Application of the Vaschy-Buckingham theorem

T able 3.3. List ofparameters, with their dimensions, involved in the settling of a spherical particle in a viscous fluid (proposal no. 1) 

A simplistic, blind analysis of the dimensions of different parameters naturally leads us to suggest the following dimensionless numbers  

Such a suggestion is hardly acceptable from the standpoint of physics governing the fall of the ball. We have merely stated that the ball is falling because it is situated in the gravitational field and because pp pf. To take this further, it is usefiil to consider, in sequence, two aspects of the phenomenon s physics  

The dynamics of the ball s fall, regarded as a solid system. 

The dynamics of the flow past the ball, which slows down its fall. 

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