Flow configuration and residence time distribution

It can be seen in Fig. 10.2 that the flow in the SCISR is in mirror symmetry with respect to the impingement plane, and also approximately in axial symmetry so it is enough to take a half volume of the SCISR, either on the right or the left side, into account in the analysis. 

It should be noted that both the process fluid and the tracer are fed at the inlet of the drawing tube and that the volume of the drawing tubes occupies about one fifth, so there must be En = 0 for r / 5. If the volumetric fraction of the plug flow region is 

Using Eq. (10.17) and the convolution integral law, the Laplace transform of each of the sub-probability density functions in Eq. (10.6) can be obtained to be 

It is noted that the right-hand side of Eq. (10.20) is just the series expansion of an exponential function. Therefore the overall residence time distribution probability density function in the SCISR is obtained to be 

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