On a new method for calculating the potential flow past a body of revolution

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A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian ... continued below

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Kaplan, Carl January 1, 1943.

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This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and one other and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 27 times . More information about this report can be viewed below.

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  • Main Title: On a new method for calculating the potential flow past a body of revolution
  • Series Title: NACA Technical Reports

Description

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

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  • : 93R21121
  • URL: http://hdl.handle.net/2060/19930091831 External Link
  • Report No.: NACA-TR-752
  • Center for AeroSpace Information Number: 19930091831
  • Archival Resource Key: ark:/67531/metadc60016

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National Advisory Committee for Aeronautics Collection

The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA).

Technical Report Archive and Image Library

This selection of materials from the Technical Report Archive and Image Library (TRAIL) includes hard-to-find reports published by various government agencies. The technical publications contain reports, images, and technical descriptions of research performed for U.S. government agencies. Topics range from mining, desalination, and radiation to broader physics, biology, and chemistry studies. Some reports include maps, foldouts, blueprints, and other oversize materials.

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Creation Date

  • January 1, 1943

Added to The UNT Digital Library

  • Nov. 17, 2011, 5:13 p.m.

Description Last Updated

  • Feb. 3, 2017, 4:37 p.m.

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Kaplan, Carl. On a new method for calculating the potential flow past a body of revolution, report, January 1, 1943; (digital.library.unt.edu/ark:/67531/metadc60016/: accessed October 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.