If the current changes, an inductor produces a voltage. If the current changes, the water can build up or form a trough at the paddlewheel.
At my most recent project we used very low RF, below the AM band, and the inductors were sometimes huge doughnuts of ferrite. Literally the size of doughnuts. Since most digital (and modern analog) boards use very tiny capacitors and resistors, and generally only a few tiny inductors or transformers for power-conversion reasons, this was unusual to me.
If you drag a magnet through the sands of certain beaches around here, you can collect magnetic iron oxide, ie magnetite. It looks like you're pulling a black sea urchin from the sand! In bulk form this is lodestone. You can mix it with epoxy and cast your own inductor cores. Or you can grind it in a coffee grinder and mix with aluminum powder (3:1 Fe2O3 to Al) and make thermite. Or you can use it to "draw" on the beach, without polluting. And you can teach kids about mining and geology in questioning how the deposits got there and got separated.
So if a paddle wheel is an inductor, what is a transformer in this hydraulic analogy? It is a pair of paddlewheels, in different streams, connected by a belt or gears.
But this doesn't work that well as an analogy since a transformer only passes alternating current. A better physical analogy would couple the height of the water at the upstream side of the paddlewheel to drive another paddlewheel in another stream. Then only alternating flows in the first current would couple the two paddlewheels. Because a steady stream in the first paddlewheel would generate no buildup of water to drive the other wheel.
Here's a crude schematic:
Of course, in a real transformer, the coupling is via (changing) magnetic flux and Maxwell's laws of electrodynamics.
BTW this post assumes you're aware of the more obvious parts of the hydraulic model of electricity, with Ohm's law, balloons as capacitors, pumps as voltage sources, etc. If you don't know what I'm talking about this will be worse than confusing.
(Later)
There are problems with this model. The coupling between the paddle wheels needs to work only if there's change in the flow. Magnetic fields in the aether. Something involving ripples in a pool, generated by varying flow, which are picked up by another circuit, to drive flow in that. More complicated than a simple gear or belt transmission as illustrated.
