Volume 2, Issue 4
The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane

L. H. Wiryanto & H. B. Supriyanto

East Asian J. Appl. Math., 2 (2012), pp. 342-352.

Published online: 2018-02

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  • 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 → ∞.

  • Keywords

Borda's mouthpiece free-surface flow boundary integral equation contraction coefficient

  • AMS Subject Headings

65E05 76B07 76M15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-342, author = {L. H. Wiryanto and H. B. Supriyanto}, title = {The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {4}, pages = {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 → ∞.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240912.141112a}, url = {http://global-sci.org/intro/article_detail/eajam/10881.html} }
TY - JOUR T1 - The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane AU - L. H. Wiryanto & H. B. Supriyanto JO - East Asian Journal on Applied Mathematics VL - 4 SP - 342 EP - 352 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.240912.141112a UR - https://global-sci.org/intro/article_detail/eajam/10881.html KW - Borda's mouthpiece KW - free-surface flow KW - boundary integral equation KW - contraction coefficient AB -

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 → ∞.

L. H. Wiryanto & H. B. Supriyanto. (1970). The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane. East Asian Journal on Applied Mathematics. 2 (4). 342-352. doi:10.4208/eajam.240912.141112a
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