After the study of fully developed and developing steady laminar flow in curved channels of shallow rectangular wet cross-section (see earlier reports in this series), steady turbulent flow in such channels is investigated as a next step towards a mathematical model of the flow in shallow river bends. A mathematical model is developed for this type of flow, using a turbulence model with a prescribed distribution of the turbulence viscosity and starting from the same similarity hypothesis as in the equivalent laminar flow models. The influence of various characteristics of the turbulence model and the admissability of the most important assumptions underlying the mathematical system that is solved are tested for the flow in a rather sharply curved flume with rather strong effects of curvature. The performance of the model is tested by comparing its results with experimental data from various laboratory flumes. The turbulence model appears to be of great importance to the secondary flow and the related quantities. The similarity hypothesis yields satisfactory results for the main flow, but it needs to be refined for the calculation of the magnitude and the direction of the bed shear stress. The model appears to be applicable to curved channels of not very sharp curvature (i.e. flows with a smallor intermediate equivalent Dean number), although the secondary flow intensity tends to be underestimated.