Abstract
The problem which is discussed in the following lines is to search for a method to calculate the resistance experienced by a fluid in turbulent motion. A definite solution has not been arrived at; a first attempt only is given.
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References
In connection with the distinction between mean motion and relative motion the reader is referred to: H. A. Lorentz, Turbulente Flüssigkeitsbewegung und Strömung durch Röhren, Abhandl. über theoretische Physik I (1907), p. 58–60.
Comp. f i. R. von Mises, Elemente der techniscben Hydromechanik I (1914) p. 57 and H. Blasius, Mitt, über Forschungsarbeiten, herausgeg. vom V. D. I., Heft 131 (1913).
Cf. F. Noether, ZS. Für angew. Math. u. Mechanik 1, p. 125, 1921.
O. Reynolds, Scientific Papers II, p. 575–577; H. A. Lorentz, l.c. p. 66–71.
Among others by Th. von Kármán at a lecture at the “Versammlung der Mathematiker und Physiker” in Jena 1921; comp. a remark in the ZS. Für angew. Math. u. Mechanik 1, p. 250, 1921.
M. Couette, Ann. de Chim. et de Phys. (6) 21, p. 457, 1890.
Th. von Kármán, ZS. Für angew. Math. u. Mechanik, l.e.
O. Reynolds, l.c. p. 570; W. Mc. F. Orr, Proc. Roy. Irish Acad. 27, p. 124–128, 1907; H. A. Lorentz, l.c. p. 48.
H. A Lorentz, l.c. p. 48–52.
Comp. a remark made by Lokentz, l.c. p. 54/55. The function defined by eq. (25) above fulfils the condition: dω/ds = 0 for s = 1 (s = r0/b).
According to Couette’s experiments turbulence sets in at R = ca. 1900.
R. von Mises, l.c. p. 63, in connection with the definition of r, given at p. 83/84. In the case of a channel of infinite depth as the one treated here, r is equal to h.
A. H. Gibson, Hydraulics and its applications (1919), p. 209 (in the formula mentioned at p. 206 is m is ½ time the quantity r introduced by von Mises; comp. Gibson, l.c. p. 194).
Comp. also L. Schiller, ZS. Für angew. Math. u. Mechanik, 3, p. 2, 1923, and others.
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Burgers, J.M. (1995). Hydrodynamics — “On the resistance experienced by a fluid in turbulent motion”. In: Nieuwstadt, F.T.M., Steketee, J.A. (eds) Selected Papers of J. M. Burgers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0195-0_1
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