601 



Where p' is the relief pressure due to the motion of the diaphragm. 



The diaphragm is assumed to deform plastically into the parabolic fom 



2r,l 1--, 



(3) 



and the energy absorbed in dishing to a moan deflect ion T) is assumed to be c^ (tj) which is known 

 from static tests. 



The kinetic energy of the diaphragm in dishing is 



Jo 



{•) 



The rate of increase of the kinetic energy is given by 

 ^2_ 



; 77 a 

 3 



ai^ at 



(5) 



while the rate of absorption of onergy plastically is 



^ * (r,) = ,;t' (r,) *) 

 (It dt 



(6) 



The rate of work on the diaphragm by the pressure p is 



P ^ 27r rdr = U7T ^ 

 dt dt 



so that the equation of motion is given In the- form 



i 77 a V ^ * ■*' N 



i'-i] 



(7) 



(B) 



4>iv'i 



77 a^ p^ (77) *) 



whence p^ (77) = ^I^ 



(9) 

 (10) 



so that the equation of motion may be written using (l) and (2) as 



i ph i^ * p^ (r,) . p^ a-' 



(-?■]'■' 



(n) 



In this equation p' Is a function of r ^nd t and at any point r = r. is given by 



(P-), 



_2 

 2t, 



1 \A 



(«) 



where the integral is taken over the whole diaphragm and R is the distance from the point P 

 (it which p" is being evaluated) to the olement dS at the point <) (Figure 4). This expression 

 is based on the ""ssumption th .t diffraction effects due to the finite size of gauge can be 

 neglected. Unfortunately, except in the very early stages for the front diaphragm of a "face on' 

 gauge, the diffractior. phenonena are far too complex to take into account. 



However, it may be noted that the gauge always has a diaphragm at each end and in practice 

 it is usually found that the front and back diaphragms show about the same anxsunt of dishing. 

 This indicates that the overall effect of diffraction on the dishing is sm-jll and suggested our 

 assumption as a reasonable simplification to make the theory tractable. 



If 



