46 



Solving for £,* 



| = |/r 2 + ^r 4 - (2k - 1)(1 + <r 2 ) 



Expressed in terms of a dimensionless cavity length 



[31] 



l > = ± 



Equation [31] becomes, using [28], 



i o = -^L-^fa + Y? . (2k- d(i +^y - 1] 



Solving for k from [30] 



k -J|1 + 2r 2 £ 2 - (1 +ol)^ 



[32; 



[33: 



Experiments to check the equations were made using a nozzle with a 

 d iff user of 5° included angle (the same nozzle used in the experiments of Ref- 

 erence 37). In an actual case, there is some difficulty in defining the cavity 

 length. For this comparison, however, the length of the cavity was taken to 

 be the farthest point downstream at which the major portion of the vapor appar- 

 ently disappeared. The cavitating region in these experiments was fairly 

 stable, and the length used was of the order of 5 percent greater than what 

 appeared to be the center of the highly disturbed region. 



To check the hypothesis of 

 the variation of k, the experimental 

 values were used in Equation [33], 

 and the results are shown in Figure 

 32. It is clear from this figure 

 that the above analysis gives good 

 results for cavities of ratio l a less 

 than about 10 without any correction 

 for the mixing process (i.e., k = 1). 

 The increasing values of k with in- 

 > 5 10 15 20 25 creasing I, are as expected, and the 



Ratio of Cavity Length to Throat Radius, l ff ' 



actual values give some clue as to 

 Figure 32 - Variation of Momentum f ma itude of k for dlf . 



Correction Coefficient with & 



Cavity Length for 5° Diffuser fusers of angle near 5°. (It should 



£ 3 



1 1 



o 



*It will be noted that the solution containing the negative sign has been discarded. This was done 

 to eliminate the possibility of imaginary solutions, and, as will be seen, appears to be correct. Nev- 

 ertheless, the existence of the alternative solution raises the interesting question of two possible 

 configurations in an actual case. Whether this can occur, and thus account for the longitudinal oscilla- 

 tions sometimes observed, would require a detailed stability analysis. 



