Equations Describing Sprinkler Droplet Velocity

Abstract

Previous investigators have used a graphical method to analyze rate of fall of water droplets through still air to show that the drag force of a water droplet is proportional to the second power of the speed. In this paper, the equations describing the movement of a droplet in still air are put in dimensionless form (with the terminal speed as the characteristic term) and analytical solutions are obtained for the horizontal and vertical velocities and displacements of a droplet, given its initial velocity components and the nozzle elevation. The resulting equations may provide a basis for modeling sprinkler distributions. The angle of projection of the droplet as it leaves the nozzle, that results in the maximum horizontal displacement of the droplet when landing on a horizontal surface, is obtained as a function of the speed with which the droplet leaves the nozzle and the elevation of the nozzle. This nozzle angle is designated as the optimum angle.