Single-magnet rotary flowmeter for liquid metals

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 tube, 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.