Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-14T10:27:16.842Z Has data issue: false hasContentIssue false
  • English
  • Français

The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane

Published online by Cambridge University Press:  28 May 2015

L. H. Wiryanto  and
H. B. Supriyanto
L. H. Wiryanto*
Affiliation:
Department of Mathematics, Bandung Institute of Technology, Jalan Ganesha 10 Bandung, Indonesia
H. B. Supriyanto
Affiliation:
Faculty of Art and Design, Bandung Institute of Technology, Jalan Ganesha 10 Bandung, Indonesia
*
Corresponding author. Email: leo@math.itb.acid
Get access

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

65E0576B0776M15Borda's mouthpiecefree-surface flowboundary integral equationcontraction coefficient
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 4 , November 2012 , pp. 342 - 352
Copyright
Copyright © Global-Science Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Milne-Thomson, L. M., Theoretical Hydrodynamics, Dover Publication, 1996, pp. 307–309.Google Scholar
[2]Wiryanto, L. H., Wijaya, J. and Supriyanto, H. B., Free surface flow under a sluice gate from deep water, Bull. Malay. Math. Sci. Soc., 34 (2011), pp. 601–609.Google Scholar
[3]Wiryanto, L. H., A jet emerging from a slit at the corner of quarter plane, J. KSIAM, 13(4) (2009), pp. 237–245.Google Scholar
[4]Frangmeier, D. D. and Strelkoff, T. S., Solution for gravity flow under a sluice gate, ASCE J. Engng. Mech. Div., 94 (1968), pp. 153–176.Google Scholar
[5]Lorock, B. E., Gravity-affected flow from planer sluice gate, ASCE J. Engng. Mech. Div., 96 (1969), pp. 1211–1226.Google Scholar
[6]Chung, Y. K., Solution of flow under sluice gates, ASCE J. Engng. Mech. Div., 98 (1972), pp. 121–140.Google Scholar
[7]J. Asavanant, and Vanden-Broeck, J.-M., Nonlinear free surface flows emerging from vessels and flows under a sluice gate, J. Austral. Math. Soc., 38 (1996), pp. 63–86.Google Scholar
[8]Vanden-Broeck, J.-M., Numerical calculations of the free-surface flow under a sluice gate, J. Fluid Mech. 330 (1996), pp. 339–347.Google Scholar
[9]Binder, B. J. and Vanden-Broeck, J.-M., Free surface flows past surfboards and sluice gates, Eur. J. Appl. Maths., 16 (2005), pp. 601–619.Google Scholar
[10]Binder, B. J. and Vanden-Broeck, J.-M., The effect of disturbances on the flows under a sluice gate and past an inclined plate, J. Fluid Mech., 576 (2007), pp. 475–490.CrossRefGoogle Scholar
[11]Vanden-Broeck, J.-M. and Tuck, E. O., Flow near the interaction of a free surface with a vertical wall, SIAM J. Appl. Math., 54 (1994), pp. 1–33.Google Scholar
[12]Dagan, G. and Tulin, M. P., Two-dimensional free-surface gravity flow past blunt bodies, J. Fluid Mech., 51 (1972), pp. 529–543.Google Scholar
[13]Mc Cue, S. W. and Forbes, L. K., Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity, J. Fluid Mech., 461 (2002), pp. 387–407.CrossRefGoogle Scholar
[14]Wiryanto, L. H., Free surface flow under a sluice gate of an inclined wall from deep water, AMZIAM J. (CTAC 2010), 52 (2011), pp. C792–C805.Google Scholar
[15]Wiryanto, L. H. and Tuck, E. O., A back-turning jet formed by a uniform shallow stream hitting a vertical wall, in Differential Equations: Theory, Numerics and Applications, Van Groesen, E. and Soewono, E. (Eds.), Kluwer Academic Press, Netherlands, 1997, pp. 371–380.CrossRefGoogle Scholar
[16]Wiryanto, L. H. and Tuck, E. O., An open-channel flow meeting a barrier and forming one or two jets, J. Austral. Math. Soc. Vol. 41 (2000), pp. 458–472.Google Scholar
[17]Wiryanto, L. H., Small Froude number solutions of flow caused by a line source, J. Indones. Math. Soc., 6 (2000), pp. 1–6.Google Scholar
[18]Hocking, G. C. and Forbes, L. K., A note on theflow induced by a line sink beneath a free surface, J. Austral. Math. Soc. B, 32 (1991), pp. 251–260.Google Scholar
[19]Hocking, G. C. and Forbes, L. K., Subcritical free-surface flow caused by a line source in afluid of finite depth, J. Eng. Math., 26 (1992), pp. 455–466.Google Scholar
[20]Wiryanto, L. H., Zero gravity of a jet emerging from a slit, J. Indones. Math. Soc., 12 (2006), pp. 89–98.Google Scholar