14 



241 



so long as cavitation does not occur, 



V 



p"(t) = 



pc 



am 



pc t 



2pce 



{ pc + am) e 



;t8] 



Let X represent a distance from the plate, measured positively in the direc- 

 tion of propagation of the incident wave. Then the pressure at any point be- 

 hind the plate, within the distance to which the reflected wave has traveled, 

 will be 



p = p(t-f) + p"(t + f) = 



e + 



pc 



2pc ^-^(«+f) pc+am ^-c(t + f) 

 am pc — am 



19] 



Cavitation will begin where p as given by this equation first sinks 

 to the breaking-pressure p^^. From this point a breaking-front will advance 

 toward the plate, perhaps all the way up to it, while another one travels 

 back into the water. The latter front travels forever, in the present case, 



provided p^ is less than 0, but the cavi- 

 tation behind it soon becomes negligible. 

 This is because the incident wave soon be- 

 comes inappreciable, and the receding 

 breaking-front soon becomes indistinguish- 

 able from that particular reflected wave 

 at which p" = P^ ' P h ^^'^ travels with this 

 wave at the speed of sound. Equation [U] 

 then gives ry = behind the front. 



The particle velocity v^ ahead 

 of the front becomes that of the reflected 

 wave or v^,_ = - (p^ - p^)/pc; hence by 



Figure 9 - Diagram illustrating 

 the Case in which Bulk 

 Cavitation occurs in the Water 



bn 



Equation [3], in which V^ = c and the signs of v^^ and v ^^ must be changed to 

 allow for the difference in the direction chosen for a positive velocity, the 

 particle velocity behind the front is - (p^ - p^)/pc. Thus the part of the 

 reflected wave from 2p^ to p^ travels on, with a discontinuity at its rear 

 face, leaving the pressure uniformly equal to p^ and the velocity uniformly 

 equal to - (p^ - p^)/pc behind it. Only a limited region of cavitation is 

 formed near the plate. 



The process by which the plate, after being returned by other 

 forces such as air pressure, destroys the cavitation again, can be followed 

 by numerical integration in any particular case that may arise. 



