  We present a theory of single-magnet flowmeter for liquid metals and compare
it with experimental results. The flowmeter consists of a freely rotating
permanent magnet, which is magnetized perpendicularly to the axle it is mounted
on. When such a magnet is placed close to a tube carrying liquid metal flow, it
rotates so that the driving torque due to the eddy currents induced by the flow
is balanced by the braking torque induced by the rotation itself. The
equilibrium rotation rate, which varies directly with the flow velocity and
inversely with the distance between the magnet and the layer, is affected
neither by the electrical conductivity of the metal nor by the magnet strength.
We obtain simple analytical solutions for the force and torque on slowly moving
and rotating magnets due to eddy currents in a layer of infinite horizontal
extent. The predicted equilibrium rotation rates qualitatively agree with the
magnet rotation rate measured on a liquid sodium flow in stainless steel duct.
