The characteristics of the trapezoidal weir flow are measured using a one-dimensional laser Doppler anemometer for two different flow conditions. The governing equations of the flow are solved using Standard k-epsilon, Realizable k-epsilon, Modified k-omega and Reynolds Stress Model based on the Reynolds-Averaged Navier-Stokes Equations and by Large Eddy and Detached Eddy Simulations. ANSYS-Fluent package program is used for the numerical analysis of flow with the same experimental conditions. The free surface of the trapezoidal weir flow is computed by the volume of fluid method. The effect of the selected grid structure on the numerical results is examined by Grid Convergence Index. Moreover, two-dimensional (2D) and three-dimensional (3D) analyses of the trapezoidal weir flow are included to estimate the effects of side walls. Experimental results of the velocity field and free surface profiles are compared to the numerical results of 2D and 3D simulations for the validation purposes. From the comparisons it is concluded that the Reynolds Stress Model estimates the flow field more accurately compared with those of the other models used in the present study. Furthermore, the flow characteristics such as turbulence kinetic energy, energy spectrum and pressure distributions for different flow rates are presented. Lastly, the discharge coefficients for different flow-weir configurations are compared experimentally and numerically.