98 Pressure in a Liquid during Collapse of a Spherical Cavity. 



So long as 2, which always exceeds 1, is less than 4, the 

 greatest value of p, viz. P, occurs at infinity; but when z 

 exceeds 4, the maximum p occurs at a finite distance given 

 by (14) and is greater than P. As the cavity fills up, 

 z becomes great, and (15) approximates to 



P.-it-ilK3' * * * ' • ^ 

 corresponding to 



r = 4*R=l-587R (17) 



It appears from (16) that before complete collapse the 

 pressure near the boundary becomes very great. For ex- 

 ample, if R = J -R , p = 1260P. 



This pressure occurs at a relatively moderate distance 

 outside the boundary. At the boundary itself the pressure 

 is zero, so long as the motion is free. Mr. Cook considers 

 the pressure here developed when the fluid strikes an abso- 

 lutely rigid sphere of radius It. If the supposition of in- 

 compressibility is still maintained, an infinite pressure 

 momentarily results; but if at this stage we admit com- 

 pressibility, the instantaneous pressure P / is finite, and is 

 given by the equation 



p/2 p /P 3 \ 



^=^ U2 =l@-l> • • - (18) 



ft being the coefficient of compressibility. P, P', ft may 

 all be expressed in atmospheres. Taking (as for water) 

 ft = 20,000, P=rl, and R^Ro, Cook finds 



P' = 10300 atmospheres = 68 tons per sq. inch, 



and it would seem that this conclusion is not greatly affected 

 by the neglect of compressibility before impact. 



The subsequent course of events might be traced as in 

 * Theory of KSound,' § 279, but it would seem that for a satis- 

 factory theory compressibility would have to be taken into 

 account at an earlier stage. 



April 13, 1917. 



