Theoretical Range and Trajectory of a Water Jet

Abstract

The trajectory of a water jet is important in many applications, including fire protection, irrigation, and decorative fountains. Increasing the maximum distance the jet travels by changing the nozzle or other variables is often desirable. This distance could be the horizontal range (also often called the reach or throw) or the maximum vertical height. Which factors control the trajectory are unclear. Consequently, a simple analytical model is developed which provides a qualitative understanding of the system. This model differs significantly from previous models. Previous models either used a dragless trajectory, which is correct according to potential flow theory if the jet does not break into droplets, or treated the trajectory as if droplets formed immediately upon leaving the nozzle. Both approaches have been noted to be unsatisfactory by past researchers. Our model compares favorably against available experimental data. Using our model, we show that the range decreases as the nozzle Froude number increases and that range increases as breakup length and droplet size increase.