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# Physics/moving conductor in a magnetic field

Question
Magnetic flow meters use Faraday induction to produce a voltage across a channel in which a conductive fluid is flowing. The basic relationship (using convenient geometry so that the cross products simplify) is

Voltage = k･v･B･L

where k is a calibration constant, v is the fluid flow speed, B is the constant external magnetic field strength and L is the distance across the channel.

My first question is, other than specifics of the electronic design and exact instrument configuration, how does the constant k depend on the conductivity of the fluid? How does one calculate the effective charge and current densities? I am particularly interested in seawater as the conducting fluid.

Secondly, given a voltage set up between the electrodes, presumably work can be down by connecting the output to a load. The situation I am envisioning is that the EMF set up by the flow through a magnetic field will be aligned along a conducting cable (oriented in the appropriate direction, of course). However, I am concerned about internal resistance of the cable "robbing" the available energy of the system. Can you explain how this set up would work (or not!)?

Thanks. BTW, I am an Expert in the Advanced Math category and so won't get scared by the math.

I looked into it a little bit, and my initial suspicion was correct.  These meters are generally intended to measure the flow velocities of conductive liquids like normal water, acids, etc...not resistive (or potentially resistive) fluids like deionized water or hydrocarbons.  In that case, the constant becomes much simpler, and the constant should be very close to 1.  In very resistive fluids, like oils, these meters are functionally not useful except as a possible measure of water or other contaminants.  Of course, the detailed design often accounts for fringing fields and things like the conductivity of any fluid that is not fully immersed in the magnetic field.  Basically, the resistivity should become important when you get above the resistivity of sea water (about 0.2 Ohm-meters on average), from what I picked up poking around at the designs.

Physics

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#### Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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