Johnson and Hsieh 



^D '^b , ^ ,„ ,, ° ■ 63 , _ 4 , 1 • 3f 



24 



1 + 0.197 H. + 2.6 X 10-^ H. (6) 



Equation (6) is an empirical equation which fits the experimental data very well 

 (3). 



By nondimensionalizing the velocity components and linear dimensions by 

 the free stream velocity u and the body size h respectively, the equations gov- 

 erning the bubble trajectory become 



3 ^^v 



(u-u,)--^;^- (7a) 



^^"^b)-"-r^. (7b) 



dr r2 R^ 24 ' ^' 2 dy ' 





equals Reynolds number of the bubble, and 



equals Reynolds number of the body. Equations (7) determine the bubble 

 trajectory. 



Therefore, the bubble trajectories are seen to depend on the body size h, 

 the free stream velocity u, the vapor cavitation number a^, the bubble radius 

 Rq, and the density and viscosity of the fluid. 



APPLICATION TO A TWO-DIMENSIONAL HALF BODY 

 IN AN INFINITE FLUID 



Equations for Bubble Trajectory 



Let h be the semithickness of the two-dimensional half body in an infinite 

 fluid; then the body can be expressed by 



X = -y cot Try , (8) 



where x and y are normalized by h . The nose of the half body is located at 

 X - -1/T7. The nondimensional velocity components and pressure gradients in 



168 



