1045 
X, both in reduced units. B = 83 in this case, representing a very light plate, or a 
charge of great duration. The cashed line represents the front of the reflected wave. Below 
it the pressure is positive due to the original shock wave. Above it the pressure is at first 
positive and then falls steeply dom into a valley of negative pressure. Except for the dis- 
continuous rise and steep fall near the front of the reflected wave (X = T) the contours for 
this case closely approximate the case of a free surface. 
Figure 132 shows similar contours for @ = 4, a heavier plate (or smaller duration). In 
both cases it will seen that the pressure falls to zero first at the plate, in a finite 
time T = h/(B “it Ln . It reaches negative vlaues first out in the water and below 
a certain limiting negative value the given contour never reaches the plate at all. 
Assuming that the theory applies between the shock wave and the cavitation front, and 
that cavitation occurs at p = O we get, on solving Equation (I-5) for the time at which the 
pressure falls to 0 at reduced distance X, : 
x 
Tet/o = -77 Ln OE Ei Ned (1-6) 
(A+ ene (4-2) e* 
In Table II, the measured values of (farthest distance of cavitation from plate) are 
substituted in Eq. (I-6) and the calctilated values of T are compared with the times computed 
from the position of the shock wave. 
In order to determine the radius of the cavitating region at the plate, it is necessary 
to take account of diffraction. 
A very rough treatment of the effect of the diffraction wave is as follows. The same 
basic Eq. (I-1) can be used to compute the time T at which the pressure in front of the plate 
has fallen from 2p, to a value equal to that outside the plate, p(7). For this purpose 
X = O (surafce of plate) and p/p, = e~! so 
T= Bay Ln fa (I-7) 
Beginning at time J a pressure wave will spread inward from the edges because the pressure 
in front of the plate is being lowered by its motion. This pressure wave will reach a radius 
pat time [1+ (R-r)/c] . If the pressure at r has fallen to zero before this time, it 
is postulated that cavitation will extend out to r, but if the diffraction wave reached ¢ 
first then cavitation will not extend to y. Consequently, this theory predicts that the maxi- 
mum radius of cavitation Re will be determined by the equation 
T+ — = 0, (1-8) 
where o¢.* the so-called cavitation time, i.e., time for p to fall to zero at the front of 
the plate. If E =() in Eq. (I-6) t = @ s0 
@ @ L uh (I-9) 
Ets Due Be2 (1-10) 
The latter equation expresses the result in a dimensionless form, in which the distance in from 
the edge of the disk, R - R, is measured in terms of the length unit c@. In the case of a 
plate surrounded by en infinite rigid baffle, T= 0 and Eq. (I-10) becomes: 
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