemblances - can anyone enlighten me as to what are the fundamental mathematical differences between modelling electronics and water?

If you keep the water slow enough to stay in laminar flow and the electronic scales large enough to avoid quantum effects, electronic and hydraulic components have an essentially 1:1 correspondence.

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.

What would be a better visualization?

What I’m saying is that it’s best to get to the point where you can reason more directly about voltage, current, charge, inductance etc.

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.

The analogy I always used as a kid was a heavy, free-spinning water wheel in the path of the water. It would tend to resist changes in current.

And the loss will be in the form of gravitational waves.

Argh is this real or not? Would energy radiated away as a result of inductance be analogous to energy radiated away by gravitational waves in the "water pressure analogy"?

I think so yes, but the effect would be very small

Probably more simply in kinetic and sound energy with water as it rumbles through the pipes and vibrates the pipes and barrels a bit.