Thursday, December 28, 2006

What are Volts & Amps? The Hydraulic Analogy for Electronics

I had a friend who had a hard time getting the difference between volts, amps and so forth and what it all actually means in the real universe. As anyone who knows L. Ron Hubbard Study Technology will tell you, a misunderstood word can be one of the nastiest things there is, in terms of its impact on one's ability to learn and work. So, here's my favourite analogy which explains this, excerpted from

The electronic Hydraulic analogy (derisively referred to as the Drain-pipe theory by Oliver Heaviside) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes at play in electronics are often difficult to understand in an intuitive way, it is common to teach electronics using analogies to more common sense objects and processes. The analogy is made to a hydraulic system of water in pipes. The "electron fluid" in a metal conductor has many similarities to such a system, and the various electronic components have similar hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid. This hydraulic analogy is still of some use in teaching, not only for the fact that the names of the quantities are often struck by analogy. The water analogy is very useful in describing some aspects of electricity, but it breaks down for others.

Basic ideas

There are two basic paradigms:

  • Version with pressure induced by gravity. Large tanks of water that are held up high, and the potential energy of the water head is the pressure source. This is reminiscent of electrical diagrams with an up arrow pointing to +V, grounded pins that otherwise are not shown connecting to anything, and so on.
  • Completely enclosed version with pumps providing pressure only; no gravity. This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit.

Component equivalents

All pipes are completely full of water, and none ever has an open end. If a pipe were to go somewhere without reconnecting to the circuit, it would have to have a cap on the end. This is because the wall of the pipe is like an insulator, and a wire just sticking out into insulating space/air is like a completely pipe-surrounded rod of water.
Equivalent to pressure.
Also called potential difference. A relative difference in pressure between two points
The amount of charge (i.e. electrons, electron holes or ions) passing through a cross section of conductor per given time, much like a hydraulic mass flow rate.
Ideal voltage source
A pump with a pressure meter on both sides. It varies the speed of the pump to keep the difference in pressure constant.
Ideal current source
Also a pump, but with a current meter (little paddle wheel). The pump changes speed to maintain a constant speed of the little paddle wheel.
A pipe with a small width. "So what makes this different from a regular-width pipe?" Nothing. All pipes have some resistance, just like all wires have some resistance.
A capacitor driven by an AC source through a diode.
A capacitor driven by an AC source through a diode.
One-way valve or check valve. If it has a rubber flap it can be blown out permanently by too much reverse bias, which is similar to the real thing.
Big spherical tanks with a sheet of thick rubber separating the two halves.
All flowing water has inertia, which has similar effects to inductance. A large, heavy, frictionless paddle wheel is like a dedicated inductor. As you try to increase a DC current, you encounter resistance as you speed up the paddle wheel, but after it is going, you can send a current at the same speed as the paddle wheel with no effort. If you try to put AC through it, the wheel will present a great resistance, as its inertia prevents you from moving it back and forth. Any real paddle wheel will have some friction associated with it, just as any real inductor has some resistance. The DC to DC converter uses inductance to change voltage in the way that a Hydraulic ram uses inertia to change pressure.
A device similar to an EGR valve, where a diaphragm controlled by a low-current signal (either constant current — BJT, or constant pressure — FET) moves a plunger which allows a larger current to flow through another section of pipe, like a globe valve.
A combination of two MOSFET transistors. As the input pressure changes, the pistons allow the output to connect to either zero or positive pressure.

Principle equivalents

EM wave speed (velocity of propagation)
Speed of sound in water. When a light switch is flipped, the electric wave travels very quickly through the wires.
Charge flow speed
Particle speed of water. The moving charges themselves move rather slowly.
Constant flow of water in a circuit of pipe
Low frequency AC
Water oscillating back and forth in a pipe
Higher-frequency AC and transmission lines
Sound being transmitted through the water pipes
Inductive spark
Used in induction coils, similar to water hammer, caused by the inertia of water

Equation examples

Some examples of equivalent electrical and hydraulic equations:

type hydraulic electric thermal
quantity volume V [m3] charge q [C] heat Q [J]
potential pressure p [Pa=J/m3] potential φ [V=J/C] temperature T [K=J/kB]
flux current ΦV [m3/s] current I [A=C/s] heat transfer rate \dot{Q} [J/s]
flux density velocity v [m/s] current density j [C/m2s] heat flux \dot{Q}'' [J/m2s]
linear model Poiseuille's law \Phi_{V} = \frac{\pi r^{4}}{8 \eta} \frac{\Delta p^{\star}}{\ell} Ohm's law j=-\sigma \nabla \phi Fourier's law \dot{Q}''=\kappa \nabla T

Limits to the analogy

If taken too far, the water analogy can create misconceptions. For it to be useful, we must remain aware of the regions where electricity and water behave very differently.

Electrons can push or pull other distant electrons via their fields, while water molecules experience forces only from direct contact with other molecules. For this reason, waves in water travel at the speed of sound, but waves in a sea of charge will travel much faster as the forces from one electron are applied to many distant electrons and not to only the neighbors in direct contact. In a hydraulic transmission line, the energy flows as mechanical waves through the water, but in an electric transmission line the energy flows as fields in the space surrounding the wires, and does not flow inside the metal. Also, an accelerating electron will drag its neighbors along while attracting them, both because of magnetic forces.
Leaking pipes
If a hole is made in a hydraulic system, the water can leak out. But the movable charges present within electrical conductors are always attracted to unmoving opposite charges in the material. The "electric fluid" can be forcibly removed from metals, but enormous voltages arise if even a tiny amount is removed. For this reason, the surfaces of conductors act as if they always have a high energy-barrier preventing leaks. Also for this reason, continuing electric currents require closed loops rather than hydraulics' open source/sink resembling spigots and buckets.
Wrap a long water-filled hose around a barrel, and the water's large mass behaves as a significant "inductance." However, in real coils the adjacent turns interact via magnetic fields, and the value of inductance increases as the square of the number of turns. It's as if we could create four times the mass of water by only doubling the length of the water hose.
Fluid Velocity
As with water hoses, the carrier drift velocity in conductors is directly proportional to current. However, charges' velocity within a conductor is typically less than centimeters per minute, and the "electrical friction" is extremely high. If charges ever flowed as fast as water can flow in pipes, the amperage would be immense, and the conductors would become incandescently hot and perhaps vaporize. To model the resistance and the charge-velocity of metals, perhaps a pipe packed with damp sand would be a better analogy than an empty, water-filled pipe.
Quantum Mechanics
Conductors and insulators contain charges at more than one quantized level of atomic orbit energy, while the water in one region of a pipe can only have a single value of pressure. For this reason there is no hydraulic explanation for such things as a battery's charge pumping ability, a diode's voltage drop, solar cell functions, Peltier effect, etc.

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