# Ludwig Prandtl (1875-1953)

Ludwig Prandtl was professor of Applied Mechanics at the University of Göttingen. His skills in both theory and technical applications were almost unrivalled. His contributions are staggering. He was the man who rationalized the field, built the most important fluid dynamics laboratory at the beginning of the 20th century and created a world reknown school at Göttingen.

His boundary layer theory (1904) has been one of the most influential findings in the history of fluid mechanics. Its consequences were far reaching, and they are still being explored, in one way or another.

The basic idea that the fluid viscosity is confined within thin layers close to solid walls brought substantial simplification to the momentum equations, whose solution was attemped in closed form by several of his students (Blasius, Pohlhausen, von Karman, Hiementz).

The de-coupling of the equations is still one of the most powerful approximations we have in fluid dynamics. Direct consequences of the theory were the introduction of the Reynolds number in fluid mechnanics, the effects of the skin friction of fluid flow, many heat transfer problems, the solution of the d’Alembert paradox.

Prandtl’s other contributions include: the introduction of the Reynolds number in fluid mechanics, airfoils and wing theory (including theories of aerodynamic interference, wing-fuselage, wing-propeller, biplane, etc); fundamental studies in the wind tunnel, high speed aerodynamics (correction formula for subsonic compressible flows), theory of turbulence. His name is linked to the following:

• Prandtl number (heat transfer problems)
• Prandtl-Glauert compressibility correction
• Prandtl’s boundary layer equation
• Prandtl’s lifting line theory
• Prandtl’s law of friction for smooth pipes
• Prandtl-Meyer expansion fans (supersonic flow)
• Prandtl’s Mixing Length Concept (theory of turbulence)

During his lifetime career at Göttingen Prandtl molded the likes of von Kármán, Munk, Schlichting, Bets, Busemann, Pohlhausen, Tollmien. Some of his own associates ended in America (most notably Munk, von Karman, Busemann), but he never moved away from Göttingen.

His work under the Nazi regime became increasingly difficult, and although not a collaborationist, he did work on projects of military interest (particularly with the Krupp industries). At the end of the war he was interviewed by the Allies on his activities. Particularly odd was the fact the he was questioned by his own former student and friend Theodore von Karman.

#### Selected References

Here is a list of publications available in the English language. Most of Prandtl’s work has been translated from original German publications. The NACA references should be the easiest to find.

• Prandtl L. Foundamentals of Hydro and Aeromechanics , Dover Publ., Inc. New York, 1957

• Prandtl L. Applied Hydro and Aeromechanics , Dover Publ., Inc. New York, 1957.

• Prandtl L. Göttingen Wind Tunnel for Testing Aircraft Models, NACA TN 66, 1920.

• Prandtl L. Induced Drag of Multiplanes, NACA TN-182, 1924, Technische Berichte, Volume III, No. 7, pp. 309-315.

• Prandtl L. Mutual Influence of Wings and Propeller, NACA TN 74, 1921.

• Prandtl L. Report on Investigation of Developed Turbulence, NACA TM 1231, 1949.

• Prandtl L. Theory of Lifting Surfaces, NACA TN 9, 1920.

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

• Prandtl L. Effects of Varying the Relative Vertical Position of Wing and Fuselage, NACA TN 75, 1921.

• Prandtl L. Some Remarks Concerning Soaring Flight, NACA TM-47, 1921.

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