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We apply the constitutive relations of kinetic theory of granular gases to the transport of cohesionless sediments driven by a gravitational liquid turbulent stream in steady uniform conditions. The sediment-laden flow forms self-equilibrated mechanisms of resistance at the bed surface, below which the sediments are at rest. This geo-physical process takes place quite often in streams at moderate slope and may be interpreted through tools common to fluid mechanics and particle physics. Taking into account the viscous dissipation of the fluctuation energy of the particles, and using approximate methods of integration of the governing differential equations, permit to obtain a set of simple formulas for predicting how depths and flow rates adjust to the angle of inclination of the bed, without requiring additional tuning parameters besides the particle and fluid properties. The agreement with laboratory experiments performed with either plastic cylinders or gravel in water is remarkable. We also provide quantitative criteria to determine the range of validity of the theory, i.e., the values of the Shields number and the angle of inclination of the bed for which the particle stresses can be mostly ascribed to collisional exchange of momentum.


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