64 



50 



CASE 2a: Same as Case 2 with Reloading after Cavitation at the Diaphragm; 

 Figure 27. After the occurrence of cavitation the remainder of the shock 

 wave should act on the water surface and accelerate it toward the diaphragm, 



unless the shock wave is so short 

 that its duration does not exceed the 

 compliance time T„. The effect on 

 the water should be especially strong 

 near the edge of the diaphragm; and 

 here, also, the motion of the dia- 

 phragm is soon checked by the support. 

 At the edge, therefore, the cavita- 

 tion must begin to disappear immedi- 

 ately, and it should then disappear 

 progressively toward the center. The 

 boundary of the cavitated area may 

 move at supersonic velocity and will 

 then be accompanied by an impulsive 

 increment of pressure. 



Such an action is hard to 

 follow analytically. The only easy case is the rather different ideal one in 

 which both diaphragm and water surface are assumed to move in the same pro- 

 portional manner, as on page Ul . Then the cavitation closes impulsively on 

 all parts of the diaphragm at once. 



If the duration of the cavitation is considerably longer than the 

 diffraction time. Equation [62] gives for the velocity acquired by the center 

 of the water surface while free 



Time 



Figure 27 - Illustration of Case 2a, 

 Cavitation at the Diaphragm 

 with Reloading 



This differs from Figure 26 in that the cavitation 



closes again and the water gives the diaphragm 



a fresh impetus outward. 



M, L ^' 



dt 



where T^ is the time of the beginning of cavitation; this time is assumed to 

 follow the arrival of the wave so closely that z/ in Equation [62] can be 

 dropped, and 0, is assumed to be equal to zero. 



When the water subsequently overtakes the diaphragm, an impulsive 

 equalization of their velocities will occur, resulting in a partial reflec- 

 tion of the kinetic energy back into the water. If the diaphragm has already 

 been brought to rest by the action of Internal stresses, their common veloc- 

 ity soon after the impact of the water should be M,z^/{M+ M,), according to 

 the first term on the right in Equation [6U], and their combined kinetic en- 

 ergy should then be 



