User:Camstr32/Ludwig prandtl

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* My additions are in bold*

Later Years

In 1901 Prandtl became a professor of fluid mechanics at the technical school in Hannover, later the Technical University Hannover and then the University of Hannover. It was here that he developed many of his most important theories. On August 8, 1904, he delivered a groundbreaking paper, Über Flüssigkeitsbewegung bei sehr kleiner Reibung (On the Motion of Fluids in Very Little Friction), at the Third International Mathematics Congress in Heidelberg. In this paper, he described the boundary layer and its importance for drag and streamlining. The paper also described flow separation as a result of the boundary layer, clearly explaining the concept of stall for the first time. Several of his students made attempts at closed-form solutions, but failed, and in the end the approximation contained in his original paper remains in widespread use.

The effect of the paper was so great that Prandtl would succeed Hans Lorenz as director of the Institute for Technical Physics at the University of Göttingen later in the year. Over the next decades he developed it into a powerhouse of aerodynamics, leading the world until the end of World War II. In 1925 the university spun off his research arm to create the Kaiser Wilhelm Institute for Flow Research (now the Max Planck Institute for Dynamics and Self-Organization).

'''Due to the complexity of Prandtl's boundary layer ideas in his 1904 paper, the spread of the concept was initially slow. Most people failed to adopt the idea due to lack of understanding. It wasn't until 1908 when two of his students at Gottingen, Blasius and Boltze, released their dissertations on the boundary layer. Blasius's dissertation explained what happened with the boundary layer when a flat plate comes in parallel contact with a uniform stream. Boltze's research was similar but applied Prandtl's theory to spherical shapes instead of flat objects. Prandtl expanded the ideas in his student's dissertations to include a thermal boundary layer associated with heat transfer.'''

'''There would be three more papers from Gottingen researchers regarding the boundary layer released by 1914. Due to similar reasons to Prandtl's 1904 paper, these 7 papers on the boundary layer would be slow to spread outside of Gottingen. Partially due to World War I, there would be a lack of papers published regarding the boundary layer until another of Prandtl's students, Theodore Von Karman, published a paper in 1921 on the momentum integral equation across the boundary layer.'''

Following earlier leads by Frederick Lanchester from 1902–1907, Prandtl worked with Albert Betz and Max Munk on the problem of a useful mathematical tool for examining lift from "real world" wings. The results were published in 1918–1919, known as the Lanchester–Prandtl wing theory. He also made specific additions to study cambered airfoils, like those on World War I aircraft, and published a simplified thin-airfoil theory for these designs. This work led to the realization that on any wing of finite length, wing-tip effects became very important to the overall performance and characterization of the wing Considerable work was included on the nature of induced drag and wingtip vortices, which had previously been ignored. Prandtl showed that an elliptical spanwise lift distribution the most efficient, giving the minimum induced drag for the given span. These tools enabled aircraft designers to make meaningful theoretical studies of their aircraft before they were built.

Prandtl later extended his theory to describe a bell-like lift distribution, obtained by washing out the wing tips until negative lift was obtained, which gave the minimum induced drag for any given aircraft weight, also suggesting that adverse yaw forces could be countered solely by wing tip aerodynamics, but this new theory was largely ignored. In the 21st century the American engineer Al Bowers has confirmed the idea, calling his experimental wing the Prandtl-D.

Prandtl and his student Theodor Meyer developed the first theories of supersonic shock waves and flow in 1908. The Prandtl–Meyer expansion fans allowed for the construction of supersonic wind tunnels. He had little time to work on the problem further until the 1920s, when he worked with Adolf Busemann and created a method for designing a supersonic nozzle in 1929. Today, all supersonic wind tunnels and rocket nozzles are designed using the same method. A full development of supersonics would have to wait for the work of Theodore von Kármán, a student of Prandtl at Göttingen.

'''Prandtl developed the concept of "circulation" which proved to be particularly important for the hydrodynamics of ship propellers. He did most of the experimental work at his lab in Göttingen from 1910-1918 with his assistant Albert Betz and student Max Munk. Most of his discoveries related to circulation would be kept secret from the western world until after World War I.'''

In 1922 Prandtl, together with Richard von Mises, founded the GAMM (the International Association of Applied Mathematics and Mechanics). and was its chairman from 1922 until 1933. Until 1945 he also worked closely with the RLM.

Other work examined the problem of compressibility at high subsonic speeds, known as the Prandtl–Glauert correction. This became very useful during World War II as aircraft began approaching supersonic speeds for the first time. He also worked on meteorology, plasticity and structural mechanics. He also made significant contributions to the field of tribology.

'''After discovering the boundary layer, Prandtl and his students looked for more applications of the boundary layer. One of his most notable students, Theodore Von Karman, moved from Germany to Cal Tech where he continued research on the boundary layer. One of the most largest challenges was finding the fluid skin friction coefficient (Cf) which would relate drag to surface area and Reynold's number (Re). Prandtl in Germany and Von Karman at Cal Tech each raced to find the coefficient first. Around 1930, the race ended in a draw as both men concluded that the inverse square of skin friction was related to the logarithmic value of the product of Reynold's number and skin friction as seen below where k and C are constants.'''

$$\frac{k}{\sqrt{c_{f}}} = \log_{10}{(Re * C_{f})} + C $$

'''Prandtl and Von Karman's work on the boundary was influential and adopted by aerodynamic and hydrodynamic experts around the world after WWI. In May 1932, the international Conference on Hydromechanical Problems of Ship Propulsion was held in Hamburg. Günther Kempf showcased a number of experiments at the conference which confirmed many of the theoretical discoveries of Von Karman and Prandtl.'''

Prandtl and the Third Reich

'''As a member of the German Physical Society (DPG), Prandtl assisted Carl Ramsauer in drafting the DPG Petition in 1941. The DPG Petition would be published in 1942 and argued that physics in Germany was falling behind that of the United States due to rejection of "Jewish Physics" (relativity and quantum theory) from German physicists. After publication of the DPG Petition, the belief of "German Physics" superiority deteriorated to allow for German students to study these new fields in school. '''