The simulation of multiphase flow interfaces, such as a water-oil system, presents a challenge in Computational Fluid Dynamics (CFD) due to the complexity of accurately tracking a moving interface while ensuring numerical stability. This work studies the implementation of the Level Set Method to track the interface between water and oil in a 2D tank with a central drainage at its lower surface, under the effects of gravity and surface tension. To achieve this, the Navier-Stokes equations for incompressible fluids are solved to calculate velocities and pressures using the intermediate velocity method. The Level Set Method is applied for interface tracking, and appropriate velocity boundary conditions are used to model the drainage. The numerical implementation is carried out in MATLAB. Results demonstrate the evolution of the interface, revealing clear patterns of deformation due to drainage and the effects of surface tension in maintaining interface cohesion. The velocity and pressure fields exhibit expected behaviours, such as increased velocities near the drainage region and pressure buildup at the tank base. It is shown that this method can also be transferred to other liquid-air interfaces at drainages, for example the output of melted plastic through the nozzle of a printer during Fused Deposition Modelling (FDM) Additive Manufacturing (AM).