Design of Minimum Seepage Loss Canal Sections with Drainage Layer at Shallow Depth
Publication: Journal of Irrigation and Drainage Engineering
Volume 127, Issue 5
Abstract
This paper presents an analytical solution for the quantity of seepage from a rectangular canal underlain by a drainage layer at shallow depth. The solution has been obtained using inverse hodograph and conformal mapping. Using the solution for the rectangular canal and the existing analytical solutions for triangular and trapezoidal canals, simplified algebraic equations for computation of seepage loss from these canals, when the drainage layer lies at finite depth, have been presented, which replace the cumbersome evaluation of complex integrals. Using these seepage loss equations and a general uniform flow equation, simplified equations for the design variables of minimum seepage loss sections have been obtained for each of the three canal shapes by applying a nonlinear optimization technique. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for design of the minimum seepage loss section. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Avriel, M. ( 1976). Nonlinear programming analysis and methods, Prentice-Hall, Englewood Cliffs, N.J.
2.
Bandini, A. (1966). “Economic problem of irrigation canals: Seepage losses.”J. Irrig. and Drain. Div., ASCE, 92(4), 35–57.
3.
Bazaraa, M. S., and Shetty, C. M. ( 1979). Nonlinear programming: Theory and algorithms, Wiley, New York.
4.
Bruch, J. C. ( 1966). “Studies of free surface flow and two dimensional dispersion in porous media.” PhD thesis, Dept. Civ. Engrg., Stanford University, Stanford, Calif.
5.
Bruch, J. C., and Street, R. L. (1967a). “Seepage from an array of triangular channels.”J. Engrg. Mech. Div., ASCE, 93(3), 63–82.
6.
Bruch, J. C., and Street, R. L. (1967b). “Free surface flow in porous media.”J. Irrig. and Drain. Div., ASCE, 93(3), 125–145.
7.
Byrd, P. F., and Friedman, M. D. ( 1971). Handbook of elliptic integrals for engineers and scientists, Springer, Berlin.
8.
Burley, D. M. ( 1974). Studies in optimization, International Text Book Co., Beds, U.K.
9.
Chahar, B. R. ( 2000). “Optimal design of channel sections considering seepage and evaporation losses.” PhD thesis, Dept. of Civ. Engrg., University of Roorkee, Roorkee, India.
10.
Churchhouse, R. F. ( 1981). Numerical methods. Handbook of applied mathematics, Vol. 3, Wiley, New York.
11.
El Nimr, A. (1963). “Seepage from parallel trapezoidal channels.”J. Engrg. Mech. Div., ASCE, 89(4), 1–11.
12.
Fox, R. L. ( 1971). Optimization methods for engineering design, Addison-Wesley, Reading, Mass.
13.
Garg, S. P., and Chawla, A. S. (1970). “Seepage from trapezoidal channels.”J. Hydr. Div., ASCE, 96(6), 1261–1282.
14.
Hammad, H. Y. (1960). “Seepage losses from parallel channels.”J. Engrg. Mech. Div., ASCE, 86(4), 42–50.
15.
Harr, M. E. ( 1962). Groundwater and seepage, McGraw-Hill, New York.
16.
Himmelblau, D. M. ( 1972). Applied nonlinear programming, McGraw-Hill, New York.
17.
Ilyinsky, N. B., and Kacimov, A. R. ( 1984). “Seepage-limitation optimization of the shape of an irrigation channel by the inverse boundary value problem method.” J. Fluid Dyn., 19(4), 404–410.
18.
Indian Bureau of Standards (IBS). ( 1980). “Measurement of seepage losses from canals.” IS:9452, Parts 1 and 2, New Delhi.
19.
Indian Bureau of Standards (IBS). ( 1982). “Criteria for design of lined canals and guidelines for selection of type of lining.” IS:10430, New Delhi.
20.
International Commission on Irrigation and Drainage (ICID). ( 1967). “Controlling seepage losses from irrigation canals.” Worldwide survey, New Delhi.
21.
Kacimov, A. R. (1992). “Seepage optimization for trapezoidal channel.”J. Irrig. and Drain. Engrg., ASCE, 118(4), 520–526.
22.
Morel-Seytoux, H. J. (1964). “Domain variations in channel seepage flow.”J. Hydr. Div., ASCE, 90(2), 55–79.
23.
Muskat, M. ( 1946). Flow of homogeneous fluids through porous media, J. W. Edwards Brothers, Inc., Ann Arbor, Mich.
24.
Polubarinova-Kochina, P. Ya. ( 1962). Theory of ground water movement, Princeton University Press, Princeton, N.J.
25.
Preissmann, A. ( 1957). “A propos de la filtration au-dessous des canaux.” Houille Blanche, 12, 181–188 (in French).
26.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. ( 1992). Numerical recipes in FORTRAN, Cambridge University Press, Cambridge, U.K.
27.
Rohwer, C., and Stout, O. V. P. ( 1948). “Seepage losses from irrigation canals.” Tech. Bull. 38, Colorado Agricultural Experiment Station, Fort Collins, Colo.
28.
Sharma, H. D., and Chawla, A. S. (1979). “Canal seepage with boundary at finite depth.”J. Hydr. Div., ASCE, 105(7), 877–897.
29.
Swamee, P. K. (1994). “Normal-depth equations for irrigation canals.”J. Irrig. and Drain. Engrg., ASCE, 120(5), 942–948.
30.
Swamee, P. K. (1995). “Optimal irrigation canal sections.”J. Irrig. and Drain. Engrg., ASCE, 121(6), 467–469.
31.
Swamee, P. K., Mishra, G. C., and Chahar, B. R. (2000). “Design of minimum seepage loss canal sections.”J. Irrig. and Drain. Engrg., ASCE, 126(1), 28–32.
32.
Wachyan, E., and Rushton, K. R. ( 1987). “Water losses from irrigation canals.” J. Hydro., Amsterdam, 92(3-4), 275–288.
33.
Youngs, E. G. ( 1986). “Water-table heights and discharge rates with artesian flow to interceptor land drains.” J. Hydro., Amsterdam, 87(3-4), 255–266.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 127 • Issue 5 • October 2001
Pages: 287 - 294
History
Received: May 30, 2000
Published online: Oct 1, 2001
Published in print: Oct 2001
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.