The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane
Year: 2012
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 342–352
Abstract
Borda's mouthpiece consists of a long straight tube projecting into a large vessel, where fluid enters the tube in a free surface flow that tends to become uniform far downstream in the tube. A two-dimensional approximation to this flow under gravity in the upper part of the tube leads to an evaluation of the contraction coefficient, the ratio of the constant depth of the uniform flow to the width of the tube. The analysis also applies to flow under gravity past a sluice gate, if the semi-infinite wall above the channel is rotated to the vertical. The contraction coefficient depends upon the Froude number F, and is generally less than the zero gravity value of 1/2 that is approached as $F → ∞$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240912.141112a
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 342–352
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Borda's mouthpiece free-surface flow boundary integral equation contraction coefficient.