The water metaphor is useful for visualizing certain aspects of electricity and electronics, however, it breaks down when discussing certain concepts. It is an important tool for making an abstract concept concrete, and is useful for discussing electric potential, switches, and simple flow of electrons, but it is misleading when used to discuss current and circuits.
The usual discussion is that voltage is analogous to the push of the water supply, current is the water actually flowing, and electrical resistance is like constricting the pipe thereby limiting the water flow and, by extension, the current. This is more or less true, but confusion arises because when you constrict a water pipe, the water actually flows faster and with more force, even though less water may actually be flowing. The speed of electrons moving through wires is actually an extremely subtle issue and not a concern for artists working with electricity.
At the faucet handle (valve), the metaphor is pretty close to matching (mostly because the constriction happens before the water enters the faucet, which has a relatively large cross section dampening the extra pressure and speed created at the valve), but if you constrict the water flow at the end of a pipe, by putting a finger over it, the speed increases dramatically, the amount of actual water flowing changes only slightly, and the pressure increases, sometimes by a lot. This is NOT true with electricity. Resistance in a circuit does not make electrons flow faster, it makes them slower, nor does it make them push harder. It does, however, like a water valve, create more turbulence, and wire diameter like water pipes, changes the speed too. Remember, current is NOT the speed of electron flow (though they’re related). In fact, other than making a CRT work, electron speed is not something we ever need to worry about. Electron speed is fairly slow: in wire it’s around 1 millimeter per second; in a vacuum (like the inside of a CRT) it is around 1/10 the speed of light. Electricity, strictly speaking, is actually a wave phenomenon, not a particle one, and as such, moves pretty close to the speed of light.
But remember, the actual path of electrons isn’t important, electrons bounce around in all directions with an overall tendency to move in the direction of electron flow; it’s more that when one pushes in on one end, another pops out the other, and for practical purposes, that happens nearly instantaneously. Current is a measure of the actual number of electric charge particles flowing past a point over a given time. Speed is the distance covered over time. When things move, potential energy is converted into kinetic energy. Resistance is actually taking away energy from electrons and turning it into heat rather than slowing them down.
Another breakdown concerns electric circuits. If the water metaphor is constructed as a closed loop and a pump – like our body’s circulatory system, then it’s more or less okay, as long as we ignore the fact that we need to power the pump. If it’s constructed using a tower, then it’s not clear how the water gets back to the top. The energy loss (entropy), inherent in all things and all processes, will guarantee that the water does not have enough energy to get back to the bucket on top of the tower.