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Blasius theorem

In fluid dynamics, Blasius theorem states that [1][2][3] the force experienced by a two-dimensional fixed body in a steady irrotational flow is given by

and the moment about the origin experienced by the body is given by

Here,

  • is the force acting on the body,
  • is the density of the fluid,
  • is the contour flush around the body,
  • is the complex potential ( is the velocity potential, is the stream function),
  • is the complex velocity ( is the velocity vector),
  • is the complex variable ( is the position vector),
  • is the real part of the complex number, and
  • is the moment about the coordinate origin acting on the body.

The first formula is sometimes called Blasius–Chaplygin formula.[4]

The theorem is named after Paul Richard Heinrich Blasius, who derived it in 1911.[5] The Kutta–Joukowski theorem directly follows from this theorem.

References

  1. ^ Lamb, H. (1993). Hydrodynamics. Cambridge university press. pp. 91
  2. ^ Milne-Thomson, L. M. (1949). Theoretical hydrodynamics (Vol. 8, No. 00). London: Macmillan.
  3. ^ Acheson, D. J. (1991). Elementary fluid dynamics.
  4. ^ Eremenko, Alexandre (2013). "Why airplanes fly, and ships sail" (PDF). Purdue University.{{cite web}}: CS1 maint: numeric names: authors list (link)
  5. ^ Blasius, H. (1911). Mitteilung zur Abhandlung über: Funktionstheoretische Methoden in der Hydrodynamik. Zeitschrift für Mathematik und Physik, 59, 43-44.
Quelle: https://en.wikipedia.org/wiki/Blasius_theorem