SURFACE AND OTHER EFFECTS 397 



This correction has been made in obtaining the small charge velocities 

 quoted in the preceding paragraph, the difference being eight per cent 

 in this case. A second small error is in the fact that the use of an image 

 source of equal' strength to represent the surface reflection is not exactly 

 correct, because the resulting particle velocity u^ has associated with it 

 a Bernoulli pressure — {i)poUz'^. The necessary correction to com- 

 pensate this tension is evidently of order (l/poCoU) (^PouJ^) = Uz/2co, 

 which is ordinarily negligible. 



The influence of cavitation so far considered is only a part of the 

 entire stor3^ Although it has been sometimes assumed that tensions 

 amounting to as much as 600 Ib./in.^ are necessary before cavitations 

 can form, this estimate appears from a variety of evidence to be much 

 too high (see section 10.4), at least for water in the open sea. If cavi- 

 tation occurs as close as one inch from a free surface in a typical case, it 

 is not unreasonable to think that the upper surface of the dome breaks 

 up into a spray rather than as a solid mass of water, particularly if this 

 surface is not absolutely smooth. 



What happens underneath the surface spray is a more complicated 

 question, which has been discussed by Kennard (56) in detail. Kennard 

 has shown that when cavitation is once estabhshed the isobaric surface 

 of pressure (Pb) at which it first forms must either spread with a velocity 

 exceeding that of sound, or not advance at all if the pressure gradient 

 and particle motion do not permit this rapid an advance. Initial^, the 

 cavitation below the free surface must therefore spread rapidly down- 

 ward in the water, and at a depth where the negative pressure Pb can 

 no longer, so to speak, keep up with itself, the cavitated region ends. 

 A mass of cavitated water at negative pressure (not necessarily as large 

 as Pb in magnitude, its value depending on whether the bubbles formed 

 contain air or saturated water vapor only) and upward velocity is there- 

 fore realized. The vertical extent of this region is uncertain, because 

 of the lack of precise knowledge as to the proper value of Pb, but it seems 

 clear that it must be only a fraction of the charge depth. ^ This water 

 will therefore rise upward behind the surface of the spray dome and 

 then fall back. Estimates of the details of the motion can only be made 

 by rather tedious calculations from the position and magnitude of the 

 direct and reflected pressure waves for specific values of Pb, and in 

 addition the problem remains as to what extent the cavitated region is 

 broken up and the pressure in its interior increased to atmospheric. 

 These and related questions will be found taken up in detail in Ken- 

 nard's report. 



B. Developjnent of the dome. The initial velocity of the upper sur- 



2 It should be pointed out, however, that measurements of pressure at a depth of 

 600 feet from a charge at the same depth have shown a surface cutoff in the tail of 

 the shock wave; the pressure at this time could not be determined with any accuracy. 



