I'm sure you can also figure this one out! There are several ways
I can think of, some involving putting the wire in a fluid, which
appears to be what you are asking about.
1) Submerge your bundle of wire in water (or other appropriate
fluid -- if the wire is made up of sodium, water is not recommended --
it will explode. Try oil in this case). Use a graduated cylinder or
other container which measures the fluid level accurately. Note the
change in fluid level -- the change in volume is the volume of the
wire. Divde the volume of the wire by its cross-sectional area, and
voila, you have the length. To be careful about: make sure you shake
off *all* of the air bubbles which will invariably accompany your
tangle of wire into the water.
2) Archimedes principle speaks about the buoyant force on objects
submerged in a fluid. You could weigh the bundle of wire when it is
dry, tie a thread to a bit of the bundle and dip it all into water (or
other fluid, and shake off the bubbles!). Measure the force is needed
on the thread to hold up the wire (preferably with the same scale, and
make sure you hold the scale the same way as when measuring the dry
wire). The difference in these weights is the weight of the water
displaced, and water has a mass of 1 gram per cubic centimeter. This
lets you compute the volume of the wire again (without having to
measure a water level, which can be tricky). You still need to know the
cross-sectional area of the wire to get the length once you have the
3) Best of all, but no credit to poor Mr. Archimedes: just weigh
the dry wire and look up or measure the weight per unit length of the
wire and divide.
4) Also no Archimedes: you could measure the resistance of the wire
and divide by the resistance per unit length. Some things to be careful
about here -- the wire has to be insulated, so that the places where it
touches itself in the tangles do not create short circuits. Contact
resistance also can be a problem.
5) Also no Archimedes: Get an electronic pulse generator and an
oscilloscope. Pulses travel at about 1 foot per nanosecond through most
wires; use the scope to measure the propatation time of short pulses in
the wire. Again warning: short circuits mess this up.
(published on 10/22/2007)