The availavility of the ω-ψ method to simulate the flow field in an open channel with gradually varied bed slope was studied. But the eddy viscosity, included in the simulation and very important factor in hydraulics, could not be well-considered at that stage, since, for such flow, the boundary condition was dominant rather than the eddy viscosity. In this paper, the fundamental feature of that factor is studied through the simulation of the two-dimensional boundary layer flow on the flat plate in an open channel. For the turbulent boundary layer flow, the relation between eddy viscosity as a mean value of the flow field and mesh size or Reynolds number is made clear. On the other hand, for the laminar flow, the apparent relation among such factors is not found.