TECHNICAL PAPERS
May 1, 1986

Derivation of Lewis‐Kostiakov Intake Equation

Publication: Journal of Irrigation and Drainage Engineering
Volume 112, Issue 2

Abstract

The empirical Lewis‐Kostiakov intake equation takes a power form in an algebraic equation that explicitly relates the cumulative infiltration depth, d, to the intake time, t, as d=ktn, in which k and n are the empirical constants. Although users of this well‐known intake (infiltration) equation are convinced that k and n have physical meanings, this equation is still regarded as empirical. This paper presents the physical derivation of the Fok power‐law infiltration equations to enable the interpretation of the physical meanings of k and n according to the infiltration time zones.

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References

1.
Bishop, A. A., “Relation of Intake Rate to Length of Run in Surface Irrigation,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 91, No. IR1, Paper No. 2769, Mar., 1962, pp. 23–29.
2.
Clemmens, A. J., “Infiltration Equations for Border Irrigation Models,” Advances in Infiltration, ASAE, Dec., 1983, pp. 266–274.
3.
Criddle, W. D., et al., “Methods for Evaluating Irrigation Systems,” Agricultural Handbook No. 82, Soil Conservation Service, U.S. Dept. of Agriculture, Washington, D.C., 1956.
4.
Fok, Y.‐S., “Infiltration Equations in Exponential Forms,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 93, No. IR4, Paper No. 5686, Dec., 1967, pp. 125–135.
5.
Fok, Y.‐S., and Bishop, A. A., “Analysis of Water Advance During Surface Irrigation,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 91, No. IR1, Paper No. 4259, Mar., 1965, pp. 99–116.
6.
Fok, Y.‐S., and Hansen, V. E., “One‐Dimensional Infiltration into Homogeneous Soil,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 92, No. IR3, Paper No. 4912, Sept., 1966, pp. 35–48.
7.
Fok, Y.‐S., and Willardson, L. S., “Subsurface Irrigation System Analysis and Design,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 97, No. IR3, Paper No. 8380, Sept., 1971, pp. 449–454.
8.
Green, W. H., and Ampt, G. A., “Studies on Soil Physics: I. Flow of Air Through Soils,” Journal of Agricultural Science, Vol. 4, 1911, pp. 1–24.
9.
Hall, W. A., “Evaluating Irrigation Border Flow,” Agricultural Engineering, ASCE, Vol. 37, Apr., 1956, pp. 263–265.
10.
Kostiakov, A. N., “On the Dynamics of the Coefficient of Water Percolation in Soils and on the Necessity of Studying It from a Dynamic Point of View for Purposes of Amelioration,” Transactions, Committee International Society of Soil Science, Part A, 1931, pp. 17–21.
11.
Lewis, M. R., “The Rate of Infiltration of Water in Irrigation Practice,” Transactions of the American Geophysical Union, 1937, pp. 361–368.
12.
Philip, J. R., “The Theory of Infiltration: 1. The Infiltration Equation and Its Solution,” Soil Science, Vol. 83, pp. 345–357.
13.
Rawls, W. J., and Brakensiek, D. L., “A Procedure to Predict Green and Ampt Infiltration Parameters,” Advances in Infiltration, ASCE, Dec., 1983, pp. 102–112.
14.
Richards, L. A., “Capillary Conduction of Liquids Through Porous Mediums,” Physics, Vol. 1, 1931, pp. 318–333.
15.
Strelkoff, T., and Souza, F., “Modeling Effect of Depth on Furrow Infiltration,” Journal of Irrigation and Drainage Engineering, ASCE, Vol. 110, No. 4, Paper No. 19366, 1984, pp. 375–387.
16.
Wilke, O., and Smerdon, E. T., “A Solution of the Irrigation Advance Problem,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 91, No. IR3, Paper No. 4471, Sept., 1965, pp. 23–34.
17.
Wu, I‐P., and Bishop, A. A., “Graphical Relation of Intake, Length of Run and Time,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 96, No. IR3, Paper No. 7506, 1970, pp. 233–240.

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Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 112Issue 2May 1986
Pages: 164 - 171

History

Published online: May 1, 1986
Published in print: May 1986

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Authors

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Yu‐Si Fok, M. ASCE
Prof., Dept. of Civ. Engrg., and Researcher, Water Resources Research Center, Univ. of Hawaii at Manoa, Honolulu, HI 96822

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