Subject: Re: may i apply the fluidodinamics at the electrons flow?

Date: Mon Aug 27 17:42:28 2001
Posted by Benjamin Monreal

Hola Arturo,

That's an interesting question. The fundamental physics underneath fluid flow and electron flow are very, very different. Conduction of electrons through metals is a quantum-mechanical problem, involving probability waves "diffracting" though a crystal. Flow of liquid or gas through a pipe is a classical and statistical problem, involving large numbers of classical particles bouncing off one another and exchanging energy.

It's interesting, then, that the two systems do have many similar behaviors. Let's look at some analogies:

• The rate of fluid flow through a pipe is (sometimes) proportional to the cross-sectional area of the pipe, and inversely proportional to the length.
• The rate of electron flow through a resistive material is proportional to the cross-sectional area of the material, and inversely proportional to the length.
This is something called "conductance" (in fluids) and "conductivity" (in electricity); the idea is that it's harder to flow through long, narrow pipes than short, wide ones.
• The rate of flow through a pipe is (usually) proportional to the pressure difference between the ends.
• The current through a resistor is (usually) proportional to the voltage difference between the ends
This was called "Ohm's Law" (V = I R, voltage = current * resistance) when it was discovered for electricity. The analogy to fluids is so good that we sometimes speak of "fluid Ohm's Law" for fluids; (pressure drop = flow rate * fluid resistance). Moreover, resistances combine the same way for fluids and electricity; thus you can analyze flow through a network of pipes the same way you analyze flow through a network of wires.
• Both electrons and fluid material are "conserved" - the same amount of current (or water) that enters your system, eventually leaves it, or else must be stored inside somewhere.
• Both electrons and fluids always move from a higher potential to the lower potential. Energy, momentum, charge, and quantity are conserved in a closed system.
• You can probably construct analogies for "capacitors" and "inductors" for fluids. A plumber's "stand pipe", a vertical pipe that both fills and drains from the bottom, behaves like a fluid "capacitor". A massive paddlewheel or turbine that stores the water's kinetic energy might behave like an fluid "inductor". But these are not common usages, I don't think.
Unfortunately, that's as far as the analogy seems to go. Running electrons through wires is similar to running water through pipes, according to the (immensely useful) laws above, but none of the details are analogous:
• There's no analogy to "turbulence" for electricity.
• Electron flow usually gets slower at high temperatures (since resistance increases). Fluid flow gets faster (since velocity decreases).
• Most electronic devices - transistors, diodes, tunnel junctions, etc., depend on quantum principles and have no fluid analogies.
• Electrons repel one another; particles in a fluid do not.
• None of the equations involving forces (aerodynamic lift, etc.) really work for electricity.
• There's no analogy to "magnetic fields" for fluids, although they are extremely important for electrons.
• Electrons do not have anything analogous to "viscosity", boundary layer drag, Venturi effects, thixotropism, etc.
• Electrons in a wire, believe it or not, actually drift extremely slowly - mere millimeters per second, I think - in the current's direction, even though they are bouncing around at hundreds of miles per hour in random directions. (The electric fields travel extremely fast, giving the appearance that electricity is "instantaneous") In fluids, individual particles move quite quickly in the direction of the flow.
More interesting than "why do these analogies fail" is "why do these analogies work?" It's due to some of the amazing simplicity of mathematics. Basic electricity and fluids are examples of "linear systems". Many simple questions we would ask about flow rates, pressures, distance, time, etc., pipe size, can be answered by an equation that looks like "y = a x + b", also called a "linear equation". This is true of many, many systems in physics, engineering, biology, economics, etc.. Ultimately, any linear equation looks just like every other linear equation; moreover, any sum of linear equations looks the same - you'll always be describing things with "y = a x + b", although the constants a and b will change from system to system. So perhaps it's not so surprising that (linear) electron flow closely resembles (linear) fluid flow.

You'll find linear equations describing pendulums, sound waves, water waves, electronic oscillators, flow rates, profit/loss margins, absorbtion/excretion of medicine ... all over the place! Fluids and circuits are just two examples. But, beyond the linear equations (and the fact that the human brain is good at noticing analogies like wire=pipe, voltage=pressure, current=flow) they do not have a lot in common at the level of basic physics.

Gracias por su pregunta interesante,

-Ben