A GENERALIZED FORM OF THE SAINT-VENANT EQ UATION WITH VELOCITY AND SHEAR-STRESS PROFILES

The Saint-Venant equations for unsteady, non uniform open-channel flow are obtained by partial integration of the Prandtl equations for newt onian or non newtonian fluids. The equations are integrated with self- similar solutions near steady, uniform flow and are extended to turbul ent mean flow. For weakly unsteady, non uniform flow, a closed-form so lution is given for a) the Saint-Venant kinetic energy integral with a dissipation coefficient depending only on the Reynolds number and the roughness, b) the friction coefficient varying in space and time and c) velocity and shear stress profiles varying in space and time.