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On the Resistance to the Rotation of a Disc Immersed in a Fluid

Published online by Cambridge University Press:  24 October 2008

S. Goldstein
S. Goldstein*
Affiliation:
St John's College
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Extract

The motion of a fluid due to the rotation of an immersed plane disc about an axis perpendicular to itself is turbulent if ωa2/ν is greater than about 105, where ω is the angular velocity of the disc, a its radius, and ν the kinematic viscosity of the fluid. The torque opposing the rotation, due to the surface friction of the fluid, was calculated originally by Kármán, both when the motion of the fluid is steady and when it is turbulent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 2 , April 1935 , pp. 232 - 241
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

† Zeitschrift für angew. Math. u. Mech. 1 (1921), 244–50.Google Scholar

‡ Proc. Camb. Phil. Soc. 30 (1934), 365–75.CrossRefGoogle Scholar

† Kármán gives 0·462 instead of 0·526 in the formula for δ, but this appears to be a misprint: the constant in the formula for the moment agrees with that given below.

‡ Kármán, , Journal of the Aeronautical Sciences, 1 (1934), 1–20;CrossRefGoogle Scholar Prandtl, , Zeitschrift des Vereines Deutscher Ingenieure, 77 (1933), 105–13.Google Scholar These are collected accounts of some of the latest researches, and contain further references to original papers.

† See Kempf, , Vorträge aus dem Gebiete der Hydro- und Aerodynamik, Innsbruck (1922) (published in Berlin, 1924), pp. 168–70Google Scholar, where Schmidt's results are also given.