p = Local static pressure 



p = Static pressure of stream at infinity 



p^ = Cavity pressure 



p = Pressure on the body 



a = Cavitation number 



1 r, 2 



2*^ ~ 



p = Constant fluid density 



^ = Perturbation velocity potential such that v = V(f) 



Vc = Vc^^^ 



■ c X = 



Figure 1 - Schematic Cavitation Flow 



Cavity 



x=l 



On the solid boundary the streamline slope is specified 



dyp / ^ _ v(x,yo) _ V (x, Vq ) r _ uix,yg)-u(x,y^) ^ M^^Vq) -u(x,y,) Y] HI 

 dx ^'"' U^ + uix;^)- f/, L f/o ^ U, '} 



Where the velocity U^ has been used as a nondimensionalizing factor because theoretical and 

 experimental results indicate that the velocities on the cavitating body are nearly proportional 

 to U ^. This fact has led to the statement of the "principle of stability of the pressure coeffi- 

 cient." (Reference 1, page 66). 



On the cavity wall the static pressure is specified as constant = p^ or, equivalently, 

 the cavitation number a is specified. From Bernoulli's equation it follows that 



= ^^ +o(^r= 2(^-i)+o(^) 



u. 



U^ 



[2] 



From the Cauchy-Riemann equations it may be inferred that the perturbation velocity 

 changes very slowly in space if streamline slopes and curvatures are small, so that some justi- 

 fication exists for satisfying the linearized boundary conditions on the a;-axis instead of on the 



