Water Column Oscillation in Partially Immersed Vertical Tubes
Publication: Journal of Engineering Mechanics
Volume 145, Issue 9
Abstract
Theoretical and laboratory studies were presented for the water column oscillation in a vertical tube partially immersed in a reservoir. Three types of oscillations were studied, with the top of the tube being fully open (free oscillation), the top capped with a hose for ventilation (damped oscillation), and the top fully capped (capped oscillation). Governing equations of the oscillations were established and good estimations of the oscillatory characteristics were obtained. In the experiments, the periods of the free oscillations and the damped oscillations were close, whereas the period of the capped oscillations was shorter, which was due to the effect of the trapped air in the tube above the water column. The damped oscillation had quicker decay than the free oscillation. Due to the finite size of the reservoir used in the experiments, the recorded oscillations were the superposition of the water column movement in the vertical tube and the surface wave of the reservoir. The former dominated the oscillation at the beginning, whereas the latter became dominant in the end. By approximating the two components as sinusoidal waves, the beats in the recorded oscillations were estimated, and the results were in good agreement with the experiments.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first author thanks the support of CAPES/Brazil, which, through process BEX 5723/15-9, allowed the collaborative study with the University of Alberta. The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), and thank Mr. Perry Fedun for the construction of some of the experimental setups.
References
Camino, G. A., N. Rajaratnam, and D. Z. Zhu. 2014. “Choking conditions inside plunging flow dropshafts.” Can. J. Civ. Eng. 41 (7): 624–632. https://doi.org/10.1139/cjce-2014-0033.
Guo, J., K. Woldeyesus, J. Zhang, and X. Ju. 2017. “Time evolution of water surface oscillations in surge tanks.” J. Hydraul. Res. 55 (5): 657–667. https://doi.org/10.1080/00221686.2017.1289267.
Lorenceau, É., D. Quéré, J. Ollitrault, and C. Clanet. 2002. “Gravitational oscillations of a liquid column in a pipe.” Phys. Fluids 14 (6): 1985–1992. https://doi.org/10.1063/1.1476670.
Quéré, D., É. Raphaël, and J. Ollitrault. 1999. “Rebounds in a capillary tube.” Langmuir 15 (10): 3679–3682. https://doi.org/10.1021/la9801615.
Roberson, J. A., J. J. Cassidy, and M. H. Chaudhry. 1998. Hydraulic engineering. New York: Wiley.
Safwat, H. M. 1984. “On free liquid oscillations in irregular basins.” J. Eng. Mech. 110 (7): 1147–1160. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:7(1147).
Schulz, H. E., and D. Z. Zhu. 2017. “Oscillations of water levels in vertical semi-immersed tubes: Analytical solutions and experimental verification.” J. Appl. Fluid Mech. 10 (6): 1515–1525. https://doi.org/10.29252/jafm.73.245.27652.
Van der Westhuizen, S. F., and P. S. Els. 2015. “Comparison of different gas models to calculate the spring force of a hydropneumatic suspension.” J. Terramech. 57 (Feb): 41–59. https://doi.org/10.1016/j.jterra.2014.11.002.
Wang, C., J. Yang, and H. Nilsson. 2015. “Simulation of water level fluctuations in a hydraulic system using a coupled liquid-gas model.” Water 7 (8): 4446–4476. https://doi.org/10.3390/w7084446.
Weidman, P., and I. Kliakhandler. 2014. “Gravitational oscillations of a capped liquid-air column.” Phys. Fluids 26 (4): 47101. https://doi.org/10.1063/1.4870761.
Willems, P., K. Arnbjerg-Nielsen, J. Olsson, and V. Nguyen. 2012. “Climate change impact assessment on urban rainfall extremes and urban drainage: Methods and shortcomings.” Atmos. Res. 103 (Jan): 106–118. https://doi.org/10.1016/j.atmosres.2011.04.003.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 9 • September 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Aug 29, 2018
Accepted: Jan 4, 2019
Published online: Jun 24, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 24, 2019
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.