RTD for Combinations of Noninteracting Regions

If an impulse input is used at the beginning of a combination of independent regions, such that the RTD of any one region is unaffected by the presence of the others, the combination RTD is given by the convolution formula, Eq. 12.2-12  

Changing the order of integration, and defining the new variable 6 - fi, leads to 

NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS 605 

This can be put into dimensionless form for consideration of the width of the overall RTD  

By consecutively repeating these manipulations for multiple region convolutions, the moments would be 

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