Abstract: The theoretical relationships among hydraulic performance parameters of variable-rate sprinklers for high uniformity precision irrigation were researched. The operating equation that describes the internal connection of discharge, rotating speed and spray range of the variable-rate sprinkler was derived using mathematical theory of limitation and double integral. The operating equation indicates that the discharge of the variable-rate sprinkler is proportional to the product of rotating speed and square spray range. To illustrate the application of the operating equation, the theoretical models of spray range, discharge and rotating speed of the variable-rate square wetted area sprinkler were derived. The results of this research provide theoretical basis for the design of variable-rate sprinklers and square wetted area variable-rate sprinklers.