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

Date: Mon Aug 27 17:42:28 2001
Posted by Benjamin Monreal
Position: Grad student, Physics, MIT

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:

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: 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,


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