THEORY OF OPTIMUM SHAPES IN FREE-SURFACE FLOWS. PART 2. MINIMUM DRAG PROFILES IN INFINITE CAVITY FLOWS

The problem considered is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process yields, by analogy with the classical Euler differential equation, a pair of coupled nonlinear singular integral equations. It is shown that the optimal plate shapes must have blunt noses. The problem is next formulated by a method using finite Fourier series expansions, and optimal shapes are obtained for various ratios of plate arc-length to plate width. (Author)

  • Supplemental Notes:
    • Revision of report dated 8 September 1971. See also Part 1, MRIS #044627. Sponsored in part by National Science Foundation. Also available in Journal of Fluid Mechanics, V55, Pt 3, pp 457-472, 1972.
  • Corporate Authors:

    California Institute of Technology

    Division of Engineering and Applied Science
    1200 East California Boulevard
    Pasadena, CA  USA  91125
  • Authors:
    • Whitney, A K
  • Publication Date: 1972-7-6

Media Info

  • Pagination: 18 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00044628
  • Record Type: Publication
  • Source Agency: National Technical Information Service
  • Report/Paper Numbers: E156.4
  • Contract Numbers: Nonr-220(5)
  • Files: TRIS
  • Created Date: Sep 4 1973 12:00AM