411 



a. The laws of the non-compresslve motion of water require 

 that pressure differences and the squares of velocities shall vary 

 In the same ratio, or 



Ap » v^ 



b. The Intervention of gravity requires that all pressure 

 differences shall vary, as do gravity heads. In proportion to the 

 linear dimensions, or 



Ap o' L 



where L Is any convenient linear dimension. 



c. If a confined mass of gas Is present. Its pressure must 

 usually remain unchanged with scale, on the assumption that the 

 mass of gas present Is varied In proportion to the cube of the 

 linear dimensions. Hence, all pressures must remain unchanged. 



d. Certain boundary conditions, such as exposure to the at- 

 mosphere or the presence of cavitation, may fix the actual value 

 of the pressure at certain points. 



The hydrodynamlcal requirement a. Is consistent with many types of 

 similitude. The addition of the gravity requirement b. restricts the choice 

 to one In which v^ « L, as In ship model testing. Then, also, Ap o^ v^ <> L. 



If the migration effect on a gas globe is large, the gas has little 

 effect on the radial and translatory motion, so that the pressure in the gas 

 globe may be assumed to be zero. The pressure at certain points Is then 

 fixed, as In d. To keep Ap « L, the atmospheric pressure must then be adjust- 

 ed in proportion to L. Furthermore, since the kinetic energy in the water Is 

 proportional to L'v^ or to L*, and since this energy may be assumed to be a 

 fixed fraction of the energy released by the charge, and since the latter 

 energy is proportional to the weight of the charge W, it follows that W must 

 be varied in proportion to L*. Thus linear dimensions and pressures vary in 

 proportion to W*. and, since v^ « L, velocities and times vary in proportion 

 toWK The atmospheric pressure must also be varied in proportion toW*; and 

 the depth of the water must be varied in the same ratio if the depth is sig- 

 nificant. In corresponding positions, the maximum radius R2 and the migra- 

 tory displacement of the gas globe likewise vary as W*. 



When the migratory displacement is small relative to Bg, the simil- 

 itude is not exact, because the motion is then appreciably Influenced by the 

 pressure of the gas. The partial failure of similitude in this case is not 

 apparent from the approximate equations written in this report, because these 

 equations are based upon a fixed value of R2/R0, whereas in reality this ratio 

 will vary somewhat with the hydrostatic pressure. 



