Analysis of Seepage from Polygon Channels
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 4
Abstract
An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and a Schwarz-Christoffel transformation. The symmetry about the vertical axis has been utilized in obtaining the solution for half of the seepage domain only. The solution also includes relations for variation in seepage velocity along the channel perimeter and a set of parametric equations for the location of phreatic line. From this generalized case, particular solutions have also been deduced for rectangular and triangular channels with a drainage layer at finite depth and trapezoidal, rectangular, and triangular channels with a drainage layer and water table at infinite depth. Moreover, the analysis includes solutions for a slit, which is also a special case of polygon channels, for both cases of the drainage layer. These solutions are useful in quantifying seepage loss and/or artificial recharge of groundwater through polygon channels.
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Acknowledgments
The writer is grateful to All India Council for Technical Education, New Delhi for sponsoring this study under the scheme Career Award for Young Teachers (F. No. 1-15/FD/CA(18)/2001-2002). The writer would like to thank Dr. A. R. Kacimov and two other anonymous reviewers for their insightful review and constructive suggestions, which resulted in a significant improvement of the manuscript. The writer is also thankful to his Ph.D. student, Mahender Choudhary, for his assistance at various stages of the work.
References
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover, New York.
Bouwer, H. (1965). “Theoretical aspects of seepage from open channels.” J. Hydr. Div., 91(HY3), 37–59.
Bruch, J. C., and Street, R. L. (1967a). “Free surface flow in porous media.” J. Irrig. and Drain. Div., 93(3), 125–145.
Bruch, J. C., and Street, R. L. (1967b). “Seepage from an array of triangular channels.” J. Engrg. Mech. Div., 93(3), 63–82.
Byrd, P. F., and Friedman, M. D. (1971). Handbook of elliptic integrals for engineers and scientists, Springer, Berlin.
Chahar, B. R. (2000). “Optimal design of channel sections considering seepage and evaporation losses.” Ph.D. thesis, Dept. of Civil Engineering., Univ. of Roorkee, Roorkee, India.
Chahar, B. R. (2001). “Extension of Vederikov’s graph for seepage from canals.” Ground Water, 39(2), 272–275.
Chahar, B. R. (2005). “Seepage from canals.” Project Rep. F. No. 1-15/FD/CA(18)/2001-2002, All India Council for Technical Education, New Delhi.
El Nimr, A. (1963). “Seepage from parallel trapezoidal channels.” J. Engrg. Mech. Div., 89(4), 1–11.
Garg, S. P., and Chawla, A. S. (1970). “Seepage from trapezoidal channels.” J. Hydr. Div., 96(6), 1261–1282.
Harr, M. E. (1962). Groundwater and seepage, McGraw-Hill, New York.
International Commission on Irrigation and Drainage. (1967). “Controlling seepage losses from irrigation canals.” Worldwide Survey, New Delhi, India.
Jeppson, R. W. (1968). “Seepage from ditches—Solution by finite differences.” J. Hydr. Div., 94(HY1), 259–283.
Kacimov, A. R. (1992). “Seepage optimization for trapezoidal channel.” J. Irrig. Drain. Eng., 118(4), 520–526.
Liggett, J. A., and Liu, P. L.-F. (1983). The boundary integral equation method for porous media flow, Allen & Unwin, London.
Morel-Seytoux, H. J. (1964). “Domain variations in channel seepage flow.” J. Hydr. Div., 90(HY2), 55–79.
Muskat, M. (1982). Flow of homogeneous fluids through porous media, Int. Human Resources Development Corporation, Boston.
Pinder, G. F., and Gray, W. G. (1977). Finite element simulation in surface and subsurface hydrology, Academic, London.
Polubarinova-Kochina, P. Y. (1962). Theory of ground water movement, Princeton University Press, Princeton, N.J.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes in Fortran, Cambridge University Press, Cambridge.
Remson, I., Hornberger, G. M., and Molz, F. J. (1971). Numerical methods in subsurface hydrology, Wiley-Interscience, New York.
Rohwer, C., and Stout, O. V. P. (1948). “Seepage losses from irrigation canals.” Technical Bulletin No. 38, Colorado Agricultural Experiment Station, Fort Collins, Colo.
Sharma, H. D., and Chawla, A. S. (1974). “Analysis of canal seepage to interceptor drain.” J. Irrig. and Drain. Div., 100(3), 351–369.
Sharma, H. D., and Chawla, A. S. (1979). “Canal seepage with boundary at finite depth.” J. Hydr. Div., 105(7), 877–879.
Strack, O. D. L. (1989). Groundwater mechanics, Prentice-Hall, Englewood Cliffs, N.J.
Swamee, P. K., Mishra, G. C., and Chahar, B. R. (2000). “Design of minimum seepage loss canal sections.” J. Irrig. Drain. Eng., 126(1), 28–32.
Swamee, P. K., Mishra, G. C., and Chahar, B. R. (2001). “Design of minimum seepage loss canal sections with drainage layer at shallow depth.” J. Irrig. Drain. Eng., 127(5), 287–294.
Swamee, P. K., Mishra, G. C., and Chahar, B. R. (2002a). “Design of minimum water loss canal sections.” J. Hydraul. Res., 40(2), 215–220.
Swamee, P. K., Mishra, G. C., and Chahar, B. R. (2002b). “Optimal design of transmission canal.” J. Irrig. Drain. Eng., 128(4), 234–243.
Wachyan, E., and Rushton, K. R. (1987). “Water losses from irrigation canals.” J. Hydrol., 92(3–4), 275–288.
Worstell, R. V. (1976). “Estimating seepage losses from canal systems.” J. Irrig. and Drain. Div., 102(1), 137–147.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 4 • April 2007
Pages: 451 - 460
Copyright
© 2007 ASCE.
History
Received: Aug 11, 2005
Accepted: Aug 9, 2006
Published online: Apr 1, 2007
Published in print: Apr 2007
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