Deducing a Drain Spacing Formula by Applying Dimensional Analysis and Self-Similarity Theory
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Irrigation and Drainage Engineering
Volume 142, Issue 4
Abstract
For designing a steady-state drainage system, a drain flow formula coupled with the Dupuit-Forcheimer form of the differential equation of groundwater flow is used. First, the most-applied drain flow formulas in steady-state conditions are reviewed and compared using as a dependent variable the ratio between the maximum water table height and the distance between two lines of parallel drains. These equation are also tested using experimental field data measured in three plots drained by surface pipe drains having different values of drain spacing. Then, applying the dimensional analysis and the self-similarity theory, a new drain spacing formula is theoretically deduced and compared with the solutions available in the literature. Finally, the analysis shows that the most-applied drain flow formulas have the general mathematical shape deduced by dimensional analysis and self-similarity condition.
Get full access to this article
View all available purchase options and get full access to this article.
References
Barenblatt, G. I. (1979). Similarity, self-similarity and intermediate asymptotics, Consultants Bureau, New York.
Barenblatt, G. I. (1987). Dimensional analysis, Gordon & Breach, Science, Amsterdam, Netherlands.
Bourfa, S., and Zimmer, D. (2000). “Water-table shapes and drain flow rates in shallow drainage systems.” J. Hydrol., 235(3), 264–275.
Coles, E. D. (1968). “Some notes on drainage design procedure.” Proc., South African Sugar Technologists’ Association, 189–199.
Di Stefano, C., and Ferro, V. (2013). “Experimental study of the stage-discharge relationship for an upstream inclined grid with longitudinal bars.” J. Irrig. Drain. Eng., 691–695.
Diurović, N., and Stričević, R. (2003). “Some properties of Kirkham’s method for drain spacing determination in marshy-gley soil.” J. Agric. Sci., 48(1), 59–67.
Ferro, V. (1997). “Applying hypothesis of self-similarity for flow-resistance of small-diameter plastic pipes.” J. Irrig. Drain. Eng., 175–179.
Ferro, V. (2000). “Simultaneous flow over and under a gate.” J. Irrig. Drain. Eng., 190–193.
Guitjens, J. C., Ayars, J. E., Grismer, M. E., and Willardson, L. S. (1997). “Drainage design for water quality management: Overview.” J. Irrig. Drain. Eng., 148–153.
Hooghoudt, S. B. (1940). “Bijdragen tot de kennis van eenige natuurkundige grootheden van de grond.” Verslagen Van Landboouwkundige Onderzoekinge, 46(14), 515–707 (in Dutch).
Kao, C., Bourfa, S., and Zimmer, D. (2001). “Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches.” J. Hydrol., 250(1), 122–133.
Kirkham, D. (1958). “Seepage of steady rainfall through soil into drains.” Trans. Am. Geophys. Union, 39(5), 892–908.
Kirkham, D. (1961). “The upper limit for the height of water table in drainage design formulas.” Transactions 7th Int. Congress Soil Science, Vol. I, Madison, WI, 486–492.
Kirkham, D. (1966). “Steady-state theories for drainage.” J. Irrig. Drain. Eng., 92(2), 19–39.
Miles, J. C., and Kimitto, K. (1989). “New drain flow formula.” J. Irrig. Drain. Eng., 215–230.
Mishra, G. C., and Singh, V. (2007). “A new drain spacing formula.” J. Hydrol. Sci., 52(2), 338–351.
Moody, W. T. (1966). “Non linear differential equation for drain spacing.” J. Irrig. Drain. Eng., 92(2), 1–9.
Sakkas, G. (1975). “Generalized nomographic solution of Hooghoudt equations.” J. Irrig. Drain. Eng., 101(1), 21–39.
Sakkas, G., and Antonopoulos, V. Z. (1981). “Simple equations for Hooghoudt equivalent depth.” J. Irrig. Drain. Eng., 107(4), 411–414.
Van der Ploegg, R. R., Horton, R., and Kirkham, D. (1999). “Steady flow to drains and wells.” Agricultural drainage, R. W. Skaggs and J. van Schilfgaarde, eds., ASA/CSSA/SSSA, Madison, WI, 213–263.
Van Schilfgaarde, J. (1970). “Theory of flows to drain.” Advances in hydrosciences, V. T. Chow, ed., Vol. 6, Academic Press, New York, 43–106.
Wesseling, J. (1964). “A comparison of the steady state drain spacing formulas of Hooghoudt and Kirkham in connection with design practice.” J. Hydrol., 2, 25–32.
Wiskow, E., and van der Ploeg, R. R. (2003). “Calculation of drain spacing formulas for optimal rainstorm flood control.” J. Hydrol., 272(1–4), 163–174.
Youngs, E. G. (1990). “An examination of computed steady-state water-table heights in unconfined aquifers: Dupuit-Forchheimer estimates and exact analytical results.” J. Hydrol., 119(1–4), 201–214.
Yousfi, A., Mechergui, M., and Ritzema, H. (2014). “A drain-spacing equation that takes the horizontal flow in the unsaturated zone above the groundwater table into account.” Irrig. Drain., 63, 373–382.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 142 • Issue 4 • April 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jul 29, 2015
Accepted: Oct 27, 2015
Published online: Jan 7, 2016
Published in print: Apr 1, 2016
Discussion open until: Jun 7, 2016
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.