The Dressier equations with flow resistance and varying channel width for unsteady free-surface flow over curved beds are presented, and a generalized Bresse profile equation for steady curved-flow is derived. Experimental measurements on steady flow over a highly curved spillway demonstrate that the Dressier equations predict the free surface, the bed pressure, and the tangential flow velocity distribution accurately, but the predictions by the classical Saint-Venant equations are almost meaningless. Since both theories require gradual variations in bed geometry, applications to intervals with rapid changes are not valid. For the small intervals of our spillway geometry where the curvature and its derivative vary rapidly, the Dressier solution shows small, but rapid, variations, whereas the measurements indicate a more gradual variation over wider intervals.