Applying Science and Applied Science: What’s the Difference?

Abstract

Prandtl’s work on the boundary layer theory is an interesting example for illustrating several important issues in philosophy of science such as the relation between theories and models and whether it is possible to distinguish, in a principled way, between pure and applied science. In what follows I discuss several proposals by the symposium participants regarding the interpretation of Prandtl’s work and whether it should be characterized as an instance of applied science. My own interpretation of this example (1999) emphasised the degree of autonomy embedded in Prandtl’s boundary layer model and the way it became integrated in the larger theoretical context of hydrodynamics. In addition to extending that discussion here I also claim that the characterization of applied science which formed the basis for the symposium does not enable us to successfully distinguish applied science from the general practice of ‘applying’ basic scientific knowledge in a variety of contexts.

Notes

[1] In fact, Heisenberg said of Prandtl that he could see the solutions of the differential equations without solving them.

[2] Interestingly, the discussion of similarity relations appears in volume 2, which deals with ‘applied’ issues, while the Navier–Stokes equations are discussed in volume 1 under the heading of ‘fundamental theory’.

[3] While it is certainly true that Prandtl would have made use of knowledge regarding the Reynolds number and frictional forces in his development of the boundary layer theory, it also seems clear that he would not have arrived at the results he did simply on the basis of this knowledge. Without the demonstration of the formation of vortices in his tank, which suggested the division of the fluid into two regions, the mathematical model of the boundary layer would not have emerged in the way that it did. Nothing in the theoretical context of the problem pointed the way toward the solution Prandtl so ingeniously arrived at. Not only is this a case of supplying a solvable boundary layer (BL) equation, but one also needed to determine where specific BL, NS, and E equations apply. This requires classifying different types of flows such as those close to the leading edge, inviscid flow behind the shock, and so on.

[4] Hence, Heidelberger’s remark that ‘If the water tunnel had not served as the source for the phenomenological model but only as confirmation after the development of the mathematical model. … the model. … could not claim any autonomy over its kingdom’ (Heidelberger 2006) is somewhat misleading as a statement of my position.

[5] Although Heidelberger is right that one cannot ‘read off’ the notion of a boundary layer from observing flows in the tunnel, since the first experiments of Reynolds (in 1883) advances in fluid mechanics have involved the continual development of new techniques for visualizing flows. What the observations did reveal is that the fluid can be divided into two regions, a crucial aspect of the boundary layer concept. And, as Sterrett has pointed out, experiments by Froude on ship models had already revealed a skin phenomenon that would later be identified as the boundary layer.

Additional information

Notes on contributors

Margaret Morrison

Margaret Morrison is at University of Toronto, Canada.