Eddy size distribution in a turbulent flow

It is possible to apply the same consideration to the eddy size distribution in a turbulent flow because eddies in a turbulent flow are produced by the impeller, shear stress, and so on, without artificiality. There is no difficulty in considering the following relationships between the wavenumber k and the diameter of eddy l in a turbulent flow  

The number and volume of the respective scale of eddies can be obtained by using Eq. (5.27), and the eddy size distribution can be shown in the following equation by assuming that the energy per unit volume of the eddy is equal irrespective of the eddies  

There are a fair number of PSD functions to express the practical PSD. However, these functions are only mathematical expressions and have no physical basis or significance. Additionally, there is a problem when the practical PSD is expressed by using different PSD functions, for example, Rosin-Rammler PSD function, normal PSD function, and log-normal PSD function. This is because it becomes difficult to correlate the values of a parameter and operation condition. Therefore, it is indispensable to clarify whether a new PSD defined by Eq. (5.18) has an advantage over the traditional PSD. 

Traditional PSD Table 5.1 (Rosin-Rammler PSD function, normal PSD function, log-normal PSD function). 

The usefulness of the newly presented PSD shown in Eq. (5.17) is examined by the Rosin-Rammler PSD function  

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