yAx) = 



^%[/fK^]-fI' 



di 



tan 



■/3ES".- WW 



The first term on the right of Equation [14b] represents an elliptical shape of length 

 I and fineness ratio 



2(1 + 1) 



The contribution of the second term is largest just behind the cavitating body, and becomes 

 small at the rear of the cavity. For small cavitation numbers the after shape of the cavity is 

 very nearly of elliptical shape. The cavity then has the shape shown schematically in 

 Figure 3. 



Contribution from Second Integral 



Ellipse of Length I and 

 Maximum Thickness 



or I 



20*f) 



Cavity Shape 



Figure 3 - Cavity Shape for Small Cavitation Numbers 



The position of maximum cavity width is obtained at the position where the cavity 

 source strength is zero. From Equation [13a] 



c7f/,,7r fO dy. V l-t 



dt 



2U, J_e dt y_^(^_t) 

 where yfjfj is the maximum cavity width. Using Equation [16] it may then be shown that 



2 -^<-< 2 



and 



y(x) ^ 



al 



For small values of a, it may be shown, using Equation [16], that 



TTa}_cdt Y-7 



[14c] 



[14d] 



[16a] 



