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Facultad de Ingeniería 
Departamento de Ingeniería Mecánica 
Carrera: Ingeniería Civil Aeroespacial 
 
Curso: Aerodinámica 
Información adicional 
Fuente: 
Introduction to Flight, John D. Anderson, Jr. 
McGraw-Hill, ISBN 0-07-109282-X 
 
 
 
 
 
Historical Note: Prandtl and the development of the boundary layer concept 1 
 
 
HISTORICAL NOTE: PRANDTL AND THE DEVELOPMENT OF THE 
BOUNDARY LAYER CONCEPT 
 
The modern science of aerodynamics has its roots as far back as Isaac Newton, who 
devoted the entire second book of his Principia (1687) to fluid dynamics-especially to the 
formulation of "laws of resistance" (drag). He noted that drag is a function of fluid density, 
velocity, and shape of the body in motion. However, Newton was unable to formulate the 
correct equation for drag. Indeed, he derived a formula which gave the drag on an 
inclined object as proportional to the sine squared of the angle of attack. Later, Newton's 
sine-squared law was used to demonstrate the "impossibility of heavier-than-air flight" and 
served to hinder the intellectual advancement of flight in the 19th century. Ironically, the 
physical assumptions used by Newton in deriving his sine-squared law approximately 
reflect the conditions of hypersonic flight, and the newtonian law has been used since 
1950 in the design of high-Mach-number vehicles. However, Newton correctly reasoned 
the mechanism of shear stress in a fluid. In section 9 of book 2 of Principia, Newton states 
the following hypothesis: "The resistance arising from want of lubricity in the parts of a fluid 
is ... proportional to the velocity with which the parts of the fluid are separated from each 
other." This is the first statement in history of the friction law for laminar flow; it is embodied 
in Eq. (4.89), which describes a "newtonian fluid." 
 
 
 
Further attempts to understand fluid dynamic drag were made by the French 
mathematician Jean le Rond d'Alembert, who is noted for developing the calculus of 
partial differences (leading to the mathematics of partial differential equations). In 1768, 
d'Alembert applied the equations of motion for an incompressible, inviscid (frictionless) flow 
about a two-dimensional body in a moving fluid and found that no drag is obtained. He 
wrote: "I do not see then, I admit, how one can explain the resistance of fluids by the 
Información adicional – Aerodinámica 
 
 
 
 
Historical Note: Prandtl and the development of the boundary layer concept 2 
 
theory in a satisfactory manner. It seems to me on the contrary that this theory, dealt with 
and studied with profound attention gives, at least in most cases, resistance absolutely 
zero: a singular paradox which I leave to geometricians to explain." That this theoretical 
result of zero drag is truly a paradox was clearly recognized by d'Alembert, who also 
conducted experimental research on drag and who was among the first to discover that 
drag was proportional to the square of the velocity. 
 
D'Alembert's paradox arose due to the neglect of friction in the classical theory. It was not 
until a century later that the effect of friction was properly incorporated in the classical 
equations of motion by the work of M. Navier (1785-1836) and Sir George Stokes 
(1819-1903). The so-called Navier-Stokes equations stand today as the classical 
formulation of fluid dynamics. However, in general they are nonlinear equations and are 
extremely difficult to solve; indeed, only with the numerical power of modern high-speed 
digital computers are "exact" solutions of the Navier-Stokes equations finally being 
obtained for general flow fields. Also in the 19th century, the first experiments on transition 
from laminar to turbulent flow were carried out by Osborne Reynolds (1842-1912). In his 
classic paper of 1883 entitled "An Experimental Investigation of the Circumstances which 
Determine whether the Motion of Water in Parallel Channels Shall Be Direct or Sinuous, and 
of the Law of Resistance in Parallel Channels," Reynolds observed a filament of colored 
dye in a pipe flow and noted that transition from laminar to turbulent flow always 
corresponded to approximately the same value of a dimensionless number ρVD/µ where D 
was the diameter of the pipe. This was the origin of the Reynolds number. 
 
Therefore, at the beginning of the 20th century, when the Wright brothers were deeply 
involved in the development of the first successful airplane, the development of theoretical 
fluid dynamics still had not led to practical results for aerodynamic drag. It was this 
environment into which Ludwig Prandtl was born on February 4, 1875, at Freising, in 
Bavaria, Germany. Prandtl was a genius who had the talent of cutting through a maze of 
complex physical phenomena to extract the most salient points and putting them in simple 
mathematical form. Educated as a physicist, Prandtl was appointed in 1904 as professor of 
applied mechanics at Göttingen University in Germany, a post he occupied until his death 
in 1953. 
 
In the period from 1902 to 1904, Prandtl made one of the most important contributions to 
fluid dynamics. Thinking about the viscous flow over a body, he reasoned that the flow 
velocity right at the surface was zero and that if the Reynolds number was high enough, 
the influence of friction was limited to a thin layer (Prandtl first called it a transition layer) 
near the surface. Therefore, the analysis of the flow field could be divided into two distinct 
regions-one close to the surface, which included friction, and the other farther away, in 
which friction could be neglected. In one of the most important fluid dynamics papers in 
history, entitled "Über Flüssigkeitsbewegung bei sehr kleiner Reibung," Prandtl reported his 
thoughts to the Third International Mathematical Congress at Heidelberg in 1904. In this 
paper, Prandtl observed: 
 
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Historical Note: Prandtl and the development of the boundary layer concept 3 
 
A very satisfactory explanation of the physical process in the boundary layer 
(Grenzschicht) between a fluid and a solid body could be obtained by the hypothesis 
of an adhesion of the fluid to the walls, that is, by the hypothesis of a zero relative 
velocity between fluid and wall. If the viscosity is very small and the fluid path along 
the wall not too long, the fluid velocity ought to resume its normal value at a very 
short distance from the wall. In the thin transition layer however, the sharp changes of 
velocity, even with small coefficient of friction, produce marked results. 
 
In the same paper, Prandtl's theory is applied to the prediction of flow separation: 
 
In given cases, in certain points fully determined by external conditions, the fluid flow 
ought to separate from the wall. That is, there ought to be a layer of fluid which, 
having been set in rotation by the friction on the wall, insinuates itself into the free 
fluid, transforming completely the motion of the latter.... 
 
Prandtl's boundary layer hypothesis allows the Navier-Stokes equations to be reduced to a 
simpler form; by 1908, Prandtl and one of his students, H. Blasius, had solved these simpler 
boundary layer equations for laminar flow over a flat plate, yielding the equations for 
boundary layer thickness and skin friction drag given by Eqs. (4.91 ) and (4.93). Finally, 
after centuries of effort, the first rational resistance laws describing fluid dynamic drag due 
to friction had been obtained. 
 
 
 
 
 
 
Prandtl's work was a stroke of genius, and it revolutionized theoretical aerodynamics. 
However, possibly due to the language barrier, it only slowly diffused through the 
worldwide technical community. Serious work on boundary layer theory did not emerge in 
England and the United States until the 1920s. By that time, Prandtl and his students at 
Göttingen had applied it to various aerodynamic shapes and were including the effects of 
turbulence. 
 
Prandtl has been called thefather of aerodynamics, and rightly so. His contributions 
extend far beyond boundary layer theory; for example, he pioneered the development of 
wing lift and drag theory. Moreover, he was interested in more fields than just fluid 
dynamics-he made several important contributions to structural mechanics as well. 
 
Información adicional – Aerodinámica 
 
 
 
 
Historical Note: Prandtl and the development of the boundary layer concept 4 
 
As a note on Prandtl's personal life, he had the singleness of purpose which seems to drive 
many giants of humanity. However, his almost complete preoccupation with his work led to 
a somewhat naive outlook on life. Theodore von Karman, one of Prandtl's most illustrious 
students, relates that Prandtl would rather find fancy in the examination of children's toys 
than participate in social gatherings. When Prandtl was almost 40, he suddenly decided 
that it was time to get married, and he wrote to a friend for the hand of one of his two 
daughters-Prandtl did not care which one! During the 1930s and early 1940s, Prandtl had 
mixed emotions about the political problems of the day. He continued his research work at 
Göttingen under Hitler's Nazi regime but became continually confused about the course of 
events. Von Karman writes about Prandtl in his autobiography: 
 
I saw Prandtl once again for the last time right after the Nazi surrender. He was a 
sad figure. The roof of his house in Göttingen, he mourned, had been destroyed by 
an American bomb. He couldn't understand why this had been done to him! He was 
also deeply shaken by the collapse of Germany. He lived only a few years after that, 
and though he did engage in some research work in meteorology, he died, I 
believe, a broken man, still puzzled by the ways of mankind. 
 
Prandtl died in Göttingen on August 15, 1953. Of any fluid dynamicist or aerodynamicist in 
history, Prandtl came closest to deserving a Nobel Prize. Why he never received one is an 
unanswered question. However, as long as there are flight vehicles, and as long as 
students study the discipline of fluid dynamics, the name of Ludwig Prandtl will be 
enshrined for posterity.