Spatially Varied Open-Channel Flow with Increasing Discharge Equation
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 3
Abstract
Flow visualization techniques and velocity measurements of jets in crossflow prove that the jet follows a distinct trajectory as if immiscible with the cross stream. Such observations reveal similarities between open channels receiving lateral inflow and vegetated flows. In the latter, the vegetation effect is accounted for as an increase in resistance, represented by a drag force. Using a similar approach, a new equation accounting for drag is developed for spatially varied flow (SVF) with increasing discharge. Experimental water surface profiles (WSP) from a number of studies with different arrangements of SVF were used to validate the performance of the proposed equation. A sensitivity analysis revealed that for the data considered the influence of nonuniform velocity distributions was minimal thus momentum correction factor, was assumed equal to unity. The Blasius equation was used to estimate friction slope. WSPs estimated from the proposed equation were a closer match to measurements than the general equation for different channel bottom slopes and lateral inflow rates. The analogous results imply that the proposed equation is generic for any conditions of SVF with increasing discharge.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors recognize the assistance provided by Mr. Adel Amidi in conducting part of the experiments used in this paper.
References
Andreopoulos, J., and Rodi, W. (1984). “Experimental investigation of jets in a crossflow.” J. Fluid Mech., 138(-1), 93–127.
Avery, S. T., and Novak, P. (1978). “Oxygen transfer at hydraulic structures.” J. Hydraul. Div., 104(11), 1521–40.
Baptist, M. J., et al. (2007). “On inducing equations for vegetation resistance.” J. Hydraul. Res., 45(4), 435–450.
Beecham, S., Khiadani, M. H., and Kandasamy, J. (2005). “Friction factors for spatially varied flow with increasing discharge.” J. Hydraul. Eng., 792–799.
Chadwick, A., Morfett, J., and Borthwick, M. (2004). Hydraulics in civil and environmental engineering, 4th Ed., Spon Press, London.
Chakraborty, S. (2015). “Flow characteristics of a transverse water jet into an unconfined water channel.” ⟨http://ro.ecu.edu.au/theses/1751⟩.
Cheng, N. (2013). “Calculation of drag coefficient for arrays of emergent circular cylinders with pseudofluid model.” J. Hydraul. Eng., 602–611.
Chow, V. T. (1969). “Spatially varied flow equations.” Water Resour. Res., 5(5), 1124–1128.
Demuren, A. O. (1994). “Modeling jets in cross flow.” Chapter 17, Encyclopedia of fluid mechanics, N. P. Cheremisinoff, ed., Vol. 2, Gulf Publishing Company, Houston, 1986.
Diez, F. J., Torregrosa, M. M., and Pothos, S. (2011). “A comparison between round turbulent jets and particle-laden jets in crossflow by using time-resolved stereoscopic particle image velocimetry.” J. Fluids Eng., 133(9), .
Gill, A. M. (2010). “Perturbation solution of spatially varied flow in open channels.” J. Hydraul. Res., 15(4), 337–350.
Gutmark, E. J., Ibrahim, I. M., and Murugappan, S. (2011). “Dynamics of single and twin circular jets in crossflow.” Exp. Fluids, 50(3), 653–663.
Hager, W. H., and Bremen, R. (1990). “Flow features in side-channel spill-ways.” 22nd Convegno di Idraulica e Costruzioni Idrauliche, Vol. 4, Cosenza, Italy, 91–105.
Hager, W. H., and Pfister, M. (2011). “Historical development of side-channel spillway in hydraulic engineering.” Proc., 34th World Congress of the Int. Association for Hydro-Environment Research and Engineering, Engineers Australia, Barton, Australia, 3906–3913.
Hinds, J. (1926). “Side channel spillways: Hydraulic theory, economic factors, and experimental determination of losses.” Trans. Am. Soc. Civ. Eng., 89(1), 881–939.
Huthoff, F., Augustijn, D., and Hulscher, S. J. M. H. (2007). “Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation.” Water Resour. Res., 43(6), 1–10.
Isaac, K. M., and Jakubowski, A. K. (1985). “Experimental study of the interaction of multiple jets with a cross flow.” AIAA J., 23(11), 1679–1683.
Isaac, K. M., and Schetz, J. A. (1982). “‘Analysis of multiple jets in a cross-flow.” J. Fluids Eng., 104(4), 489–92.
Kamotani, Y., and Greber, I. (1974). “Experiments on confined turbulent jets in cross flow.”, Cleveland.
Khiadani, M., Beecham, S., and Kandasamy, J. (2012). “Turbulence measurements in spatially-varied flow with increasing discharge.” J. Hydraul. Res., 50(4), 418–426.
Khiadani, M. H., Kandasamy, J., and Beecham, S. (2005). “Boundary shear stress in spatially varied flow with increasing discharge.” J. Hydraul. Eng., 705–714.
Khiadani, M. H., Kandasamy, J., and Beecham, S. (2007). “Velocity distributions in spatially varied flow with increasing discharge.” J. Hydraul. Eng., 721–735.
Kothyari, U. C., Hashimoto, H., and Hayashi, K. (2009). “Effect of tall vegetation on sediment transport by channel flows.” J. Hydraul. Res., 47(6), 700–710.
Kouchakzadeh, S., and Mohammad-Abadi, A. R. (2002). “Spatially varied flow in non-prismatic channels. I: Dynamic equation.” Irrig. Drain., 51(1), 41–50.
Kouchakzadeh, S., Vatankhah, A. R., and Townsend, R. D. (2001). “A modified perturbation solution procedure for spatially-varied flows.” Can. Water Resour. J., 26(3), 399–416.
Li, R., and Shen, H. W. (1973). “Effect of tall vegetations on flow and sediment.” J. Hydraul. Div., 99(5), 793–814.
Lucas, J., Lutz, N., Lais, A., Hager, W. H., and Boes, R. M. (2015). “Side-channel flow: Physical model studies.” J. Hydraul. Eng., .
MATLAB [Computer software]. MathWorks, Natick, MA.
Muppidi, S., and Mahesh, K. (2005). “Study of trajectories of jets in crossflow using direct numerical simulations.” J. Fluid Mech., 530, 81–100.
Petryk, S. (1972). Drag on cylinders in open channel flow, Univ. Microfilms.
Pratte, B. D., and Baines, W. D. (1967). “Profiles of the round turbulent jet in a cross flow.” J. Hydraul. Div., 93(6), 53–64.
Rajaratnam, N. (1976). Turbulent jets, Elsevier, New York.
Speerli, J., and Hager, W. H. (2000). “Air-water flow in bottom outlets.” Can. J. Civ. Eng., 27(3), 454–462.
Stone, B. M., and Shen, H. T. (2002). “Hydraulic resistance of flow in channels with cylindrical roughness.” J. Hydraul. Eng., 500–506.
Subramanya, K. (1982). Flow in open channels, McGraw-Hill, New Delhi, India.
Tanino, Y., and Nepf, H. M. (2008). “Laboratory investigation of mean drag in a random array of rigid, emergent cylinders.” J. Hydraul. Eng., 34–41.
Vadeleine, A., and Vaidelys, V. (2012). “Air bubbles and water droplets entrainment and removal in turbulent flows.” Mechanika, 18(1), 56–62.
Vargas-Luna, A., Crosato, A., and Uijttewaal, W. S. J. (2015). “Effects of vegetation on flow and sediment transport: Comparative analyses and validation of predicting models.” Earth Surf. Processes Landforms, 40(2), 157–176.
Wilkerson, G. V. (2007). “Flow through trapezoidal and rectangular channels with rigid cylinders.” J. Hydraul. Eng., 521–533.
Wu, P., Kirkendall, K. A., and Fuller, R. P. (1997). “Breakup processes of liquid jets in subsonic crossflows.” J. Propul. Power, 13(1), 64–73.
Yen, B. C., and Wenzel, H. G. (1970). “Dynamic equations for steady spatially varied flow.” J. Hydraul. Div., 96(3), 801–814.
Yen, B. C., Wenzel, H. G., and Yoon, Y. N. (1972). “Resistance coefficients for steady spatially varied flow.” J. Hydraul. Div., 98(8), 1395–410.
Yu, D., Ali, M. S., and Lee, J. H. W. (2006). “Multiple tandem jets in cross-flow.” J. Hydraul. Eng., 971–982.
Ziegler, H., and Wooler, P. T. (1971). “Multiple jets exhausting into a crossflow.” J. Aircraft, 8(6), 414–420.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 3 • March 2017
Copyright
©2016 American Society of Civil Engineers.
History
Received: Apr 26, 2016
Accepted: Aug 9, 2016
Published online: Oct 19, 2016
Published in print: Mar 1, 2017
Discussion open until: Mar 19, 2017
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.