In this paper the equation of a laminar uniform one-dimensional free surface flow for a Herschel-Bulkley fluid is derived. On the basis of the equation, an expression for Darcy-Weisbach friction factor is defined and the extended Reynolds number is introduced. Using results of experiments carried out using water-kaolinite clay mixtures with different solid concentrations, the friction factor is estimated for the Bingham and pseudoplastic models. Results are compared with theoretical values. Accuracy of the friction factor estimation is also given.