J^06 SURFACE AND OTHER EFFECTS 



corresponding to a relatively large inertia and slow response of the plate 

 in comparison with the duration of the incident wave. Reduced units 

 of length and time in terms of the time constants of the incident wave 

 are used, and contours are drawn for various values of P/Pm, given by 

 Eq. (10.9). The diagonal lines t/d = —x/cod and t/d = x/cod then 

 represent the fronts of the incident and reflected waves. It is seen that 

 the excess pressure at the plate decreases rapidly, becoming zero for 

 t = OAQd and reaching a maximum negative value of about — 0.2P^. 

 In this case (/3 = 4), negative pressures first occur at points in the 

 water. The contours for larger /3, corresponding to a lighter plate, are 

 compressed downward toward the line for the reflected front, as shown 

 in Fig. 10.4b for the case (3 = 83. Comparison with Fig. 10.4a shows 

 that the least pressure at the plate becomes increasingly larger. For 

 example, the value P = — O.OSP^ is just reached at the plate for /3 = 83 

 and the value P = —O.lOPm is first realized at x = O.O4co0. 



The results in this simple problem are of interest because they 

 illustrate some of the factors to be considered in motion of the water 

 near a target. For one thing, the region in which cavitation occurs in 

 front of such a plate can be used to estimate the necessary tension to 

 produce it. Experiments of this kind (31) have been performed using 

 a thin (.020 inch) sheet of cellulose acetate 6 inches in diameter backed 

 by air and photographing the water in front of the plate after reflection 

 of a shock wave. The photograph reproduced in Plate XII shows 

 cavitation bubbles extending from a point within }4 inch of the plate 

 nearly to the front of the reflected wave (approximately at B in the 

 photograph) . 



The mass of the plate used in the experiment corresponds to /3 = 83 

 in the preceding analysis, and the pressure yg inch from the plate never 

 becomes less than — O.IP^ from Fig. 10.4b (x/Cod = 0.04 in this case). 

 The peak pressure at the experimental distance of 24 inches from a 10 

 gram loose tetryl charge is approximately 900 Ib./in.^ The hydrostatic 

 pressure was 18 Ib./in.^ and a tension of 70 Ib./in.^ is therefore indicated 

 as an upper limit on the tension sustained bj^ the open sea water of this 

 experiment before cavitation occurred. 



A similar experiment with a weaker incident wave gave an even 

 smaller upper bound of 40 Ib./in.^ for the tension. These results are of 

 course only approximate because of the simplifying assumptions of the 

 analysis from which they were obtained, namely that the plate was of 

 infinite extent and rigidity and that the incident wave was plane. 

 These experiments and others of a similar nature do, however, show 

 quite conclusively that the necessary tension for cavitation, in open sea 

 water at least, can hardly exceed a few atmospheres and is probably 

 much less. This being the case, it is usually a good approximation to 

 assume that cavitation begins practically at the surface of a free plate 



