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A finite-slope Boussinesq equation is developed to model curved transcritical flow over spillways and broad-crested weirs, even with large slopes. At a number of computational points, finite difference approximations for all derivatives in the differential equation are used to give a system of nonlinear algebraic equations which can be solved by standard optimization methods. A number of laboratory experiments were performed with different transcritical flow problems including changes in channel gradients and a trapezoidal weir. The equation and the numerical model were tested using results from those experiments and from those for a steep and sharply-curved weir structure, with good results. They can be used as a computational flume to determine the head-discharge characteristics of proposed structures. A novel feature of the equation and numerical method is that higher derivatives of the bed topography are best ignored, apparently mimicking the effects of flow separation in smoothing it. [ABSTRACT FROM AUTHOR]

Choking problems occur in transitions that have a bed rise higher than a maximum allowable value. Due to the complexity of the United States Bureau of Reclamation (USBR) horseshoe cross-section, a time-consuming trial-and-error procedure is inevitable as a way to determine the maximum allowable bed rise. This paper presents straightforward solutions to calculate a choke-free maximum bed rise for practical changes in bed elevations. The maximum relative errors associated with the proposed equations are less than 1%. A graphical solution is presented to obtain the upstream operating ranges based on non-dimensional specific energy curves. In addition, a direct relationship is developed to determine the critical depth in the transition zone which bears less than 1% relative error. Finally, a choking solution is discussed by considering the energy head loss occurred in the channel transition zone. [ABSTRACT FROM AUTHOR]