MATHEMATICAL MODEL OF A LARGE RESERVOIR, ESTABLISHING AND FINDING ITS MAIN ENERGY CHARACTERISTICS
Authors: DUBCHAK Viktor , NOVYTSKA Liudmyla , MANZHOS Elvira 
Published: September 2024

Water plays an important role in the normal life of a person as a member of society. The presence or absence of fresh water reserves is one of the most important economic and social factors for the successful existence and development of any country in modern conditions. It is difficult to overestimate the importance of having large fresh water reserves for every sector of the economy. Ukraine has one of the largest such reserves in the world. Over time, as established by research and forecasts, the value and cost of fresh water will only increase. Therefore, preserving, protecting, properly utilizing and maintaining large, man-made water reservoirs is an important and always relevant task for the people of Ukraine. This strategy seems especially important in the current state of full-scale military aggression by the neighboring enemy. Thus, it seems reasonable to care about the preservation and proper use of fresh water in the context of the current geopolitical conflict. Water resources indeed play a critical role in all areas of the economy and daily life. Fresh water supplies are essential for agriculture, industry, drinking water for the population, as well as for energy and other industries.
Ukraine, as a country with large freshwater reserves, has the opportunity to use this resource to ensure sustainable development and reduce dependence on imports. Water reservoirs can also play a strategic role in the face of possible threats and military conflicts. The storage and maintenance of water reservoirs is a necessary precautionary measure in case of any possible threats to infrastructure and access to fresh water. It is also important to develop and implement strategies for water conservation and efficient use to guarantee long-term resilience and sustainability in the water supply sector.
The context of armed conflict can pose additional challenges to water management. It is therefore important to have contingency plans in place and to ensure the safety of water bodies in such circumstances. The development and improvement of water supply systems, as well as the implementation of effective water management strategies, will contribute to the sustainable development and conservation of an important natural resource, which is fresh water.
Taking into account the sufficient importance and relevance of all these issues, in the following studies, a certain mathematical model of a large modern reservoir is proposed and investigated in the form of such a volumetric geometric structure as a spatially horizontally oriented elliptical half cylinder with the corresponding parameters that correspond to the specific dimensions of a real reservoir, such as the length, width and depth of filling such a structure with water.It is believed that the height (depth) of the filling can change, and this fact is essentially the most important factor in the corresponding change in the current volume of stored water and the potential energy of the accumulated liquid.The main results of this work are the possibility of determining the value of the current volume and the accumulated potential energy of such a reservoir. The paper presents a geometric view of the model of such a structure, formulas and their results for finding the values of the mentioned energy characteristics of a reservoir of the corresponding geometry, draws conclusions, points out the advantages and possible disadvantages of the given mathematical model, and provides opportunities for the future creation of an alternative mathematical more adequate model of a modern reservoir in the form of a horizontally oriented elliptical half cone.