Dimensionless Formulation of Furrow Irrigation

Abstract

The equations governing the flow of water in irrigation furrows are put in nondimensional form by expressing each variable therein in ratio to an appropriate reference variable. Two systems of reference variables are considered, one based on normal depth in the given furrow geometry at the given inflow, the other on the given inflow and cutoff time. The first is especially valuable because of the clear physical significance of normal depth, but it is useless in horizontal furrows. The second system is pertinent to furrows set on any slope. The matter of choosing a system of reference variables is viewed in some generality to allow application to other systems, suitable for special applications, in particular, design applications. A set of formulas is presented for translation from one system to the other. The necessary input for a completely nondimensional treatment of furrow irrigation is outlined, and the concept of hypothetical dimensioned furrows is introduced. This is designed to provide a physical significance to variables entered in dimensionless form as input to a mathematical model of furrow irrigation.