Blasius: A life in research and education
W.H. Hager
Abstract
The Blasius boundary layer solution is a basic
feature of Fuid mechanics, and the ±rst application of
Prandtl’s boundary layer concept as a signi±cant issue in
engineering. This work highlights the contributions of
Blasius to hydrodynamics over a period of only six years,
which marked the initiation of boundary layer theory. His
main papers relating to aerodynamics and smooth tur-
bulent pipe Fow 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.
1
Introduction
Nineteenth-century advances in hydrodynamics were
directed mainly towards the understanding of ideal Fuid
Fow. Accordingly, successful research was directed to-
wards wave hydrodynamics. William ²roude (1810–1879)
introduced a criterion named after him, according to
which scale models involving free surface waves follow his
similarity law. Shortly afterwards, Osborne Reynolds
(1842–1912) formulated a law for viscous Fuid Fow. After
Leonhard Euler had presented equations for ideal Fuid
Fow in differential form, Navier, Saint-Venant and Stokes
generalized his equations by accounting for viscosity.
Mathematically, these relations are highly involved, how-
ever, and only special solutions such as for laminar pipe
Fow were amenable. In order to advance knowledge,
therefore, appropriate simpli±cations had to be intro-
duced.
Ludwig Prandtl (1875–1953) presented his benchmark
paper on boundary layers in 1904 (Prandtl 1904), postu-
lating that Fow around a smooth body could be subdi-
vided into two regions: (1) Close to the boundaries, Fuid
viscosity governs Fow, for which the Navier–Stokes
equations simplify to what we currently refer to as the
boundary layer equations; and (2) away from the bound-
aries, viscosity has a small effect and the Fow is inFuenced
mainly by Euler’s potential Fow 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 appli-
cation of his approach, his ±rst Ph.D. student Heinrich
Blasius was able to outline the signi±cance of the novel
formulation. The boundary layer solution for the Fat plate
at once demonstrated the power of Prandtl’s concept. The
solution was subsequently tested in a variety of Fow
con±gurations, such as in naval engineering and in aero-
dynamics, and substantial agreement was noted. Blasius
then considered problems of potential Fow theory, in a
way a step back from what he did earlier. However, his
solutions were another addition to hydrodynamics, in-
volving free surface Fow and the improvement of the Pitot
tube. Another noteworthy contribution was published in
1912 (Blasius 1912a), relating to the Blasius friction coef-
±cient for turbulent smooth pipe Fow. As the present
author was able to ±nd the daughter of Blasius, a biogra-
phy is also presented. This note, therefore, would like to