# Mathematical Model of Border Irrigation

by David W. Fonken, (M.ASCE), Irrigation Engr.; Harza Engrg. Co., Chicago, Ill.,
Delmar D. Fangmeier, (M.ASCE), Prof. of Agricultural Engrg.; Univ. of Arizona, Tucson, Ariz.,
Emmett M. Laursen, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Arizona, Tucson, Ariz.,
Thomas Carmody, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Arizona, Tucson, Ariz.,

Serial Information: Journal of the Irrigation and Drainage Division, 1980, Vol. 106, Issue 3, Pg. 203-220

Document Type: Journal Paper

Abstract:

The model can predict the rates of advance and recession and the duration and depth of infiltration at any point in a border when slope, length, roughness, inflow rate and infiltration rate are specified. It provides an accurate and economical way to analyze the hydraulics of border irrigation, and thus can enable designers and operators to find optimum combinations of discharge rate and inflow duration. Equations satisfying the laws of conservation of mass and momentum are applied to a control volume over a finite period of time. Numerical integration is accomplished by selecting quantities of time and space that are finite, yet small enough so that average values can be used to represent the range of values actually occurring over the interval. Solutions are obtained through an iterative process specified in three FORTRAN programs for the advance, and continuing and recession phases of an irrigation. The model was validated by successfully simulating field runs measured at the University of Arizona.

Subject Headings: Border irrigation | Mathematical models | Mathematics | Inflow | Infiltration | Hydraulic design | Economic factors | Numerical methods | Water discharge | Slopes