Agitated vessels dimensional analysis

Power consumption by agitation is a function of physical properties, operating condition, and vessel and impeller geometry. Dimensional analysis provides the following relationship ... 

Mathematical simulation of heat, mass, or momentum transfer in agitated vessels is often untenable, due to the three-dimensional components of the material and energy balances, and the large number of material and process variables. In such cases, dimensional analyses are the preferred method of correlation. Numerous references are available for a review of dimensional analysis in engineering applications [30-32],... 

Hiraoka, S., I. Yamada and K. Mizoguchi, Two dimensional model analysis of flow behaviour of highly viscous non-Newtonian fluid in agitated vessel with paddle impeller , J. Chem. Eng. Japan 12, 1, 56-62 (1979). 

We must now determine the heat transfer coefficients for the heating medium and for the stirred fluid. Again, we use dimensional analysis to establish correlations for determining these heat transfer coefficients. First, consider the stirred, that is, agitated, fluid inside the mixer. The geometric variables are vessel diameter D [L] and agitator blade length Lb [L], The material variables for the heated fluid inside the vessel are heat capacity Cp [L T 0 ], heat conductivity k [LMT 0 ], convective heat transfer coefficient h [MT 0 ],... 

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