Flow through a turbine flow meter is simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved steadily in rotating reference frames, and the centrifugal force and the Coriolis force are added to the equation of motion. The standard $k-{epsilon}$model is employed to evaluate turbulent viscosity. Computational results yield quantitative as well as qualitative information on the design of turbine flow meters by showing the distributions of pressure and velocity around the turbine blades.