Вплив похилу дна призматичного русла на довжину гідравлічного стрибка

Abstract. Problem. The occurrence of a hydraulic jump in road drainage systems significantly affects their reliability and can cause their destruction. Determination of measures to eliminate the negative consequences of a jump is an important task in the engineering design of road structures. There are difficulties associated with the imperfect determination of the geometric characteristics of the hydraulic jump, primarily the length of the jump, due to the use of empirical formulas and laboratory and numerical modeling. The appearance of the equation of sharply changing motion in prismatic channels made it possible to investigate the influence of various hydraulic characteristics of the flow, including the slope of the channel, on the shape of the flow surface using analytical methods. The hydraulic approach mentioned in the study of the length of the hydraulic jump needs to be checked based on a numerical simulation of the flow of real liquid and a comparative analysis of the results of hydraulic and numerical simulation. Goal. The purpose of this study is to determine the influence of the slope of the channel on the length of the hydraulic jump that occurs at the outlet section behind the connecting structure. The research aims to demonstrate the possibilities of hydraulic methods in solving problems related to sharply changing flows in open channels and to check the obtained results and conclusions using modern numerical modeling methods. Methodology. The methodological basis of the study is the use of the equation of sharply changing fluid movement in a prismatic channel in a linearized form and obtaining from it the main analytical dependencies that can be used at the stage of designing structures of road drainage systems. Results.  Using the example of the analysis of the influence of the slope of the bottom of the exit section of a one-step drop on the length of the hydraulic jump, the effectiveness of using hydraulic methods in determining the characteristics of this dangerous phenomenon is shown. Two extreme cases are considered. Channels with a wide cross-section, which made it possible to neglect the influence of the side walls, and narrow channels with the most hydraulically advantageous cross-section. The corresponding formulas have been obtained. It was concluded that as the channel width decreases compared to its depth, the jump length becomes more sensitive to changes in channel slope. Numerical calculations of perfect and wavy hydraulic jumps over a one-step drop in a channel of rectangular cross-section were carried out on the basis of a real fluid model. As a result, the dependences obtained using the equation of sharply changing fluid movement in a prismatic channel were quantitatively and qualitatively confirmed.  Originality. The proposed approach allows, while remaining within the framework of standard mathematical training offered by technical educational institutions, to effectively use hydraulic methods to study sharply changing fluid movements using the example of a hydraulic jump. Practical value. From a practical point of view, the formulas obtained in the work make it possible to qualitatively and quantitatively estimate the size of erosion formations from hydraulic jump and the size of energy quenchers to prevent the destructive consequences of this dangerous phenomenon.