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 quantummechanical 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
crosssectional area of the pipe, and inversely proportional to the
length.

The rate of electron flow through a resistive material is proportional to
the crosssectional 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
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