A technique is proposed to model flows with free surfaces using the control volume method. The free surface is tracked by determining the locations of the ambient pressure in the domain. Special conditions are imposed on the nodes in the vicinity of the free surface. Flow visualization experiments are carried out to determine the free surface shapes and velocity distributions during the filling of a cylindrical container with water. Computations are carried out to model the flow in the experimental test case using a mesh transformation and the free surface treatment. The proposed free surface treatment yields results of better accuracy as compared with the results using the free slip condition. The predicted locations and heights of the spout are reasonable.