Dimensional analysis in surface irrigation
The surface-irrigation design process requires multiple analyses of surface irrigations to test tentative values of design parameters in the search for an optimum. Preparation of general design charts can aid the design process if the users' test cases fall within the scope of the charts. The large number of independent variables in surface irrigation preclude the generation of charts covering the practical range of all independent variables, when these are in dimensioned form. Dimensionless formulations allow significant reductions in the amount of data generated and presented, without loss of generality. Relationships pertinent to surface-irrigation analyses and design are reviewed in dimensionless terms. Dimensionless forms are developed primarily from an examination of the equations governing surface-irrigation phenomena. Additionally, dimensionless forms are derived from a study of the dimensions of the pertinent variables, without recourse to the governing equations. The Buckingham Pi Theorem is derived in the context of surface irrigation. Different choices for reference variables, leading to different meanings for the resulting dimensionless parameters, have advantages and disadvantages for analysis and design of surface irrigation systems. The different systems developed in the past for border irrigation are reviewed and their consequences noted; new systems with potential for future studies are suggested. Particular attention is devoted to those dimensionless representations useful in design.