Theoretical aspects of determining the consumption of the working fluid coming out of the annular slotted regulator of resource-efficient sprinklers

Resource-efficient sprinklers are utilized for various agricultural processes. This study examines the equilibrium state of the working fluid between two cylinders with radii r1 and r2, focusing on the equilibrium condition of the liquid volume when determining the flow rate ejected through the annular space between the expander and the funnel with an improved agitator. The research investigates several key parameters, including the laminar velocity of the liquid exiting the annular slot of the agitator, velocity distribution across the cross-section, cross-sectional surface area of the annular working slot, liquid density and dynamic viscosity, average and maximum velocities of the liquid exiting the annular slot, and the length between the annular slots. The study also considers the Reynolds number to distinguish between laminar and turbulent flow regimes, as well as analyzing factors such as the average cross-section diameter of the working slit, the width of the slit opening, the flow coefficient of the working fluid, flow compression, and velocity coefficient. Furthermore, the research determines the hydraulic pressure and the flow rate of the working fluid ejected from the angular part of the funnel (α and β) of the agitator, providing a comprehensive analysis of the fluid dynamics within resource-efficient sprinklers.