181 



while a rough order of magnitude of a typical plastic radial flow rate U 

 ■Tiay be obtained from (13): 



U^_vi_ ^ vl/ pv^ or .055 V 

 so that 



U /^r 

 / 5 t 



= _^ ^ 8 o/c 

 iilastic 675 



From these results 've see that although the initial elastic effects occur 

 very rapidly, they nay result in a radial velocity distribution of 

 significantly large order of nagnitude. Because of this, it is a bit 

 unfortunate that the estimate {23) is not based en a fiwaer foundation; this 

 appears to be a subject for further investigation. 



The remaining initial conditions, other than (23) (which we now 

 take to hold at t = O) nay be listed. Tlie initial radius of the bending 

 wave is 



R(0) = a ; (24) 



the initial thicl-cness is 



H(0) = h , (25) 



the initial radial velocity at the bending vrave is 



where E = CD, for a .iiaterial of zero elastic strain range. 



Finally in order to define the final shape of the diaphragm 

 profile, we introduce the distance Z (t) of the central flat region from 

 the initial plane of the diaphragm. Clearly, 



Z = V t (27) 



so that once R is found as a function of t, elimination of t between R and Z 

 iTill yield Z = Z(R), the equation of the diaphragm profile. This concludes 

 the mathematical formulation of the theory. 



-IB- 



