412 



In any case, similitude of the type described does not extend to 

 the dimensions of the charge nor to the shock wave. These features can be 

 included only if gravitational effects are neglected. If that is done, re- 

 quirements a, c, and d can be met by keeping all pressures and velocities the 

 same at corresponding points, while linear dimensions and times are changed 

 in proportion to Wi. The effects of the gas pressure are then correctly 

 covered; and the similitude will hold for migration due solely to the pres- 

 ence of bounding surfaces. This is the type of similitude that is familiar 

 in the discussion of underwater explosions with neglect of all gravitational 

 effects. 



The various conditions requiring study thus lead to different cri- 

 teria for similitude, a situation which occurs also in other applications of 

 the ship model testing method. Thus in model tests of ship propulsion it has 

 long been the accepted practice to break down the model resistance into two 

 parts which are stepped up to full-scale values by the use of different laws 

 of similitude. 



It is hoped that a similar procedure can eventually be established 

 in the present case, so that migration effects observed on small scale can be 

 made the basis for a correction of the results of direct scaling according to 

 the nominal theory based on the solid angle subtended at the charge by the 

 tarf^et, as explained in TMB Report 492 (11 ). 



However, such a procedure is not yet possible. A study of migra- 

 tion from that point of view is being made and the results will be communi- 

 cated in a lacer report. 



NOTE ON MOMENTUM IN THE WATER 



In thinking about the motion of gas globes it is often natural to 

 resort to reasoning based upon the principle of momentum. Much greater care 

 must be used, however, in applying the principle of momentum to the noncom- 

 pressive motion of liquids than In applying the principle of energy. It is 

 very easy to go astray and arrive at the wrong conclusion. The fundamental 

 reason lies in the fact that the transmission of momentum involves only the 

 pressure itself, whereas the transmission of energy depends upon both pres- 

 sure and particle velocity; because of this difference, momentum in an in- 

 compressible liquid is more readily transmitted to great distances than is 

 energy . 



To illustrate the care that must be used in considerations of mo- 

 mentum, consider a sphere of the same mean density as water, so that it will 

 remain suspended without rising or sinking. Let an upward force be applied 

 to it, causing it to rise in accelerated motion. The sphere is thereby 



