Experimental data were collected in a laboratory flume with a gate structure at the Civil and Environmental Engineering Department of Utah State University. Four discharge equations for free orifice, submerged orifice, free non-orifice, and submerged non-orifice flow were calibrated using the measured data. The calibrated equations were applied in a mathematical hydraulic model to simulate both orifice and non-orifice flow, and the simulations often manifested numerical instability. The major cause of the numerical instability was found to be the sudden discontinuity Inherent in the discharge equations during the simulation of transitional flow regimes. Two algorithms were developed to enhance the numerical stability under the stated conditions. These algorithms are called "one regime" and "transitional discharge." The two algorithms were tested in the model and their applicability to overcome the problem of numerical instability and to make the model more robust for transitional flow cases was confirmed. Moreover, the transitional discharge algorithm can be applied to any transitional flow regime that has a potential for causing numerical instability associated with a flow rate discontinuity.; A "unified discharge" equation at a gate structure was developed for application in both orifice and non-orifice flow, and can be used for free and submerged flow regimes. A coefficient was also introduced to take into account the specific energy loss at a gate structure. This energy loss was analyzed and was found to be a function of the velocity head downstream of the gate. A new concept of the contraction coefficient for the flow downstream of a gate was also introduced. This now contraction coefficient allows the analysis and computation of the water depth at the location of the flow contraction with different gate and channel configurations.; The unified discharge equation helped a mathematical model successfully simulate the hydraulic conditions during problematic transitional flow regimes. The unified discharge equations were applied in the model as a mathematical "bridge" to overcome the discontinuity implicit in discharge equations for non-orifice flow. The simulation results confirmed the effectiveness of the unified discharge equations.; The unified discharge equations at the gate were subsequently applied in another mathematical hydraulic model for the entire range of flow regimes, including orifice and non-orifice flow. Energy head loss coefficients, calibrated from the laboratory data, were applied in this model to simulate the flume measurements. The simulation results proved the capability of the unified discharge equations to ameliorate the numerical instability caused by sudden changes in flow regime at canal gates.
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