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In an open-channel, the transition of a flow from a subcritical to a supercritical state may occur as a result of a lateral inflow or outflow that produces a streamwise discharge variation. Apparently, such a transition cannot be modeled accurately by a conventional hydrostatic pressure approach. In this study, a depth-averaged model that accounts for the effects of a spatially-varied discharge and a non-hydrostatic pressure distribution was developed and applied to simulate the transcritical flow in a lateral-spillway channel and the subcritical flow in a main channel fitted with side weirs. The model results for the axial free-surface profile and variation of discharge in the main channel were compared with the results of a shallow-flow model and experimental data, thereby resulting in a closer match to the measurements than the shallow-flow model. Overall, the investigation results confirmed the efficiency and validity of the non-hydrostatic depth-averaged model in simulating the mean flow characteristics of the subcritical and transcritical free-surface flows with spatially increasing or decreasing discharges, thus demonstrating its potential to be used as a numerical tool in engineering practice.

Venturi flumes are one of the most important flow-measuring structures commonly investigated by physical model tests in the past. The solutions to the Venturi flume flow problems were generally found on the basis of empirical equations arising from such tests. Nonetheless, the overall accuracy and range of applicability of these equations rely on the scope of the tests. Additionally, the hydraulic characteristics of free flows in short-throated flumes cannot be modelled by the conventional hydrostatic pressure approaches. In this study, a one-dimensional model, which incorporates a higher-order dynamic pressure correction for the effects of the sidewalls and streamline vertical curvatures, is applied to simulate such flows and elucidate relevant flow features. The model equations are discretised and solved using the finite difference scheme. The computed results for free surface profiles, pressure distributions at different sections and discharge characteristics are compared to measured data. The computational results exhibit good agreement with measured data. Overall, it is shown that the developed model is capable of accurately simulating the curvilinear flows in short-throated flumes with rounded transition and bottom humps. The results also highlight the detailed dependence of the discharge characteristics of the critical-flow flumes under free flow conditions on the curvature of the streamlines.

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The classical Dupuit-Forchheimer approach, commonly used in analysing unconfined groundwater-flow systems, relies on the assumption of a negligible vertical component of the flow. This approximation is valid only when the convergence of streamlines is very limited and the drawdown of the phreatic surface is small, or the thickness of the horizontal layer of the heterogeneous aquifers is sufficiently small. In this study, a higher-order one-dimensional model is proposed for groundwater-flow problems with significant inclination and curvature of the phreatic surface. The model incorporates non-hydrostatic terms that take into account the effects of the vertical velocity of the flow, and was solved with an implicit finite-difference scheme. The accuracy of the proposed model was demonstrated by simulating various unconfined seepage-and groundwater-flow problems with moderate curvilinear effects. The computational results for steady-state flows were compared with the results of the full two-dimensional potential-flow methods and experimental data, resulting in a reasonably good agreement. In general, the comparison results exhibited the efficiency and validity of the model in simulating complex unconfined flows over curved bedrock and curvilinear flows over planar bedrock with a steep slope.