Derivation and application of hydraulic equation for variable-rate contour-controlled sprinklers

Abstract

The variable-rate contour-controlled sprinkler (VRCS) for precision irrigation can throw water on a given shaped area and the flow rate is also varied with the throw distance of the sprinkler for the purpose of high uniformity irrigation. Much of past research work were concentrated on the mechanical availability of variable-rate application and the design of VRCS main construction without considering the theoretical operation principles of VRCS. This study aimed to develop the mathematic models describing the relationship between hydraulic parameters of VRCS and these models will be the theoretical guidance for the design of VRCS. The hydraulic operational equation that describes the internal connection of flow rate, rotating speed and throw distance of VRCS was derived using mathematical theory of limitation and double integral. The derived operational equation indicates that the flow rate of VRCS is proportional to the product of rotating speed and square throw distance. The square wetted area sprinklers were used to illustrate the application of the operational equation of VRCS. The theoretical throw distance equation for the square wetted area sprinkler was built. With the operational equation and theoretical throw distance equation, the theoretical flow rate and rotating speed equations of the square wetted area sprinkler were derived. These results of this study provide fundamental principles for the design of VRCS.

Key words: Variable-rate sprinkler, precision irrigation, contour-controlled wetted area, irrigation uniformity, square wetted area sprinkler, hydraulic equation.