Basic Ideas of Scale-up

Scaling is a very important tool in science and engineering, because, in general, the physical behavior of a system is not independent from dimensions. The first 

Since two geometrically similar tanks are considered, the ratio 8 = dS2/ds equals the ratio D2/D1 of the reactor diameters, and the vortex depths are in the same ratio if Re2 = Re 1 and Fr2 = Fr. It can be shown that, at constant v, these two conditions of dynamic similarity, respectively, yield the following scale-up prescriptions  

A second example of interest in the present context refers to the scaling of thermal effects. Any object (a chemical reactor such as a living body) that produces heat at a rate proportional to its volume ( 2r a Vr) and exchanges heat with a cooling device or with the ambient at a rate proportional to its lateral surface Sl and to the temperature difference with respect to the external heat sink (i.e., Qe = USe(Tt - Ta)) can maintain the same temperature, independently of its dimensions, only if the ratio USe/Vx is kept constant. In general, this condition cannot be satisfied, since the ratio SeJ V) is inversely proportional to the characteristic linear dimension, and the 

---