THEORETICAL STUDIES AND MATHEMATICAL MODEL OF HYDRAULIC PROCESSES OF A WATER LEVEL SENSOR

Abstract

The article presents the results of theoretical studies of the operation of a float-type water level sensor used as part of a hydro-automatic level regulator in drainage–irrigation systems. The efficiency of such systems largely depends on the accuracy and stability of level sensors, which ensure a timely response of the regulator to changes in hydraulic conditions. In this regard, the study of hydraulic processes that determine the actuation conditions of the float sensor is of particular relevance. A simplified theoretical and mathematical model of the sensor operation is proposed, based on the analysis of the equilibrium of forces acting on the float in the working environment. The model takes into account the action of the float’s gravitational force, the buoyant (Archimedes) force, as well as the forces of hydrostatic water pressure from the upper and lower nozzles of the hydraulic connection. The influence of the float’s geometric parameters, including its diameter, height, cross-sectional area, and submerged volume, as well as the float mass and the density of the working fluid, on the equilibrium conditions of the system is analyzed. Special attention is paid to accounting for the head in the hydraulic connection pipeline and the discharge coefficient, which makes it possible to more accurately describe real operating conditions of the sensor while considering hydraulic losses. Based on the developed model, an analytical relationship is obtained to determine the critical immersion height of the float at which the equilibrium of forces is disturbed, the float begins to rise, and the hydraulic connection is closed. It is shown that changes in structural and hydraulic parameters significantly affect the value of the critical immersion height, as well as the sensitivity and reliability of the float sensor operation. The proposed approach can be used in engineering calculations and in the design of new or modernization of existing float-type water level sensors. The obtained theoretical relationships form the basis for further experimental studies and practical verification of sensor operation under real operating conditions, as well as for improving hydro-automatic regulators in reclamation and water management systems.