Models for the Natural Vortex Length

The position of the vortex end is difficult to model. The first and, by far, the best known relation for the natural vortex length i.e. the length from the lip of the vortex finder to the position of the end of the vortex) was proposed by Alexander (1949)  

Zhongli et al. (1991) also proposed an expression for involving the same groups, but the variation in L with both of the groups D /D and D /ab was qualitatively opposite to that in Eq. (9.2.3). 

The authors own experience with vortex behavior has resulted in the following observations  

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