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The monograph presents the original designs of the authors in the field of modeling water hammers in systems important for safety of nuclear power plants. Various types of heat-hydrodynamic instability due to the inertia of the pressure-flow characteristics of pumps, accelerated closing of valves, transonic mode of one- and two-phase flows are considered as the main causes of water hammers.The heat-hydrodynamic instability phenomenon consists in appearance of conditions of self-oscillatory and/or aperiodic change of heat-hydrodynamic flow parameters (pressure, rate, steam quality, etc.) in systems of the heat engineering equipment (pumps, armature, heat exchangers, etc.) and pipelines of thermal and nuclear power plants. Appearance of heat-hydrodynamic instability conditions leads to additional hydrodynamic loads on the heat engineering equipment and pipelines (hydraulic impacts), increases a vibration state and affects reliability in operating, transitional and emergency operation. A failure to fulfil design operation functions and destruction of the heat engineering equipment and pipelines occurs in extreme conditions of of reliability-critical hydraulic impacts.