# Magnetic Flow Meters: how do They Work?

*Most recent answer: 03/30/2015*

- randy (age 61)

Palos Verdes CA

It turns out that the conductivity of the fluid doesn't enter into that calibration constant. Here's one way to think about it. Let's say, for simplicity, that the flow velocity is uniform. Then let's look at the whole situation from the reference frame at rest with respect to the fluid. In that reference frame, that has a pure magnetic field in the lab beomes in part an electric field. In nice cgs units, the electric field E in that frame is E=(v/c)B, where B is the lab magnetic field, to lowest order in v/c. So that means that in these units, with c= speed of light, :

V= (v/c)BL.

Here V is in statvolts, B is in Gauss, and L is in centimeters.

Conversion to SI units or others isn't hard.

V (in volts)= v(in meters/second) * B (in tesla) * L (in meters).

In a real instrument, the fluid velocity isn't constant throughout the tube, being largest in the middle, so the effective "L" may be a little different than the simple geometrical distance, if for "v" you use the average velocity.

If you use this voltage to drive an external circuit, that means that some current is flowing at right angles to the magnetic field and to the fluid flow. The magnetic field exerts a force on that current, in the direction opposing the fluid flow. So whatever work is done by the current has to come from work done by whatever is pushing the fluid flow, just as you suspected.

Mike W.

*(published on 03/30/2015)*