Johnsson and Stfntvedt 



d 2 = (x f - X q ) 2 + (y f - y Q ) 2 + (z f - Z q ) 2 (4) 



where 



x ,y ,z = coordinate of volume source 



o o o 



~ (q) = ~~~ [ (x f " X o ) Sin * ~ (y f ■ y o ) C ° S ^ ] = e (5) 



where 



n = RPS 



<j> = angular position of volume source 



U ~ 2 7r rn/cos /3 

 x 



where /3 = geometric pitch angle 



We assume that the cavity formation at time t displaces a 

 volume of liquid bound by the helicoidal blade surface and the plane 

 P parallel to the shaft (Z -axis) (Figure 41). 



In accordance with Figure 42 the thickness distribution in 

 the x-direction : 



r( x, r, t ) = r( r, t ) . f(x) (6) 



Admittingly, the proposed distribution has been designed to 

 suit mathematical interpretation of the extremely complex "shape" 

 of the vapour/liquid formation. 



The chordwise extent of the volume at any time when perio- 

 dicity may be assumed a valid assumption : 



x = x + z_. x sin 



torn 

 m=l 



a 2 



4 7r n mt 



V -ft 



t o 



+ e (?) 



m 



where 



= phase angle 



n = RPS 



616 



