Fluid Mechanics and Kinematic Similarity

Kinematic similarity is concerned with the motion of phases within a system and the forces inducing that motion. For example, in the formation of boundary layers during flow past flat plates and during forced convection in regularly shaped channels, there are usually three dominant forces pressure, inertia, and viscous forces. If corresponding points in two different-sized cells show at corresponding times identical ratios of fluid velocity, the two units are said to be kinematically similar and heat and mass transfer coefficients will bear a simple relation in the two cells. It can be shown by means of dimensional analysis that for a closed system under forced convection the equation of motion for a fluid reduces to a function of Re, the Reynolds number, which we have met in Chapter 2. To preserve kinematic similarity under those circumstances, Reynolds numbers in the two cells must be identical. 

As we shall see in Section 5.3.5, entrance and exit effects cause irregularities in the fluid flow and care has to be taken in predicting heat and mass transfer rates on scale-up. 

Overall chemical similarity is achieved not merely by the application of a few dimensionless numbers, but results from careful application of rigorous mathematical models. 

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