Sec. 1-4] 



MECHANICAL INPUT T /.'.I XSDUCERS 



99 



where e is the dielectric constant of the medium between the cylin- 

 ders, h the length of the cylinders, and r x and r 2 the radii of the 

 cylinder surfaces adjacent to the liquid. If the cylinder capacitor is 

 only partly filled with a liquid, the capacitance of the arrangement 

 shown in Fig. (1-4)7 is, for h% r and r > a, in good approximation. 



0= ^' +£ ""' (2) 



2 In [1 - - (a/r)] v ; 



where li is the height of the liquid level, h" the length of the cylinder 

 above the liquid surface, as indicated in Fig. (1-4)7, e' the dielec- 

 tric constant of the liquid, e" the dielectric constant of the gas above 



L <$>± 



Fig. (1-4)7. Capacitive liquid- 

 level transducer for dielectric 

 liquids. 



Fig. (1-4)8. Capacitive level 

 transducer based upon the 

 capacitance between the liquid 

 surface and an auxiliary elec- 

 trode P 9 . 



the liquid (usually = 1), r the outside radius of the inner cylinder, 

 and a the distance between the inner and outer cylinders. The stray 

 capacitance on both cylinder ends is usually in the order of several 

 lO^F and must be added to C in Eq. (2) . The outer cylinder should 

 be grounded. 



Errors are likely to occur from temperature variations which cause 

 a variation of the dielectric constant of the liquid. The error in 

 liquefied gases may be as high as 10 per cent. 



For references see W. E. Williams, Jr., and E. Maxwell, Rev. Sci. Instr., 25, 

 111 (1954); J. G. Dash and H. A. Bowse, Phys. Rev., 82, 1951 (1951). 



b. Electrode-to- Liquid Surface Capacitance. If the conductivity or 

 the dielectric constant of the liquid is sufficiently high (e.g., mercury, 

 water), the capacitance between the liquid surface and a reference 

 electrode above the surface can be used for liquid-level determina- 

 tion. A system of this type has been described by Hazen 1 and is 



1 H. L. Hazen, Elec. Eng., 56, 237 (1937). 



