19 33 



front stagnation point, or point of zero velocity, on any small rigid ob- 

 stacle in the path of the waves should be p + pv^/2; likewise, the pressure 

 on the piston of a Hilllar gage (1U) should be approximately p - pv^/2, where 

 Vp is the velocity of the piston. 



The Bernoulli effect as represented by the term pr^ in such expres- 

 sions will thus in some cases play a part in modifying the pressure field in 

 front of a target. Analysis furnishes no reason, however, to expect addi- 

 tional effects on the target from a "kinetic wave" following the shock wave. 

 The pressure field in the water constitutes the mechanism by which the water 

 Is set moving outward and then presently arrested; the pressure field is 

 physically inseparable from the motion, and its effects on the target include 

 all effects that might be ascribed to the action of the moving water. 



At any fixed distance from the center of the explosion, the pres- 

 sure in open water should fall continually as the gas globe expands, and it 

 appears from analytical results that the same should be true of the pressure 

 on the target. Thus no upward surge of pressure is to be expected "as the 

 moving water reaches the target"; the idea of a water projectile propelled 

 by the gas globe and subsequently Impinging upon the target is inappropriate 

 and misleading . 



PART 3. THEORY OF A PLANE TARGET 



The discussion has been kept in general terms up to this point, and 

 few exact formulas have been given. General analytical results are difficult 

 to obtain, and numerical integration has scarcely seemed worth while hitherto 

 because of Incomplete knowledge of the relevant fundamental data. 



There is one three-dimensional case, however, in which exact ana- 

 lytical formulas are readily written down. This is the case in which every- 

 thing of interest happens in the neighborhood of a plane surface, which may 

 be supposed to extend laterally to infinity. This case will now be taken up 

 for discussion in some detail. For generality, the fluid present will not be 

 restricted to water. 



PRESSURE ON AN INFINITE PLANE 



When waves fall upon the initially plane face of a target of effec- 

 tively infinite lateral extent, an expression is easily obtained for the re- 

 sulting pressure at any point on the face. The waves may be plane, spherical 

 or of any other type. It must be assumed, however, that they are of suffi- 

 ciently small amplitude so that the ordinary linear theory of acoustics is 

 applicable, and that the displacement of the water or other fluid at points 

 on the plane is sm311. The first conditiftn should be sufficiently well satis- 

 fied at pressures up to 10,000 pounds per square inch in water. 



