**When an electrical conductor moves perpendicular to a magnetic field, a voltage is induced in ****that conductor perpendicular to both the magnetic flux lines and the direction of motion. This ****phenomenon is known as electromagnetic induction, and it is the basic principle upon which all ****electro-mechanical generators operate.**

**In a generator mechanism, the conductor in question is typically a coil (or set of coils) made ****of copper wire. However, there is no reason the conductor must be made of copper wire. Any ****electrically conductive substance in motion is sufficient to electromagnetically induce a voltage, even ****if that substance is a liquid. Therefore, electromagnetic induction is a technique applicable to the ****measurement of liquid flow rates.**

**Consider water flowing through** **a pipe, with a magnetic field passing perpendicularly through ****the pipe:**

**The direction of liquid flow cuts perpendicularly through the lines of magnetic flux, generating a ****voltage along an axis perpendicular to both. Metal electrodes opposite each other in the pipe wall ****intercept this voltage, making it readable to an electronic circuit.**

**A voltage induced by the linear motion of a conductor through a magnetic field is called ****motional EMF, the magnitude of which is predicted by the following formula (assuming perfect ****perpendicularity between the direction of velocity, the orientation of the magnetic flux lines, and ****the axis of voltage measurement):**

**E = Blv**

**Where,**

**E = Motional EMF (volts)**

**B = Magnetic flux density (Tesla)**

**l = Length of conductor passing through the magnetic field (meters)**

**v = Velocity of conductor (meters per second)**

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**Assuming a fixed magnetic field strength (constant B) and an electrode spacing equal to the ****fixed diameter of the pipe (constant l = d), the only variable capable of influencing the magnitude ****of induced voltage is velocity (v). In our example, v is not the velocity of a wire segment, but rather ****the average velocity of the liquid flowstream (v). Since we see that this voltage will be proportional ****to average fluid velocity, it must also be proportional to volumetric flow rate, since volumetric flow ****rate is also proportional to average fluid velocity. Thus, what we have here is a type of flowmeter ****based on electromagnetic induction. These flowmeters are commonly known as magnetic flowmeters ****or simply magflow meters.**

**We may state the relationship between volumetric flow rate (Q) and motional EMF (E) more ****precisely by algebraic substitution. First, we will write the formula relating volumetric flow to ****average velocity, and then manipulate it to solve for average velocity:**

** Q = Av**

** Q****/A****= v**

**Next, we re-state the motional EMF equation, and then substitute Q /****A for v to arrive at an equation**

**relating motional EMF to volumetric flow rate (Q), magnetic flux density (B), pipe diameter (d),**

**and pipe area (A):**

** E = Bdv**

** E = Bd*****Q****/A**

** E =****BdQ****/A**

**Since we know this is a circular pipe, we know that area and diameter are directly related to ****each other by the formula A = πd2****/4 . Thus, we may substitute this definition for area into the last ****equation, to arrive at a formula with one less variable (only d, instead of both d and A):**

** E =****BdQ / ****πd2****/4**

** E =****BdQ****4****/πd2**

** E =****4BQ****/πd**

**If we wish to have a formula defining flow rate Q in terms of motional EMF (E), we may simply ****manipulate the last equation to solve for Q:**

** Q =****πdE****/4B**

**This formula will successfully predict flow rate only for absolutely perfect circumstances. In order ****to compensate for inevitable imperfections, a “proportionality constant” (k) is usually included in ****the formula:**

** Q = k ****πdE****/4B**

**Where,**

**Q = Volumetric flow rate (cubic meters per second)**

**E = Motional EMF (volts)**

**B = Magnetic flux density (Tesla)**

**d = Diameter of flowtube (meters)**

**Note the linearity of this equation. Nowhere do we encounter a power, root, or other nonlinear ****mathematical function in the equation for a magnetic flowmeter. This means no special ****characterization is required to calculate volumetric flow rate.**

**A few conditions must be met for this formula to successfully infer volumetric flow rate from ****induced voltage:**

**• The liquid must be a reasonably good conductor of electricity**

**• Both electrodes must contact the liquid**

**• The pipe must be completely filled with liquid**

**• The flowtube must be properly grounded to avoid errors caused by stray electric currents in**

**the liquid**

**The first condition is met by careful consideration of the process liquid prior to installation. ****Magnetic flowmeter manufacturers will specify the minimum conductivity value of the liquid to be ****measured. The second and third conditions are met by correct installation of the magnetic flowtube ****in the pipe. The installation must be done in such a way as to guarantee full flooding of the ****flowtube (no gas pockets). The flowtube is usually installed with electrodes across from each other ****horizontally (never vertically!) so even a momentary gas bubble will not break electrical contact ****between an electrode tip and the liquid flowstream. The following photograph shows how not to ****install magnetic flowmeters:**

**Note in this example how the electrodes are vertically oriented instead of horizontal, because the ****pipes for these two magnetic flowmeters were placed too close to allow proper clearance for the ****protruding electrodes to lie horizontally. Sadly, poor flowmeter installation is all too common in new ****projects, as many piping designers and pipefitters are ignorant of flowmeter operating principles.**

**This is one way instrument engineers and technicians may deter operational problems: by involving ****themselves in the design phase of a piping system, and helping to educate piping designers. ****Magnetic flowmeters are fairly tolerant of swirl and other large-scale turbulent fluid behavior. ****They do not require the long straight-runs of pipe upstream and downstream that orifice plates ****do, which is a great advantage in many piping systems. Upstream straight-pipe requirements of 10 ****diameters and downstream straight-pipe requirements of 5 diameters is typical.**

**Electrical conductivity of the process liquid must meet a certain minimum value, but that is all. ****It is surprising to some technicians that changes in liquid conductivity have little to no effect on ****flow measurement accuracy. It is not as though a doubling of liquid conductivity will result in a ****doubling of induced voltage! Motional EMF is strictly a function of physical dimensions, magnetic ****field strength, and fluid velocity.**

**Liquids with poor conductivity present a greater electrical resistance in the voltage-measuring ****circuit than liquids with good conductivity, but this is of little consequence because the input ****impedance of the detection circuitry is phenomenally high. The effect of liquid conductivity on ****flowmeter operation may be modeled by the following DC circuits:**

**Here, a ten-fold (one order of magnitude) change in liquid resistance barely affects the measured ****voltage (49.995 mV versus 49.95 mV) because the flow transmitter’s voltage-sensing electronic circuit ****has such a high input impedance. The liquid’s equivalent resistance value must increase dramatically ****beyond the values shown in this example before it will have any significant effect on flow measurement ****accuracy.**

**In fact, the only time fluid conductivity is a problem with magnetic flowmeters is when the ****fluid in question has negligible conductivity. Such fluids include deionized water (e.g. steam boiler ****feedwater, ultrapure water for pharmaceutical and semiconductor manufacturing) and oils. Most ****aqueous (water-based) fluids work fine with magnetic flowmeters.**

**Proper grounding of the flowtube is very important for magnetic flowmeters. The motional EMF ****generated by most liquid flowstreams is very weak (1 millivolt or less!), and therefore may be easily ****overshadowed by noise voltage present as a result of stray electric currents in the piping and/or liquid. ****To combat this problem, magnetic flowmeters are usually equipped with grounding conductors placed ****to shunt (bypass) stray electric currents around the flowtube so the only voltage intercepted by the ****electrodes will be the motional EMF produced by liquid flow, and not voltage drops created by stray ****currents through the resistance of the liquid. The following photograph shows a Rosemount model ****8700 magnetic flowtube, with two braided41-wire grounding straps clearly visible:**

**Note how both grounding straps attach to a common junction point on the flowtube housing. ****This common junction point should also be bonded to a functional earth ground when the flowtube ****is installed in the process line. On this particular flowtube you can see a stainless steel grounding ****ring on the face of the near flange, connected to one of the braided grounding straps. An identical ****grounding ring lays on the other flange, but it is not clearly visible in this photograph. These rings provide points of electrical contact with the liquid in installations where the pipe is made of plastic, or where the pipe is metal but lined with a plastic material for corrosion resistance.**

If the pipe connecting to a magnetic flowmeter’s flowtube is conductive (e.g. metal), grounding may be accomplished by joining the metal pipes’ flanges together with grounding straps to a common grounding point on the flowtube body as such:

**If the pipe connecting to a magnetic flowmeter’s flowtube is non-conductive (e.g. plastic) or ****conductive with an insulating lining (e.g. metal pipe with plastic lining), grounding to the pipe ****flanges will be pointless. In order for flowtube grounding to be effective, the grounding conductors ****must have electrical continuity to the fluid itself. Special grounding rings may be sandwiched ****between the flanges of non-conducting pipes to provide points of electrical contact with the fluid. ****These grounding rings are then joined together with grounding straps to a common grounding point ****on the flowtube body as such:**

**Some magnetic flowmeters have their signal conditioning electronics located integral to the ****flowtube assembly. A couple of examples are shown here (a pair of small Endress+Hauser flowmeters ****on the left and a large Toshiba flowmeter on the right):**

**Other magnetic flowmeters have separate electronics and flowtube assemblies, connected together ****by shielded cable. In these installations, the electronics assembly is referred to as the flow transmitter ****(FT) and the flowtube as the flow element (FE):**

**This next photograph shows an enormous (36 inch diameter!) magnetic flow element (black) and ****flow transmitter (blue, behind the person’s hand shown for scale) used to measure wastewater flow ****at a municipal sewage treatment plant:**

**Note the vertical pipe orientation, ensuring constant contact between the electrodes and the ****water during flowing conditions.**

**While in theory a permanent magnet should be able to provide the necessary magnetic flux for ****a magnetic flowmeter to function, this is never done in industrial practice. The reason for this has ****to do with a phenomenon called polarization which occurs when a DC voltage is impressed across ****a liquid containing ions (electrically charged molecules). Electrically-charged molecules (ions) tend ****to collect near poles of opposite charge, which in this case would be the flowmeter electrodes. This ****“polarization” would soon interfere with detection of the motional EMF if a magnetic flowmeter were ****to use a constant magnetic flux such as that produced by a permanent magnet. A simple solution ****to this problem is to alternate the polarity of the magnetic field, so the motional EMF polarity also ****alternates and never gives the fluid ions enough time to polarize.**

**This is why magnetic flowmeter tubes always employ electromagnet coils to generate the magnetic ****flux instead of permanent magnets. The electronics package of the flowmeter energizes these coils ****with currents of alternating polarity, so as to alternate the polarity of the induced voltage across the ****moving fluid. Permanent magnets, with their unchanging magnetic polarities, would only be able to ****create an induced voltage with constant polarity, leading to ionic polarization and subsequent flow ****measurement errors.**

**A photograph of a Foxboro magnetic flowtube with one of the protective covers removed shows ****these wire coils clearly (in blue):**

**Perhaps the simplest form of coil excitation is when the coil is energized by 60 Hz AC power ****taken from the line power source, such as the case with this Foxboro flowtube. Since motional EMF ****is proportional to fluid velocity and to the flux density of the magnetic field, the induced voltage for ****such a coil will be a sine wave whose amplitude varies with volumetric flow rate. ****Unfortunately, if there is any stray electric current traveling through the liquid to produce ****erroneous voltage drops between the electrodes, chances are it will be 60 Hz AC as well. With ****the coil energized by 60 Hz AC, any such noise voltage may be falsely interpreted as fluid flow ****because the sensor electronics has no way to distinguish between 60 Hz noise in the fluid and a 60 ****Hz motional EMF caused by fluid flow.**

**A more sophisticated solution to this problem uses a pulsed excitation power source for the ****flowtube coils. This is called DC excitation by magnetic flowmeter manufacturers, which is a bit ****misleading because these “DC” excitation signals often reverse polarity, appearing more like an AC ****square wave on an oscilloscope display. The motional EMF for one of these flowmeters will exhibit ****the same waveshape, with amplitude once again being the indicator of volumetric flow rate. The ****sensor electronics can more easily reject any AC noise voltage because the frequency and waveshape ****of the noise (60 Hz, sinusoidal) will not match that of the flow-induced motional EMF signal.**

**The most significant disadvantage of pulsed-DC magnetic flowmeters is slower response time to ****changing flow rates. In an effort to achieve a “best-of-both-worlds” result, some magnetic flowmeter ****manufacturers produce dual-frequency flowmeters which energize their flowtube coils with two mixed ****frequencies: one below 60 Hz and one above 60 Hz. The resulting voltage signal intercepted by the ****electrodes is demodulated and interpreted as a flow rate.**