240 



13 



If the simple assumption Is now made that cavitation occurs at the 

 surface of the plate as soon as the pressure sinks to a certain value p^' , 

 the time at which It occurs can be found by putting p + p" = p^' - p^ in 

 Equation [1U] and solving for (. The corresponding value of dx/dt as ob- 

 tained from Equation [13] is then the velocity with which the plate leaves 

 the water. 



For the special case in which p^^' = p^ = p^, this velocity is also 

 the maximum velocity acquired by the plate and has the value 



dx 

 Jt 



= V, 



am 



:i5] 



where 



am 



as given on page 7 of TMB Report 489 (6! 

 written 



The formula for r. 



[16] 

 can also be 



k PsL, 

 pc 



k = 2q 



1 



1-? 



:i7] 



where fc is a dimensionless number and p^/pc represents the particle velocity 

 associated with the maximum pressure In the Incident wave, A plot of k 

 against q is shown in Figure 8. 



If p ^' is less than p^, the plate is slowed down somewhat by the 

 action of the pressure p^ on its opposite face, assisted perhaps by tension 

 in the water, so that it leaves the water with a velocity less than v ^^^ . 



The initial velocities of diaphragms acted on by explosive pressure 

 waves as measured at the David W. Taylor Model Basin have always been less 

 than the calculated I'^ax. but never less than half as great. Details will be 

 reported elsewhere. 



2. Cavitation may occur 

 first in the water itself; see 

 Figure 9. 



Consideration of this 

 case is new. If a fixed breaking- 

 pressure P(^ is assumed, the point 

 at which cavitation starts may be 

 found by examining the resultant 

 pressure distribution in the water 

 near the plate. The reflected 

 pressure p"(t) at the plate Itself 

 is, from Equations [12] and [lU], 



2 



1.6 

 k 

 1.2 



08 



0.4 



5 10 



20 25 30 



Figure 8 - Plot of the Coefficient k 

 in Equation [ly] 



The broken curve continues the right-hand 

 part of the curve backward 

 on the same scale. 



