408 



The motion of the water can be resolved into three parts superposed 

 upon each other, a spherically symmetrical part associated with the radial 

 oscillations of the gas globe, a part caused by any bounding surfaces that 

 may be present, and a part associated with the motion of migration. The 

 pressure can then be divided into three corresponding parts, provided the 

 Bernoulli terra pv^/2 is omitted, so that the pressure is simply proportional 

 to the rate of change of the velocity potential. The part of the pressure 

 that is associated directly with the migratory motion is then essentially of 

 dlpole character and hence falls off relatively rapidly with distance; it may 

 therefore be dropped in a rough calculation, except near the gas globe. The 

 part due to a bounding surface, if any, is simply the pressure due to the im- 

 age of the gas globe in the surface and is easily allowed for on this basis. 

 There remains then the part of the pressure that is associated with the rad- 

 ial motion. This part is altered by the migration because the radial motion 

 is altered. 



The radial part of the pressure is given by Equations [6] or [7] on 

 page 45 of TMB Report 480 (10) with the omission of u*; it may not be cor- 

 rectly given by Equation [8] of that report, however, in which the term in u/ 

 is not negligible and is Influenced by the migratory motion. The pressure p 

 at a point distant r from the center of the gas globe is thus 



p=^A(^.«)+,^ [53] 



where p is the density of the water and p^ denotes the total hydrostatic 

 pressure at the level of the gas globe. Only the phase of Intense compres- 

 sion is of Interest, hence Equation [1] of the present report can be simpli- 

 fied as before, and even the small term 3l'i^2 can be omitted for the present 

 purpose. Thus from Equation [1] 



The approximate values employed previously for X, Y, Z can then be inserted, 

 and they may conveniently be expressed in terms of the linear displacement 

 of the gas globe from the instant of detonation to the instant of peak recom- 

 pression, which is 



Q = ^/(X, - X,)^ + (F, - Fo)^ + (2. - Zo)^ =^H^ + S^ [55] 



The pressure as thus estimated is found to depend on the ratio Q/Ri, 

 where flj is the first maximum radius, and to be proportional to Po.R,/r. The 

 impulse / =j{p - Pf^)dt, is proportional to R^Vf^/r. A single graph applicable 



