FeedWater leakages due to excessive loads and cracking caused by corrosion or fatigue failure can affect the reliability of the production facilities. In the present work, a numerical study of a small leakage accident type SB-LOCA on the feed Water Pipeline was investigated using Computational Fluid Dynamics (CFD) and Relap5 computer codes. The aim is to understand the behavior of the incompressible Water flow and its effect on the relevant parameters at the leakage location vicinity, including the mass flow rate, velocity, pressure, and temperature. For this, a mathematical model was developed and validated to evaluate the release of Water through the pipe, which is mainly based on the variables that may affect the leakage. The results of CFD show that the leakage has important effects on the distribution of main parameters of the Water flow through the pipe, which has an identical outcome from the Relap5 code simulation. The change of fluid velocity only has a little impact on the flow behavior at the leakage region.