23£ 



V = - V, , V .^ = - v., and in view of the differences in the choice of the 



en c ' on b ' 



positive direction for velocity, as illustrated in Figures 1 and U, 



Pc ~ Vb 



e 6 pc 



Here p^ and v^ represent pressure and particle velocity just behind the front, 

 so that p^ = p' + p" where p" is the pressure in the reflected wave; whereas 

 by the usual acoustic equations pcv^^ = p' - p" , It follows that 



P' = "2 (Po + P'^^c) 



Comparison of this equation with inequalities previously written involving p' 

 shows that the further behavior of the boundary will depend upon the subse- 

 quent course taken by the incident pressure p' . If p ' Increases as time goes 

 on, the boundary will at once start back toward the cavltated region as a 

 forced closing-front; whereas, if p' remains constant or decreases, the 

 boundary will remain stationary, constituting a free surface. 



FINITE GAPS 



Cavitation in the midst of a mass of liquid must ordinarily consist 

 of small bubbles which can be assumed, for analytical purposes, to be con- 

 tinuously distributed. There appear to be only two ways in which large 

 spaces or gaps can be formed in a liquid by hydrodynamic action not Involving 

 the motion of solids. 



Rotational motion may have the effect of lowering the pressure to 

 the breaking-point, as in an eddy, and then forming a cavity. Such motion, 

 however, is excluded in the present discussion. 



If the motion is of the irrotatlonal or potential type a gap can 

 form only if p^ < p , where a wave of tension falls upon the boundary of a 

 cavltated region already formed and causes the surface of the unbroken water 

 to withdraw. Such a gap will presumably take the form of a layer of especial- 

 ly large bubbles between the broken and unbroken water. 



When cavitation results from the impact of a wave of tension upon 

 the Interface between water and a solid, Its character will depend upon the 

 relative magnitudes of the breaking-pressure for a water-solid and for a 

 water-water surface. If the breaking-pressure between solid and water is 

 higher than that within the water itself, breaking will occur first at the 

 solid, with the formation of a gap or cavity. Otherwise continuously distri- 

 buted cavitation will form in the water, a layer of which will be left in 

 contact with the solid. What the facts are in the case of explosive pressure 

 waves Impinging upon painted or corroded steel is not yet known. 



