PRESSURE COEFFICIENTS OF CAPACITANCE 489 



Combination of (2), (9), (10), (11), and (12) results in 



- l\ k (13) 



T). The Effect of a Radial Pirssurc Acting on a Ci/Iindrical Ajmidus 



Consider a radial pressure acting normally to the axis of a cylindrical 

 annulus to which electrodes are affixed to the inner and outer surfaces. 

 Let the inner and outer radii be a and b respectively and assume the 

 cylinder is filled with an incompressible substance so that the inner 

 radius is not pressure dependent. The capacitance per imit length is 

 given b}^ 



2ir££o 



Cc = 



a 



so 



I dC I dE I 1 db 



CbP £dP , bbdP (14) 



In - 

 a 



We employ cylindrical coordinates (r, 6, z) where the ^-axis is taken along 

 the cylinder axis. Hooke's law becomes 



[Trr — 0-(Tee + Tzz)] (15) 



[t80 - airrr + Tzz)] (16) 



SCI — 2 ") ^^" ~ ^^^'^ ~^ "^^^^^ ^^'^^ 



Equilibrium of an arbitrarj- volume element demands" 



r.. = ^ + ^ (18) 



r- 



and 



Tee = A--^ (19) 



where A and B are constants with respect to spatial coordinates. (^4 

 - J. Prescott, Applied Elasticity, Dover Publications, New York, 1946, p. 330. 



