Using the particle image velocimetry (PIV) technique, the laboratory experiments are conducted to measure the velocity fields of two-dimensional turbulent free surface flows upstream of rectangular and triangular broad-crested weirs. The experimental flow cases are analyzed theoretically by a computational fluid dynamics (CFD) modeling in which the finite element method is used to solve the governing equations. In the CFD simulation, the volume of fluid (VOF) method is used to compute the free surfaces of the flows. Using the standard k-epsilon and standard k-omega turbulence models, the numerical results for the velocity fields and flow profiles are compared with the experimental results for validation purposes. The computed results using k-omega turbulence model on compressed mesh systems are found in good agreement with measured data. The flow cases are also analyzed theoretically using the potential flow (PF) approach, and the numerical results for the velocity fields are compared with measurements.