The nappe profile of a free overfall

Enrico Marchi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 2, page 131-140
  • ISSN: 1120-6330

Abstract

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The phenomenon of the free overfall at the sharp drop of a channel bed has been deeply investigated experimentally since the pioneering work of Rouse (1933). Its behaviour is well known at least in the usual case of a wide rectangular channel. However, no complete theoretical solution has yet been obtained. Assuming the steady flow to be two-dimensional, irrotational and frictionless, an analytical solution for the flow field is obtained accounting for the presence of two free boundaries. By applying the conservation laws we then derive an equation for the lower nappe profile which is found to fit the observed data satisfactorily.

How to cite

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Marchi, Enrico. "The nappe profile of a free overfall." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.2 (1992): 131-140. <http://eudml.org/doc/244246>.

@article{Marchi1992,
abstract = {The phenomenon of the free overfall at the sharp drop of a channel bed has been deeply investigated experimentally since the pioneering work of Rouse (1933). Its behaviour is well known at least in the usual case of a wide rectangular channel. However, no complete theoretical solution has yet been obtained. Assuming the steady flow to be two-dimensional, irrotational and frictionless, an analytical solution for the flow field is obtained accounting for the presence of two free boundaries. By applying the conservation laws we then derive an equation for the lower nappe profile which is found to fit the observed data satisfactorily.},
author = {Marchi, Enrico},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Open-channel; Free overfall; Nappe; rectangular channel; steady flow; analytical solution; two free boundaries; conservation laws},
language = {eng},
month = {6},
number = {2},
pages = {131-140},
publisher = {Accademia Nazionale dei Lincei},
title = {The nappe profile of a free overfall},
url = {http://eudml.org/doc/244246},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Marchi, Enrico
TI - The nappe profile of a free overfall
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/6//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 2
SP - 131
EP - 140
AB - The phenomenon of the free overfall at the sharp drop of a channel bed has been deeply investigated experimentally since the pioneering work of Rouse (1933). Its behaviour is well known at least in the usual case of a wide rectangular channel. However, no complete theoretical solution has yet been obtained. Assuming the steady flow to be two-dimensional, irrotational and frictionless, an analytical solution for the flow field is obtained accounting for the presence of two free boundaries. By applying the conservation laws we then derive an equation for the lower nappe profile which is found to fit the observed data satisfactorily.
LA - eng
KW - Open-channel; Free overfall; Nappe; rectangular channel; steady flow; analytical solution; two free boundaries; conservation laws
UR - http://eudml.org/doc/244246
ER -

References

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  1. BENJAMIN, T. B. - LIGHTHILL, M. J., On Cnoidal Waves and Bores. Proc. Roy. Soc. A, vol. 224, 1954, 448-460. Zbl0055.45605MR76526
  2. D'ALPAOS, L., Effetti scala nei moti di efflusso fortemente accelerati. XX Conv. Idr. e Costr. Idr., Padova1986. 
  3. FRASER, W. B., Gravity-deflected Jets in Two-Dimensional Flow. M.E. Thesis, University of Canterburg, N.Z., 1961 (see [5]). 
  4. HAY, N. - MARKLAND, E., The Determination of the Discharge over Weirs by the Electrolytic Tank. Proc. I.C.E. col.10, London1958, 59. 
  5. HENDERSON, F. M., Open Channel Flow. The Macmillan Co., New York1966. Zbl0193.55002
  6. NAUDASCHER, E., Scale Effects in Gate Model Test. Symposium on Scale Effects in Modelling Hydraulic Structures, A.I.R.H., Technishe Akademie Esslingen1984. 
  7. ROUSE, H., Verteilung der hydraulischen Energie bei einem Lotrechten Absturz. Verlag von R. Oldenbourg, Munchen und Berlin1933. JFM59.1465.01
  8. ROUSE, H., Discharge Characteristics of the Free Overfall. Civil Engineering, vol. 6, 4, 1936, 257-260. 
  9. SOUTHWELL, R. V. - VAISEY, G., Relaxation Methods Applied to Engineering Problems: XII, Fluid Motions Characterized by «free» Streamlines. Phil. Trans. Roy. Soc. A, vol. 240, 1946, 117. Zbl0063.01421MR18062JFM66.0589.02

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