410 



/g 2 = — ^ V^ 2 pound-seconds per square inch [56b] 



in which r and R2 are In feet, p„ in pounds per square inch and /0.2 in pound- 

 seconds per square inch. 



If there is a plane bounding surface in the neighborhood, a correc- 

 tion is then to be added representing the effect of a phantom gas globe lo- 

 cated at the mirror image in the surface of the actual one. The pressure and 

 impulse due to the image are calculated from the same formulas as those due 

 to the actual gas globe, with r made equal ta the distance from the image. 

 The total pressure and impulse are then the sum of these respective quanti- 

 ties for the actual globe and the image if the surface is rigid, or the dif- 

 ference if the surface is a free one. At the surface itself, the effect of 

 the image is to double the excess of pressure above hydrostatic pressure on a 

 rigid surface, or to keep the pressure at the hydrostatic level on a free 

 surface. 



From Figure 17 it is seen that, as the migration increases, the 

 peak pressure decreases, but the width of the peak increases so that the im- 

 pulse due to it is about constant. At Q = Rz/3, the peak pressure has de- 

 creased by about a third; the rate of decrease then becomes greater, so that 

 at Q = 1 the peak pressure is only a tenth of what it would be in the absence 

 of migration. 



The increase in /0.2 ^^ large values of Q/R2 in the figure arises 

 from the fact that the total range of pressure becomes small and the peak, 

 defined as extending from one-fifth of the maximum to one-fifth on the other 

 side, comes to include almost the entire range of positive pressure. The 

 ratio of /0.2 to the total positive impulse increases from about 1 /3 at Q = 

 to U/5 at Q = /?2. 



MIGRATION OF A GAS GLOBE IN A TROUGH OR BOX 



The necessary formulas have been written out for a charge detonated 

 inside a rectangular box partly filled with water; this obviously includes as 

 special cases a deep well of rectangular cross section or a trough with par- 

 allel vertical sides. The series obtained in these cases are complicated, 

 however, and for this reason no results will be cited here. 



MIGRATION AND SIMILITUDE 



In considering similitude as it applies to phenomena of migration, 

 it should be noted that physical processes of four different types are in- 

 volved and each process imposes Its own characteristic requirements for si- 

 militude. These differing requirements are not entirely reconcilable. Thus, 

 in order that similar motions may occur on different scales: 



