Dimensional Analysis and Dynamic Scaling

What if we wanted to operate the unit at 60°C We would have to return to the lab and remeasure the data at 60°C. We had no means of extrapolating the data to different conditions. As you will learn later, thermodynamics provides the tools needed to extrapolate equilibrium data. But lacking a knowledge of thermodynamics, is there a way to extrapolate More generally, how does one extrapolate in systems too complex to yield an analytical solution How does one design a large unit too complex to be analyzed mathematically Should one build the unit and hope for the best That approach would cost too much in time and money. Our government and the military use this approach because they have a lot of time and money. You will not have this luxury. 

Instead, we use a third means of modeling We will study a small working example and extrapolate the process to industrial size. Or, as was stated eloquently by Leo Baekeland (1863-1944), inventor of Bakelite, the first synthetic plastic. 

Commit your blunders on a small scale and make your profits on a large scale. 

But is it possible to extrapolate the behavior of a model to predict the behavior of a large unit One of the earliest to recognize this connection was Leonardo da Vinci (-1500) (Zlokamik 1991 5)  

Vitruvius says that small models are of no avail for ascertaining the effects of large 

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Dimensional analysis and dynamic scaling allow one to predict, for example, the performance of a full-sized system based on the performance of a small prototype of the system. One constructs a model of the system, tests the model under various operating conditions, and then applies dynamic scaling to predict how the actual system would behave, with the operating conditions scaled as well. 

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