The main object of interest was a typical fuel assembly, which constitutes a core of the nuclear reactor. The aim of the paper is to describe the phenomena and calculate thermal-hydraulic characteristic parameters in the fuel assembly for a European Pressurized Reactor (EPR). To perform thermal-hydraulic calculations, the RELAP5 code was used. This code allows to simulate steady and transient states for reactor applications. It is also an appropriate calculation tool in the event of a loss-of-coolant accident in light water reactors. The fuel assembly model with nodalization in the RELAP5 (Reactor Excursion and Leak Analysis Program) code was presented. The calculations of two steady states for the fuel assembly were performed: the nominal steady-state conditions and the coolant flow rate decreased to 60% of the nominal EPR flow rate. The calculation for one transient state for a linearly decreasing flow rate of coolant was simulated until a new level was stabilized and SCRAM occurred. To check the correctness of the obtained results, the authors compared them against the reactor technical documentation available in the bibliography. The obtained results concerning steady states nearly match the design data. The hypothetical transient showed the importance of the need for correct cooling in the reactor during occurrences exceeding normal operation. The performed analysis indicated consequences of the coolant flow rate limitations during the reactor operation.