23 

 and that one of the boundary layer equations is 



*u«-jj£ [20] 



where k is the curvature of the surface and y is the direction normal to the 

 surface. 42 That the same result is obtained here is seen directly from 

 Equation [20]. 



Although satisfactory theoretical formulations of the value of the 

 pressure gradient across turbulent boundary layers are not available, meas- 

 urements made by Lyon 43 in the turbulent layer of streamline bodies give the 

 desired results. In regions of negative pressure, it was found that ^£>0 

 and in regions of positive pressure, -^-<0. Thus, here, again, for unsepar- 

 ated turbulent boundary layers, cavitation will occur at the body and not out- 

 side the boundary layer. This result must, of course, be qualified in view 

 of Equation [10], since the maximum turbulent velocity fluctuations occur at 

 a small distance from the wall or body. 34 



NOTE ON THE PROPAGATION OP CAVITATED REGIONS 



So far, an attempt has been made to give an accurate qualitative 

 description of the process involved in the inception of cavitation. Nothing 

 has been said as to the propagation of a cavitated region. It is not in- 

 tended to discuss this problem in detail. However, an analysis of this prob- 

 lem has been made by Kennard 44 and the results are summarized here. Assuming 

 irrotational motion of an ideal liquid, Kennard assumed that the pressure 

 falls to a given rupture -pressure and then rises immediately to a fixed cavity 

 pressure. He found that "the boundary of the cavitated region either advances 

 as a breaking-front, moving with supersonic velocity, or remains stationary 

 as a free surface, or recedes toward the cavitated region as a closing-front." 

 The various conditions for these motions and the pertinent formulas are given 

 in Reference 38. 



DYNAMICS OF TRANSIENT CAVITATION BUBBLES 



THE MOTION OP SMALL TRANSIENT CAVITIES 



Cavitation nuclei which grow beyond the critical size, reach a max- 

 imum, collapse and then undergo oscillations while maintaining their identity 

 as small, individual cavities before disappearing, have been characterized 

 herein as "transient" cavities. Studies of the motion of such cavities have 

 been made by various investigators. Mueller 45 published motion picture frames 

 in 1928 showing cavitation on a hydrofoil. These photographs showed clearly 

 the growth and collapse of individual cavities, but evidently no oscillations 



