54 40 



As the edge advances, the particle velocity of the liquid In a di- 

 rection normal to the plate changes impulsively by 



Az = 



(l - U 1551 



PK-Prl. c2\2 



PC \ U 



where p^ is the pressure in the cavltated region, assumed uniform; see Equa- 

 tion [^^^] in the Appendix. Or, if U is Infinite, as in the instantaneous 

 occurrence of cavitation over a finite area, 



4i=^i^ [56] 



pc 



as In one-dimensional motion. If Vh ~ Vcf or if 1/ = c, Az = 0. Otherwise 

 Ak 4 0, since the liquid cannot penetrate the plate; this agrees with the 

 fact that pj ^ Pj. 



The analogous formula for a closing-edge is 



^ = h^ t57] 



tan 9 



where z, and Zp are normal velocities of liquid surface and plate Just ahead 

 of the edge In the cavltated area, and B is the angle at which the edge meets 

 the plate; see Equation [152] In the Appendix, and Figure 22. Thus U^ c on- 

 ly if 2, - Zp ^ c tan 6, As an exceptional case, it appears that the liquid 

 surface might roll onto the surface like a rug being rolled onto the floor, 

 with Zi = Zj, and d •= at the edge of contact. If z, > z^, the pressure In 

 the liquid adjacent to the plate rises impulsively, as the edge passes, from 

 Pc to Pc + Ap where 



Ap = pc(i,-ip){l- -^p [58] 



or, if [/ = «>, as where closure of cavitation occurs simultaneously over a 

 certain area, 



Ap = pc\^Zi - Zpj [59] 



See Equation [151] in the Appendix. Equation [59] is familiar In one- 

 dimensional water-hammer theory. 



Before and after the passage of the edge, each element of the liq- 

 uid surface will follow one of the differential equations already written 

 down. In the cavltated region this will be Equation [24] or 



p rid^z\ dS 



2 



'^m..^ -''•*''-'' !«°i 



