Research Article
Apr 1982
Schwarz-Christoffel Theory of Flow Past an Opening
Authors: Cheng-lung Chen, M.ASCE, and Ming-Yang SuAuthor Affiliations
Publication: Journal of the Engineering Mechanics Division
Volume 108, Issue 2
Abstract
The Schwarz-Christoffel transformation for a steady two-dimensional plane flow past an eccentric, normal constriction of zero thickness is formulated. The transformation formula contains two unknown complex constants and four unknown parameters (real numbers). It is found that there are five identities for the parameters and two additional equations for two additional physical parameters representing the geometry of the constriction in the channel. Except one of the identities, they are all expressed in the form of elliptic integrals of the first and third kinds; four of them are sufficient for unique solutions of the four parameters. The five identities that do not contain the physical parameters cannot be used in the method of solution alone, but the remaining two equations relating the two physical parameters to the four unknown parameters of the transformation can be reduced to a set of three simple trigonometric relationships, from which the analytical solutions of the parameters are obtained. Once the parameters are determined, the corresponding flow pattern can be readily computed from the transformation.
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Published In
Journal of the Engineering Mechanics Division
Volume 108 • Issue 2 • April 1982
Pages: 399 - 418
Copyright
© 1982 American Society of Civil Engineers.
History
Published in print: Apr 1982
Published online: Feb 3, 2021
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Affiliations
Cheng-lung Chen, M.ASCE
Hydro., U.S. Geological Survey, Gulf Coast Hydroscience Center, National Space Technology Lab., NSTL Station, Miss. 39529
Ming-Yang Su
Oceanographer, Naval Ocean Research and Development Activity, Oceanography Div., National Space Technology Lab., NSTL Station, Miss. 39529
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