A turbulence model was developed for computing surface velocity coefficients and discharge under steady, uniform flow conditions for rectangular and compound open-channel cross sections. Reynolds-Average Navier-Stokes (RANS) equations, Reynolds stress equations, and kinetic energy and dissipation equations were applied in the model using the finite-volume method with the SIMPLER algorithm. The models show graphical results of the velocity distributions in the longitudinal bed slope direction, secondary velocities, pressure, turbulence kinetic energy, and kinetic energy dissipation rate across the cross section. Also, the surface velocity coefficients were computed at increments of one-eighth of the base width from the vertical walls to the center of the cross section, and the submergence depth of the floating object from zero to 30 cm, with a 5-cm depth increment. Four different sets of Reynolds stress equations (one set by Boussinesq hypothesis and three sets of algebraic stress model) were used to calculate the results. Only one version of the algebraic stress model was successful in predicting the depression of the maximum streamwise velocity below the water surface. The model was calibrated and verified using laboratory data collected at Utah State University. Calculated discharges from the turbulence model had very good agreement with the laboratory data. The surface velocity coefficients from model results were generally lower than the results from the laboratory data, but higher than the values published by the United States Bureau of Reclamation. Standard cross sections of rectangular and compound cross sections were defined to simulate the model results and model sensitivity to parameter changes. The model results were summarized to show the relationship between surface velocity coefficient and channel characteristics compared with the published values by the USBR. For rectangular cross sections, the coefficients from the model are higher than the published USBR values. But the coefficients from the model and USBR are in very close agreement for the tested compound cross sections. The published coefficients by the USBR are a function of only average water depth. However, the model results show that the coefficients are also related to channel size, surface roughness height, float submergence depth, and lateral location of the float object. These factors should be included in the determination of the surface velocity coefficient to improve the discharge estimations from the application of the float method.