Model experiments and scale-up

In the above example a process characteristic has been developed, which represents so to speak a visiting card of the process. This often expensive and time-consuming method is however unnecessary, if a given process condition has only to be scaled-up from the model to the industrial plant (or vice versa). Take for example the above example and assuming that the Ne(Rc) characteristic in Fig. 1.36 is not known. 

Let us assume - and this is essential - that the flow condition in this case is governed solely by the Reynolds number and that the process is described by an unknown dependence Ne(Re). Then one can calculate the Re number of the industrial plant  

Let us further assume that we have a geometrically similar laboratory device of D = 0.2 m and d = 0.1 m and that the stirrer speed can be arbitrarily chosen. Which must be the stirrer speed to obtain Re = idem using water (v = 1 x 10 ra /s) as model liquid The answer is 

Under these conditions the stirrer power must be measured and the power number Ne = P/(pn d5) calculated. We find Ne = 8.0. Since for Re = idem Ne = idem applies, the power consumption Pr of the industrial stirrer can be calculated  

From Ne = 8.0 found in laboratory measurement, the power P of the blade stirrer of d = 2 m and a rotational speed of n = 10 min is calculated as follows  

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