43 



If this is the situation, the oscillations in the direction of motion can be 

 expected. On the other hand, the oscillations of the jet in the transverse 

 direction (see, e.g., Reference 8) might be associated with an underpressure 

 near the point where the jet leaves the boundary. Here, the viscous drag of 

 liquid on gas can give rise to underpressures which are sufficient to pull the 

 jet toward the conduit wall (the so-called "Coanda effect;" see for example, 

 Reference ~[k) . With a curving boundary and with the unstable conditions in 

 such vortex flows, the underpressures can be expected to change in a rather 

 random fashion around the periphery of the jet with consequent oscillations 

 of the type observed. (This effect has also been proposed to explain the fi- 

 nite angles of separation of the cavity surface from the obstacles used in the 

 TMB tests, the underpressure being assumed to be of importance only at the 

 point of separation. However, though this may be a contributing cause, the 

 conditions in a separated wake alone would give rise to this discontinuity. ) 



As pointed out in the foregoing, it is of interest for engineering 

 applications to be able to predict the position of the end of a cavitating 

 region, and thus where damage may be expected to occur. For the three- 

 dimensional cavity in an unlimited liquid, practical results are not as yet 

 available. An approximate analysis of the point of cavity termination in a 

 nozzle can, however, be carried out along the lines suggested above. Although 

 no attempt will be made to give results suitable for design, an analysis will 

 be carried out to show that the problem can be treated purely as a hydrody- 

 namic one in which the vapor phase plays no significant role in determining 

 the motion. The analysis is carried out for a nozzle with a conical d iff user 

 of small angle, and pressures are referred to positions which coincide with 

 piezometers located in a nozzle of this type available at the Taylor Model 

 Basin for tests. 



In the computations , we assume that the diameter of the jet passing 

 through the cavitating region remains constant and equal to the diameter of 

 the throat. Actually, this jet may contract or, because of the underpressure 

 effects at the throat, may expand. For the purpose of this calculation, it 

 will be sufficient to assume that, on the average, the diameter is approxi- 

 mately equal to the throat diameter. An essential difficulty in such an analy- 

 sis stems from a lack of knowledge of the velocity distribution and, hence, 

 the longitudinal momentum distribution in the region just downstream from the 

 end of the cavity. Here, the mixing of the jet with the slower moving fluid 

 produces a highly turbulent zone of nonuniform and fluctuating velocity dis- 

 tribution — the characteristics of which are but imperfectly known. Thus, if 

 the average velocity in this region is used in writing the momentum equation, 

 the term containing this velocity must be modified by a coefficient which is 



