I 3 1 2 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



istics which render the method almost ideal, there are 

 other favorable properties of great practical value. 

 Most important, the method is applicable to unopened 

 blood vessels and therefore requires neither damaging 

 the vessel wall nor using anticoagulants. For this 

 reason, the method can be applied to the anesthetized 

 animal and man under surgery and by implanting 

 electromagnetic probes, measurements can be made 

 on conscious and freely moving animals. 



The electrical flow signal is produced by the motion 

 of the fluid across the lines of a magnetic field. For 

 explanation, a simple physical experiment is shown 

 in figure 25. A metal strip is moving at a velocity ;' 

 in the direction indicated by the arrows. This direc- 

 tion is at right angles to the lines of magnetic force 

 present between the magnet poles N and S so that a 

 voltage (potential difference) is generated in the metal 

 strip according to Faraday's induction law. The 

 induced voltage, which is directed perpendicularly to 

 the lines of magnetic force and to v, is picked up by 

 sliding contacts ("electrodes") e t and c 2 , and measured 

 by the voltmeter I'. Assuming that the magnetic field 

 permeating the metal strip between the electrodes is 

 homogeneous and that the lines of force, the velocity 

 v, and the line extended between the electrodes are 

 directed mutually at right angles to each other, the 

 induced voltage E ind is: 



~ind 



BDvIO volts 



(12) 



where B = density of magnetic flux (gauss); D = 

 width of the metal strip, which is also the distance 

 between the electrodes (cm); v = instantaneous 

 velocity of the metal strip (cm/ sec). Reversal either 

 of the direction of the magnetic field or of the motion 

 will reverse the polarity of the induced voltage. Small 

 deviations from the assumed right-angle arrangement 

 between the directions of B and v, say by ±10 per 

 cent, have little effect on £,„,,. 



Now suppose that the moving metal strip in figure 

 25 is replaced by a conductive fluid streaming through 

 a tube (fig. 26). The tube wall may consist of insu- 

 lating material, and the electrodes e t and e 2 which are 

 inserted into the wall may be in contact with the 

 fluid. In this case, also, equation 12 is generally valid 

 if D is the diameter of the fluid column and ;■ the 

 instantaneous fluid velocity. The velocity, however, 

 will usually not be uniform within the space between 

 the electrodes (as is the case for the solid strip of fig. 

 25). The induced voltage must therefore be calcu- 

 lated from the total sum of all differentials v.dr 



fig. 25. So-called unipolar induction in a metal strip 

 moving across the lines of magnetic force. For explanation see 

 text. 



fig. 26. Basic arrangement for electromagnetic flow meas- 

 urement. Metal strip of fig. 25 is replaced by conductive fluid 

 streaming through a tube. For explanation see text. 



existing along D, i.e., from 



fvdr - D7 



(12a) 



where v R = velocity averaged over the diameter D 

 or radius R. Thus, this velocity has to be used in 

 equation 1 2 instead of v, and the induced voltage is 

 obviously dependent on the velocity profile. This 

 would be an essential drawback of the method, if 

 there were not an additional compensating effect 

 which is of the greatest importance. Let us assume 

 that, as in case of steady laminar flow, the fluid near 

 the axis runs much faster than that near the wall. The 

 outer fluid layers, in which smaller voltages per unit 

 length are induced than in the inner layers, act as a 

 sort of load resistor to the latter, and circular electric 

 currents take place within the fluid thus bringing 

 about a change in the originally induced voltage 

 distribution. Making a valuable theoretical and 

 experimental contribution to the achievements of 

 earlier workers (see historical notes), Thurlemann 



