17 31 



Since It is the excess of pressure above pp that accelerates the 

 plate, the total pressure in the water at the plate will be 



d z 



In the case of the exponential wave represented by Equation [2], m d z/dt is 

 given by Equation [4]. In this case, by equating dp/dt to zero, the minimum 

 value of p is found to occur at the time t = 2T^, where T„ is given by Equs- 

 tion [5a], and to have the magnitude 



1 + X 



Pn,in = P0-2p„x'-^ • [TO] 



Thus, if cavitation occurs when the pressure sinks to a certain breaking- 

 pressure Pj, which cannot exceed the vapor pressure and may be negative, then 

 cavitation can occur only if p^^^ < Pj or 



2Pm^ ' ' > Po - P* 



Here it can be shown that the factor 2x i-* has a maximum value of 

 2/e^ = 0.27 at I = 1 and decreases toward zero as x ^ or x -*• ». 



The maximum depths at which cavitation can occur, as calculated 

 from this formula, come out too large to be of interest. The shock wave from 

 300 pounds of TNT, for example, falling on an air-backed steel plate 1 inch 

 thick at a distance of 50 feet, could cause cavitation at zero pressure down 

 to a depth of 700 feet below the surface. 



Both in the action of shock waves on ships and in comparable model 

 tests the necessary conditions for the occurrence of cavitation due to elastic 

 overshoot at a pressure not far from zero appear to be met, and observations 

 on the initial velocities of diaphragms at the Taylor Model Basin Indicate 

 that it does occur. 



For a Hllllar gage, on the other hand, the compliance time, or the 

 time in which the piston would attain maximum velocity if it were not stopped 

 by anything, is much longer than the diffraction time. Thus cavitation is 

 not to be expected on the face of the piston. 



A more detailed discussion of the phenomena accompanying cavitation 

 near a plate or diaphragm will be given later in this report, on pages 58 

 to 42, 



THE BERNOULLI PRESSURE AND THE DEVIATION FROM HOOKE'S LAW 



At this point it may be worth while to digress slightly for a mo- 

 ment and consider one or two minor matters. The question is often asked, 

 whether the expression for the pressure caused by the impact of a plane wave 



