6l 75 



A fair approximate estimate of the high-pressure part of the shock 

 wave at a distance of R feet from 1 pound of TNT, according to measurements 

 by Hllliar (l4) or with piezoelectric gages (22) seems to be 



p = —^ — e iD/in 



The time constant of the wave is thus about T„ = 0.115 millisecond. This is 

 comparable with the diffraction time for the diaphragm or T^ = 10.5/59 = 0.1 8 

 millisecond, but it is much less than the swing time, which is given by Equa- 

 tion [66] as 0.6U millisecond. The swing time will be longer if water load- 

 ing is Included. 



Thus, if cavitation does not occur, Case 1 as described on page 46 

 of the present report is present. Deflections calculated on this assumption, 

 from Equation [11], are shown in Table 2 as 2„„ ^ao. They are decidedly 

 larger* than the observed values. The discrepancy is probably great enough 

 to outweigh possible sources of error in the necessarily simplified mode of 

 calculation that is employed here. It may be concluded, therefore, that the 

 diaphragms were protected in some way, probably by the occurrence of cavi- 

 tation. 



The pressure on the diaphragm should sink very quickly from its 

 initial peak value. The value of i In Equation [5b] is 5.7/(8700 x 0.000733/1) 

 or 0.89/^, where h is the thickness of the diaphragm in inches. Hence, for 

 h = 0,125 Inch, X = 7'1, and the compliance time, at which the pressure has 

 become hydrostatic and the diaphragm is moving at maximum velocity, is, from 

 Equation [5a], T^ = In 7.1/(8700 x 6.1) second = 0.037 millisecond. This is 

 a small fraction of the swing time. For thinner diaphragms T„ will be even 

 less. The pressure will then become negative, and cavitation is to be ex- 

 pected. 



On the assumption that cavitation occurs at the surface of the dia- 

 phragm as soon as the pressure on it sinks below the hydrostatic value, the 

 maximum velocity of the diaphragm is v„ as given by Equation [7]. Velocities 

 calculated from this equation, with p„ = ^'^600/R, pc = 5-7. ^ - 0.8^/h, are 

 given as a matter of interest as v„ in Table 2. If no further energy is de- 

 livered to the diaphragm by the water, and if it takes on a nearly spherical 

 shape, its central net deflection z will -be given approximately by Equations 

 [80a] and [81]. Values calculated from these equations, using a = 10.5 

 inches and the values of a given in the table, are shown in Table 2 as z^,,,. 

 They are much smaller than the observed values. Even smaller calculated 



In the original report (21 ) much smaller calculated values are given owing to the use of a different 

 method of calculation. The method employed in this report is believed to be preferable. 



