Quimica Experimental

Experiments in Fluids 34 (2003) 566–571 DOI 10.1007/s00348-002-0582-9

Blasius: A life in research and education
W.H. Hager

566 Abstract The Blasius boundary layer solution is a basic feature of fluid mechanics, and the first application of Prandtl’s boundary layer concept as a significant issue in engineering. This work highlights the contributions of Blasius to hydrodynamics over a period ofonly six years, which marked the initiation of boundary layer theory. His main papers relating to aerodynamics and smooth turbulent pipe flow are also reviewed, and a biography puts his career into the general environment of Germany over the period of two World Wars. A complete bibliography of Blasius is provided. aries, viscosity has a small effect and the flow is influenced mainly by Euler’spotential flow theory. The solutions pertaining to these two domains are suitably matched at the interface, and this approach was the key to advancing the questions of turbulence. While Prandtl at that time presented no direct application of his approach, his first Ph.D. student Heinrich Blasius was able to outline the significance of the novel formulation. The boundary layer solution for the flat plate atonce demonstrated the power of Prandtl’s concept. The solution was subsequently tested in a variety of flow configurations, such as in naval engineering and in aerodynamics, and substantial agreement was noted. Blasius then considered problems of potential flow theory, in a way a step back from what he did earlier. However, his solutions were another addition to hydrodynamics, involving free surfaceflow and the improvement of the Pitot tube. Another noteworthy contribution was published in 1912 (Blasius 1912a), relating to the Blasius friction coefficient for turbulent smooth pipe flow. As the present author was able to find the daughter of Blasius, a biography is also presented. This note, therefore, would like to highlight a mathematical hydraulician, known by name to all those working influid mechanics, but not the history and biography of one of the founders of modern fluid mechanics (Fig. 1).

1 Introduction Nineteenth-century advances in hydrodynamics were directed mainly towards the understanding of ideal fluid flow. Accordingly, successful research was directed towards wave hydrodynamics. William Froude (1810–1879) introduced a criterion named after him, according to which scalemodels involving free surface waves follow his similarity law. Shortly afterwards, Osborne Reynolds (1842–1912) formulated a law for viscous fluid flow. After Leonhard Euler had presented equations for ideal fluid flow in differential form, Navier, Saint-Venant and Stokes generalized his equations by accounting for viscosity. Mathematically, these relations are highly involved, however, and only specialsolutions such as for laminar pipe flow were amenable. In order to advance knowledge, therefore, appropriate simplifications had to be introduced. Ludwig Prandtl (1875–1953) presented his benchmark paper on boundary layers in 1904 (Prandtl 1904), postulating that flow around a smooth body could be subdivided into two regions: (1) Close to the boundaries, fluid viscosity governs flow, for which theNavier–Stokes equations simplify to what we currently refer to as the boundary layer equations; and (2) away from the boundReceived: 15 April 2002 / Accepted: 21 October 2002 Published online: 29 March 2003 Ó Springer-Verlag 2003 W.H. Hager VAW, ETH-Zentrum, 8092 Zurich, Switzerland E-mail: hager@vaw.baug.ethz.ch I should like to acknowledge the kindness and help of Mrs. Elfriede Blasius, Hamburg,the daughter of Heinrich Blasius for help in preparing this paper.

2 Blasius’ 1907 paper ¨ Hardly had Prandtl begun research at Gottingen university when his first Ph.D. student Blasius began working on a problem that was the foundation of both Prandtl’s and Blasius’ reputation. The Blasius’ aim was to overcome the enigma of turbulence by considering the phenomenon of boundary layer flow. As...