Super cavitating Propeller Theory 



K e ^0, then the induced velocity and pressure equations (9) - (11) can be 

 expressed: 



aiid 



uJO,r*,0) = u^(r*) = u^ir*)j, + u^Cr*)^, , 

 u^(0,r*,0) = u,(r*) = u,(r*)r+ u,(r*)p^ , 



a = a(r*,0*)p + cr(v*,6*)^^ . 



(12) 

 (13) 



(14) 



It should be noted that the normality condition still applies for the loading 

 contribution to induced velocity. This can be shown easily, since 



r - r* cos ^ / I 



R~3 " Br Ir 



and 



with 



(r*-r cos i//) - FT sin i// ■. 



j-.riav ^ -I- 



R Br I R i Br I R 



CD rr\ ^CO _C0 



Thus, 



"«(r*)i 



H 



dr(r) 



dr 



y^ B I dr 



(15) 



and 



"t(''*)r = - -T ^a(r*)r • 



(16) 



Considerable simplification is also possible for the induced velocity components 

 due to the cavities since 



r* Bt I R_ 



k. 



r sin i// 

 r* R 3 R 3 



Thus, 



939 



