The results of the analysis of the technical and reference literature related to the technical fire extinguishing means showed that there is no complete data regarding the technical characteristics of the carriage trunks, which relate to the length of the continuous water jet depending on the fluid pressure, the diameter of the nozzle, the angle of its inclination and placement heights above the ground. The firefighting barrel trunks are mainly used for localization and extinguishing of open fires (for example, in open warehouses of timber, forest fires, etc.). In the process of eliminating such fires, it is necessary to control the flow of a continuous jet into the fire cell by changing the pressure, the diameter of the nozzle, the angle of the barrel and the like. Therefore, to solve this problem in terms of controlling the process of extinguishing a fire, the task is to conduct experimental studies and to obtain on the basis of the experimental results of an empirical mathematical model, which would take into account the influence on the length of the continuous jet of the above factors. According to the results of experimental studies, to obtain a mathematical model for determining the length of flow of a continuous stream of water by a flap barrel from the variables that influence the process of its control during the elimination of fire. To achieve this goal, it is necessary to solve the following tasks: 1) to carry out experimental studies to determine the length of the flow of continuous jet of water with a pallet barrel from the variables that affect the process of its management in the elimination of fire; 2) mathematically process the results of the experiment and obtain a mathematical model to determine the flow length of a continuous stream of water supplied by a carriage shaft; 3) to develop a methodology for controlling the process of choosing the length of a continuous stream of water, which is fed by a carriage barrel when extinguishing a fire. Experimental studies were conducted using a fractional experiment to solve the first problem. For experimental research used: 1) fire truck MAZ AC-4-60 (5309) -505M; 2) PLS-20P carriage barrel; 3) fire hoses for connecting the carriage barrel to the centrifugal pump of the fire tanker; 4) roulette at 5 m; 5) a goniometer for measuring and setting the angle of the barrel relative to the earth's surface; 6) barrel nozzles d = 25 mm and d = 32 mm. Based on the results of the experiment, a nonlinear mathematical model was developed to determine the flow length of a continuous stream of water supplied by a carriage shaft. The model developed also takes into account the effect on the length of the jet supply the height of placement of the carriage trunk above the ground. The mathematical model for determining the flow length of a continuous jet of water with a carriage trunk gave the opportunity to develop a method of controlling the flow length of a continuous jet of water. Conclusions and specific suggestions: The results of experimental studies to determine the length of the flow of continuous jet of water by a barrel trunk from variable factors made it possible to clarify the technical capabilities of carriage trunks and to develop a method of controlling the process of water supply in the event of fire elimination. A nonlinear mathematical model was developed to determine the flow length of a continuous jet of water by a carriage barrel, the adequacy of which was tested according to the Fisher criterion. To control the process of water supply, depending on the required distance to the fire, a step-by-step method is proposed to increase or decrease the length of the continuous flow of water by a flap barrel.
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