Fluid injection from slot or holes into cross-flow produces highly complicated flow fields. Physical situations encountering the above problem range from turbine blade cooling to waste discharge into rivers. In this paper, the flow field created by a two-dimensional slot cooling geometry is examined using the finite volume approach with a second-order upwind differencing scheme. The time-averaged Navier -Stokes equations were solved on a collocated Cartesian grid with a two-equation model of turbulence. Attempting to solve the flow field by assuming a uniform velocity profile at the slot exit leads to inaccurate results, while extending the solution domain improves significantly the results, but proves to be costly, both in memory and in computing time (particularly in the case of multiple holes). A pressure-type boundary condition, based on uniform total pressure, is developed for the slot exit (easily applied to a three-dimensional geometry), which yields more accurate results than the widely used uniform velocity assumption. It is also found that the implementation of low Reynolds number turbulence models on this geometry provides no significant differences from the standard k -m model.