Significance of Averaging Coefficients in Open‐Channel Flow Equations
Publication: Journal of Hydraulic Engineering
Volume 120, Issue 2
Abstract
The Saint‐Venant equations commonly applied to solving unsteady open‐channel flow problems consist of a continuity equation and a momentum equation. In deriving the momentum equation, the pressure distribution is assumed to be hydrostatic, and the effect of nonuniform cross‐sectional velocity distribution is assumed to be small. Thus, the momentum and pressure correct coefficients , , and are usually assumed to be equal to unity in applications. The effects of these assumptions on the solution of the flow equations have not been explored. The purpose of this paper is to investigate the significance of these assumptions by means of numerically solving the nearly exact unsteady open‐channel flow equations with systematically changing values of the coefficients. The results confirm that the effects of these coefficients are relatively small when the flow is nearly steady and uniform, and their effects increase with flow unsteadiness. These coefficients have a greater impact on the solution for velocity than for depth. The results also indicate more effects for convectively decelerating flow than for accelerating flow, especially when there is significant downstream backwater effect.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Amein, M. (1968). “An implicit method for numerical flood routing.” Water Resour. Res., 4(4), 719–726.
2.
Boussinesq, J. (1877). “Essai sur la théorie des eau courantes [on the theory of flowing waters].” Mémoires présentés par divers savants à l'Académie des Sciences, Paris, France, 23, 261–529 (in French).
3.
Chen, C.‐L. (1992). “Momentum and energy coefficients based on power‐law velocity profile.” J. Hydr. Engrg., ASCE, 118(11), 1571–1584.
4.
Chiu, C.‐L., and Murray, D. W. (1992). “Variation of velocity distribution along nonuniform open‐channel flow.” J. Hydr. Engrg., ASCE, 118(7), 989–1001.
5.
Chow, V. T. (1959). Open‐channel hydraulics. McGraw‐Hill Book Co., New York, N.Y.
6.
Coriolis, G. (1836). “Sur 'éstablissement de la formule qui donne la figure des remous, et ur a correction qu'on doit y introduire pour tenir compte des ifférences de vitesse dans les divers points d'une même ection d'un courant [on the backwater‐curve formula and the orrections to be introduced to account for the difference of the elocities t various points in the same cross section].” Mémoire No. 268, Annales des Ponts et haussées, Paris, France, Ser. 1(11), 314–335 (in French).
7.
Doodge, J. C. I., and Napiorkowski, J. J. (1987). “The effect of the downstream boundary conditions in the linearized St. Venant equations.” Quarterly J. of Mech. and Appl. Math., 40(May), 245–256.
8.
Jaeger, C. (1968). “Boundary shear in open‐channel flow, energy and total momentum.” Water Power, 20(9), 366–367.
9.
Li, D., and Hager, W. H. (1991). “Correction coefficients for uniform channel flow.” Can. J. Civ. Engrg., 18(1), 156–158.
10.
O'Brien, M. P., and Johnson, J. W. (1934). “Velocity‐head correction for hydraulic flow.” Engrg. News‐Record, 113, 214–216.
11.
Preissmann, A. (1961). “Propagation des intumescences dans les canaux et riviéres (propagation of translatory waves in channels and rivers).” Proc., 1st Congress of the French Association for Computation (AFCAL), Grenoble, France, 422–433 (in French).
12.
Price, R. K. (1974). “Comparison of four numerical methods for flood routing.” J. Hydr. Div., ASCE, 100(7), 879–899.
13.
Price, R. K. (1985). “Flood routing.” Developments in hydraulic engineering—3, P. Novak, ed., Elsevier Applied Science Publishers, New York, N.Y., 129–173.
14.
Rehbock, T. (1922). “Die Bestimmung der Lage der Energielinie bei fliessenden Gewässern mit Hilfe des Geschwindigkeitshöhen‐Ausgleichwertes [Determination of the position of energy line in flowing water using the velocity correction coefficient].” Der Bauingenieur, Berlin, Germany, 3(15), 435–455 (in German).
15.
Samuels, P. G. (1989). “Backwater lengths in rivers.” Proc., Instn. Civ. Engrs., London, England, Part 2(87), 571–582.
16.
Smith, M. W. (1991). “Sediment transport in shallow flow on an impervious surface,” MS thesis, University of Virginia, Charlottesville, Va.
17.
Streeter, V. L. (1942). “The kinetic energy and momentum correction factors for pipes and for open channels of great width.” Civ. Engrg., 12(4), 212–213.
18.
Wormleaton, P. R., and Karmegam, M. (1984). “Parameter optimization in flood routing.” J. Hydr. Engrg., ASCE, 110(12), 1799–1814.
19.
Yen, B. C. (1973). “Open‐channel flow equations revisited.” Engrg. Mech. Div., ASCE, 99(5), 979–1009.
20.
Yen, B. C. (1979). “Chapter 13: unsteady flow mathematical techniques.” Modeling of river, H. W. Shen, ed., Wiley‐Interscience, New York, N.Y., 13.1–13.33.
21.
Yen, B. C. (1991). “Hydraulic resistance in open channels.” Channel resistance: centennial of Manning's formula, B. C. Yen, ed., Water Resources Publications, Highlands Ranch, Colo.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 120 • Issue 2 • February 1994
Pages: 169 - 190
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Mar 22, 1993
Published online: Feb 1, 1994
Published in print: Feb 1994
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.