# Ludwig Prandtl

2005

Niall McMahon

2005 - 100 Years Since Publication of *Über Flüssigkeitsbewegung bei sehr kleiner Reibung*.

A short collection of biographical and technical links.

Born: 1875

Died: 1953

### Introduction

Ludwig Prandtl was a physicist who, just over a hundred years ago, revolutionised the study of fluid mechanics. It was in 1904 that he delivered a lecture to the Third International Congress of Mathematicians in Heidelberg. He that reconciled the theoretical and empirical aspects of fluid mechanics with the concept of a boundary layer. The paper was entitled "Über Flüssigkeitsbewegung bei sehr kleiner Reibung" or "On the motion of fluids of very small viscosity". An English translation of this paper is freely available from the National Advisory Committee for Aeronautics Technical Report Server as NACA Technical Memorandum 452 (*Note*).

### Biography

*See also Prandtl's Scientific Course of Life* and *Ludwig Prandtl*.

Prandtl was born in Freising, a town about 30km north-east of Munich. He studied mechanical engineering at the Technische Universität München.

#### Extracts from Online Sources

"For his PhD dissertation he sumbitted his work on buckling of beams in 1899...On the strong recommendation of his former mentor Föppl he was asked by Felix Klein in 1904 to organize a new department of mechanics to the University of Göttingen. He accepted and became a professor of Applied Mechanics there in 1904 with a career that lasted the until his retirement in 1953."
*Boundary Layer Theory*, Robinson Computer Lab and the Department of Mechanical Engineering, Ohio State University.

"He was director of technical physics at the University of Göttingen (1904--53), and director of the Kaiser Wilhelm Institute for fluid mechanics from 1925." *Ludwig Prandtl*, Biography.com.

"At Göttingen, Prandtl gave theoretical aerodynamics its modern form. His work helped Fokker to shape the airplanes that gave Allied armies such headaches over the trenches in WW-I. Prandtl's students were still shaping fluid mechanics when I was a student. One of them, Theodore von Karman, worked at Cal Tech. And there he wrote about Prandtl in his own autobiography."
*Boundary Layers*, John H. Lienhard, University of Houston.

"Prandtl gave modern wing theory its practical mathematical form. He is considered the father of aerodynamic theory, for there is hardly a part of it to which he did not contribute, and many of its fundamental concepts originated in his fertile mind."
*Ludwig Prandtl*, The Allstar Network, Florida International University.

"Prandtl's contribution of the boundary layer was to realize that we can view the flow as being divided into two regions. The bulk of the flow can be regarded as a potential flow essentially the same as that studied by the mathematicians. Only in a small region near the body do viscous effects dominate." Mechanical Engineering at Bradley University. *Note:* the original link is broken.

"His discovery in 1904 of the Boundary Layer which adjoins the surface of a body moving in a fluid led to an understanding of skin friction drag and of the way in which streamlining reduces the drag of airplane wings and other moving bodies. His work on wing theory, published in 1918 - 1919, followed that of F.W. Lanchester (1902-1907), but was carried out independently and elucidated the flow over airplane wings of finite span. Prandtl's work and decisive advances in boundary layer and wing theories became the basic material of aeronautics. He also made important contributions to the theories of supersonic flow and of turbulence, and contributed much to the development of wind tunnels and other aerodynamic equipment. In addition, he devised the soap-film analogy for the torsion of non-circular sections and wrote on the theory of plasticity and of meteorology."
*History of Heat Transfer*, the Henry Samueli School of Engineering and Applied Science at UCLA.

In 1922 Prandtl, along with Richard Von Mises, founded die Gesellschaft für Angewandte Mathematik und Mechanik (the International Association of Applied Mathematics and Mechanics), GAMM.

"The GAMM was founded in 1922 von Ludwig Prandtl and Richard von Mises. The society promotes scientific development in all areas of applied mathematics and mechanics. As legacy of the founding father the society cultivates international cooperation in applied mathematics as well in all areas of mechanics and physics relating to the foundations of the enginiering sciences. Historically, the society has played an essential role in the advancement of hydro- and aerodynamics, solid state mechanics as well as numerical and instrumental mathematics. GAMM is a society with a distinctly international organisation, currently more then 2500 members comprising."
*About the GAMM*, Gesellschaft für Angewandte Mathematik und Mechanik.

Perhaps a little apocryphal, "Prandtl's life, he said, was marked by overtones of naïveté. When Prandtl was thirty-four, he decided it was time to marry, so he went to his old professor (*Föppl*) to ask his daughter's hand in marriage. But Prandtl didn't say which daughter. The canny professor and his wife had a hurried caucus and prudently decided it should be the older one. That was fine. The marriage was a long and happy one."
*Boundary Layers*, John H. Lienhard, University of Houston.

Ludwig Prandtl died on August 15th 1953.

### References

#### Über Flüssigkeitsbewegung bei sehr kleiner Reibung

[English Translation] *On the motion of fluids of very small viscosity*. National Advisory Committee for Aeronautics Technical Report Server, NACA Technical Memorandum 452.

[Original Publication] Prandtl, L. (1904).*Über Flüssigkeitsbewegung bei sehr kleiner Reibung*. Verh. III. Intern. Math. Kongr., Heidelberg, 1904, S. 484-491, Teubner, Leipzig, 1905 (*Source:* *Laminar Boundary-Layer Theory:
a 20th Century Paradox?* by Stephen J. Cowley).

[German Reprint] Prandtl, Ludwig, 1904, *Über Flüssigkeitsbewegung bei sehr kleiner Reibung*. In *Ludwig Prandtl, Gesammelte Abhandlungen zur angewandten Mechanik, Hydro- und Aerodynamik (Collected Works)*, ed. by W. Tollmien, H. Schlichting and H. Goertler, volume II. Springer, Berlin 1961 (*Sources:* Leon van Dommelen and Hermann Schlichting's Boundary-Layer Theory).

#### Papers Authored by Prandtl and Translated for NACA

*See also Selection of publications by Ludwig Prandtl*.

##### NACA Technical Notes

*A selection from the National Advisory Committee for Aeronautics (NACA) online archive*.

L. Prandtl, *Göttingen Wind Tunnel for testing aircraft models*, NACA TN 66, Nov 1920.

L. Prandtl, *Theory of lifting surfaces*, NACA TN 9, Jul 1920.

L. Prandtl, *Theory of lifting surfaces*, NACA TN 10, Aug 1920.

L. Prandtl, *Mutual influence of wings and propeller*, NACA TN 74, Dec 1921

William Knight, L. Prandtl, T. von Karman G. Costanzi W. Margoulis R. Verduzio R. Katzmayr E. B. Wolff A. F. Zahm, *Standardization and aerodynamics*, NACA TN-134, March, 1923

L. Prandtl, *Induced drag of multiplanes*, NACA TN-182
February, 1924. (Technische Berichte,. Volume III, No. 7, pp. 309-315).

##### NACA Technical Memoranda

L. Prandtl, *Recent progress in the theory of air flow as applied to aeronautics*, NACA TM-55, 1922.

L. Prandtl, *Some remarks concerning soaring flight*, NACA TM-47, October 1921. *Extract* : "...the axiom, 'no soaring without a wind with an upward trend' can probably be accepted as correct".

L. Prandtl, * Report on investigation of developed turbulence*, NACA TM-1231, 1949.

##### NACA Reports

L. Prandtl, *Applications of modern hydrodynamics to aeronautics*, NACA Report 116, 1923.

#### Other Papers Related to Prandtl's Work in the NACA Archives

Hermann Schlicting's book *Boundary Layer Theory* is renowned as the definitive analysis of Prandtl's work. These online lecture notes for NACA cover much of the material contained in that book.

Schlichting, H. *Lecture series "Boundary layer theory" - part I : Laminar flows
*, NACA Technical Memorandum 1217, 1949.

Schlichting, H. *Lecture series "Boundary layer theory" - part II : Turbulent flows
*, NACA Technical Memorandum 1218, 1949.

Mangler, W *General solution of Prandtl's boundary-layer equation*, NACA Technical Memorandum 1278, 1950.

*Please Note:* there are many more papers in the NACA archives relating to the many topics inspired by Prandtl's work.

#### Some Texts

*Ludwig Prandtl: Gesammelte Abhandlungen zur angewandten Mechanik, Hydro- und Aerodynamik* (Collected Works), ed. by W. Tollmien, H. Schlichting and H. Goertler, volume II. Springer, Berlin 1961.

Fundamentals of Hydro and Aeromechanics, L. Prandtl, O.G. Tietjens. Dover Publications, 1957.

Applied Hydro and Aeromechanics, L. Prandtl, O.G. Tietjens. Dover Publications, December 1934.

Boundary-Layer Theory, Hermann Schlichting et al, Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, November 1999.

#### Online Resources

*Ludwig Prandtl Exhibition* : An Exhibition on the Occasion of his 125th Birthday. *Note :* this is a high-quality site with a complete list of Prandtl's life and publications.

*Ludwig Prandtl* : Father of Modern Fluid Mechanics. *Note :* a part of fluidmech.net.

*Ludwig Prandtl* : from Wikipedia.

#### Eclectic Links

*Ludwig Prandtl (1875-1953) experimenting with his hand-made water tunnel, in Hannover, 1904*. An interesting photograph, hosted by Engineering & Computational Sciences at Old Dominion University.

### Acknowledgements

- All those whose sites I've linked to.
- Professor Mark Cramer of Virginia Tech for his useful comments, for his amazingly comprehensive Fluid Mechanics website and for linking to this site.
- Professor Robert McLachlan of Massey University in New Zealand for providing the reference to NACA Technical Memorandum 452, the English translation of Prandtl's most important paper and for motivating me to update the site.