The Air as an Ideal Fluid:. Classical Hydrodynamics and the. Foundations of Aerodynamics

The following investigations proceed on the assumption that the fluid with which we deal may be treated as practically continuous and homogeneous in structure; i. e. we assume that the properties of the smallest portions into which we can conceive them to be divided are the same as those of the substance in bulk.

Horace lamb, Treatise on the Mathematical Theory of the Motion of Fluids (1879)1

Let me now prepare the ground for an account of the theory of lift and drag. The disputes over the correct analysis of lift and drag provide the central topic of this book. It was here that the scientists and engineers who addressed the new problems of aerodynamics called upon the highly mathematical techniques of what used to be called, simply, “hydrodynamics.” The modern label, which better captures the true generality of the subject, is “fluid dynam­ics.” Fluid dynamics provided the intellectual resources that were common to both the British and German work on lift and drag, although the stance toward that common heritage was often very different in the two cases. It is vital to have a secure sense of what the two groups of experts were disagree­ing about. The present chapter is a description of this common heritage and these shared resources. It is meant to provide background and orientation. In it I do my best to explain the basic concepts in simple terms, though this hardly does justice to the ideas and techniques that are mentioned. I sketch some of the initial, mathematical steps that went into their construction in order to convey something of the style and feel of the work. At the end of the chapter, I summarize the main points in nonmathematical terms.

Two members of the British Advisory Committee for Aeronautics—Lord Rayleigh and Sir George Greenhill—made important contributions to the field of hydrodynamics in the 1870s and 1880s. The numerous references to papers and results by Rayleigh and Greenhill in the standard textbooks of hydrodynamics of that time, for example, Lamb’s Hydrodynamics, attest to their prominence in the field.2 Rayleigh had arrived at some classical re­sults, which are described later in this chapter, and Greenhill had written

the authoritative article on hydrodynamics in the eleventh edition of the Encyclopaedia Britannica. Significantly the encyclopedia had two lengthy and detailed entries that dealt with fluid flow. One was the article titled “Hydro­mechanics” written by Greenhill; the other article was titled “Hydraulics” and was written by a distinguished engineer.3 The former presentation was filled with mathematics, while the latter was filled with descriptions and dia­grams of turbine machinery. The reason it was felt necessary to recognize this division of labor in drawing up the encyclopedia is relevant to my story and will become clear in what follows.

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