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Area rule for integral quantities

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Abstract

In hydrodynamics and aerodynamics there is an “area rule” for nearly axisymmetric bodies. It states that the drag [1–3], the coefficient of heat transfer and the ablation [4], and also the wake parameters [5] of a three-dimensional body are equal to the analogous quantities for an axisymmetric body which has the same distribution of the cross sectional area along the axis. In some cases, the area rule holds for bodies which depart strongly from axial symmetry [6]. It is shown in the present paper that equality also holds for other integral quantities and not only in hydrodynamic problems.

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Literature cited

  1. M. N. Kogan, “Drag of bodies which are nearly bodies of revolution,” Inzh. Zh.,1, No. 3 (1961).

  2. V. M. Dvoretskii, M. Ya. Ivanov, B. A. Konyaev, and A. N. Kraiko, “On the “equivalence” rule for flows of an ideal gas,” Prikl. Mat. Mekh.,38, No. 8 (1974).

  3. V. V. Lunev, Hypersonic Aerodynamics [in Russian], Mashinostroenie, Moscow (1975).

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  4. É. Z. Apshtein and N. N. Pilyugin, “Area rule for the coefficient of heat transfer of three-dimensional ablating bodies in the case of heat fluxes which depend locally on the angle of the surface,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2 (1979).

  5. N. N. Pilyugin, S. G. Tikhomirov, and S. Yu. Chernyavskii, “Area rule for the wake of a three-dimensional body,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gasa, No. 3 (1980).

  6. K. Oswatitsch, “The area rule,” Appl. Mech. Rev.,10, No. 12 (1957).

  7. N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydrodynamics, Part 1, New York (1964).

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Authors and Affiliations

  1. Moscow

    É. Z. Apshtein & N. G. Kolotilova

Authors
  1. É. Z. Apshtein
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  2. N. G. Kolotilova
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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–159, July–August, 1981.

We thank Yu. B. Lifshits for helpful comments.

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Apshtein, É.Z., Kolotilova, N.G. Area rule for integral quantities. Fluid Dyn 16, 621–623 (1981). https://doi.org/10.1007/BF01094612

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  • DOI: https://doi.org/10.1007/BF01094612

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