44 



a function of the actual distribution. For nozzles having diffusers of small 

 angle, this coefficient would be expected to be very close to one for cavities 

 of small length since, for such cavities, the expansion from the jet diameter 

 to d iff user diameter is small and the motion as observed in tests is not par- 

 ticularly disturbed. As the cavitating zone increases, the ratio of diffuser 

 diameter to jet diameter at the "jump" increases, the jet oscillates, and the 

 motion becomes progressively more violent in this region, with greater nonuni- 

 formity in the velocity distribution, so that the coefficient would be ex- 

 pected to increase. 



Referring to Figure 31 , let r, be the radius of the jet (assumed 

 equal to the throat radius), r { the radius of the diffuser at the position of 



/////////// 



Figure 31 - Notation for Computation of Cavity Length in a Diffuser 



the end of the cavitating region, r 2 the radius at a reference position down- 

 stream of the "jump", u. the velocity of the jet, u t the average velocity just 

 downstream of the "jump", U 2 the velocity at the positions of r 2 , p the pres- 

 sure across the jet (which may be taken as vapor pressure), p and P 2 the 

 pressures at the positions of v x and r 2 , respectively, I the length of the 

 cavity (this length is defined more precisely later when discussing the exper- 

 iments), and k the momentum-correction coefficient. 



The momentum and continuity relations across the jump are 



and 



kpr t 2 Ul 2 - pr t 2 u. 2 = -r l 2 (p l -p y ) 



r t Uj = r | -u | 



[22a; 



[22b; 



Eliminating r. and r, 

 jj i 



Pv = 



■pUj (kUj - u ,) 



[23] 



