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A theory for free outflow beneath radial gates

Published online by Cambridge University Press:  29 March 2006

Bruce E. Larock
Bruce E. Larock
Affiliation:
University of California, Davis
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Abstract

An analysis is made of the free outflow of fluid from those underflow gates known as radial or Tainter gates. Attention is focused on a correct treatment of the effects of gate curvature and of gravity on the flow. The rapidly convergent, iterative solution is based on the combined use of conformal mapping and the Riemann-Hilbert solution to a mixed boundary-value problem. A limited comparison with some experimental results shows agreement to be good.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 4 , 15 May 1970 , pp. 851 - 864
Copyright
© 1970 Cambridge University Press

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References

Babb, A., Moayeri, M. & Amorocho, J. 1966 Discharge coefficients of radial gates. University of California, Davis, Water Science and Engineering Paper 1013.Google Scholar
Benjamin, T. B. 1956 On the flow in channels when rigid obstacles are placed in the stream. J. Fluid Mech. 1, 227.Google Scholar
Cheng, H. K. & Rott, N. 1954 Generalizations of the inversion formula of thin airfoil theory. J. Rat. Mech. Anal. 3, 357.Google Scholar
Churchill, R. B. 1960 Complex Variables and Applications (2nd edn.). New York: McGraw-Hill.
Fangmeier, D. D. & Strelkoff, T. S. 1968 Solution for gravity flow under a sluice gate. J. Engng Mech. Div., Am. Soc. Civ. Engrs, 94, 153.Google Scholar
Henderson, F. M. 1966 Open Channel Flow. New York: Macmillan.
Klassen, V. J. 1967 Flow from a sluice gate under gravity. J. Math. Analysis Applic. 19, 253.Google Scholar
Larock, B. E. 1969a Gravity-affected flow from planar sluice gates. J. Hydraul. Div. Am. Soc. Civ. Engrs, 95, 1211.Google Scholar
Larock, B. E. 1969b Jets from two-dimensional symmetric nozzles of arbitrary shape. J. Fluid Mech. 37, 479.Google Scholar
Larock, B. E. & Street, R. L. 1965 A Riemann-Hilbert problem for non-linear, fully cavitating flow. J. Ship Res. 9, 170.Google Scholar
Larock, B. E. & Street, R. L. 1967 A nonlinear theory for a fully cavitating hydrofoil in a transverse gravity field. J. Fluid Mech. 29, 317.Google Scholar
Metzler, D. E. 1948 A model study of Tainter-gate operation. M.S. Thesis, State University of Iowa.
Pajer, G. 1937 Über den Stromungsvorgang an einer unterstromten scharfkantigen Planschutze. Z. angew. Math. Mech. 17, 259.Google Scholar
Perry, B. 1957 Methods for calculating the effect of gravity on two-dimensional free surface flows. Ph.D. Thesis, Stanford University.
Rayleigh, Lord 1876 Notes on hydrodynamics. Phil. Mag. (5) 2, 441.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.
Southwell, R. B. & Vaisey, G. 1946 Relaxation methods applied to engineering problems. 12. Fluid motions characterized by ‘free’ streamlines. Phil. Trans. A 240, 117.Google Scholar
Toch, A. 1955 Discharge characteristics of Tainter gates. Trans. Am. Soc. Civ. Engrs, 120, 290.Google Scholar
Von Mises, R. 1917 Berechnung von Ausfluss-und Überfallzahlen. Z. Ver. dt. Ing. 61, 447, 469, 493.Google Scholar