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Elements of Fluid Mechanics (Air and Water)

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The Aero- and Hydromechanics of Keel Yachts

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Abstract

This chapter describes basic elements and phenomena of fluid mechanics for both air and water, that are underlying the more complex mechanisms of the flows of air and water about the sails, hull, and appendages. After distinguishing different types of forces, the conservation laws of fluid dynamics and their consequences for the scaling laws of these different types of forces are discussed. This is followed by a description of the properties of high-Reynolds-number flows about lifting surfaces and non-lifting bodies. The chapter concludes with a description of unsteady, periodic flow phenomena and the main properties of water surface waves.

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Notes

  1. 1.

    We will see later, in Sect. 6.5, that an exception is formed by the wave-making resistance, which consists of pressure drag.

  2. 2.

    As already mentioned and as we will see later (Sect. 5.8), both water and air at low speeds can be considered as incompressible for all practical purposes.

  3. 3.

    Shown is the friction drag according to Eq. (5.11.9a).

  4. 4.

    This is known as Stokes’ theorem (1854).

  5. 5.

    In mathematical terms this can be written as, where V is the velocity and ds the length of an elementary contour line segment. See also p. 152.

  6. 6.

    The radian is the basic, dimensionless measure of angle. The 360° contained by a full circle are equal to 2 radians.

  7. 7.

    See Eqs. (5.10.1) and (5.10.2) in Sect. 5.10 for the definition of the lift and drag coefficients.

  8. 8.

    Note that only the starboard halves of the lifting surfaces are shown in Fig. 5.15.7.

  9. 9.

    In this figure span, area and aspect ratio are those of the exposed wing/fin.

  10. 10.

    Here we consider the moment with respect to an axis in the span-wise direction of the fin.

  11. 11.

    The phenomenon is named after the fluid dynamicist Theodore von Kármán, who was the first to describe its mechanism (1911).

  12. 12.

    For a sailing yacht this would, for example, be a keel or a sail oscillating in yaw, roll, or pitch.

  13. 13.

    A diagram of this kind is known as a histogram.

  14. 14.

    Named after the British scientist William Froude, mentioned earlier, in Chap. 1.

  15. 15.

    The indication is a very rough one because waves of significant height are no longer sinusoidal.

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  1. Uithoorn, The Netherlands

    J. W. Slooff

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Slooff, J. (2015). Elements of Fluid Mechanics (Air and Water). In: The Aero- and Hydromechanics of Keel Yachts. Springer, Cham. https://doi.org/10.1007/978-3-319-13275-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-13275-4_5

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