| Summary: | 碩士 === 國立成功大學 === 水利及海洋工程學系 === 105 === Floods occur when the flow chokes in the transition from the subcritical flow at upstream to the supercritical flow at downstream, for example, the flow over a high submerged weir. In this case, the curvilinear flow path makes non-hydrostatic pressure distribution and non-uniform flow velocity in the cross section. In consequence, the complete dynamic condition at curved free-surface involves the square of free-surface slope in addition to the conventional one-dimensional open channel flow theory because the ratio of vertical to horizontal velocity component there is exactly the slope of free-surface. To deal with the unknown variables of flow discharge, critical point and free-surface elevations, we used the one-dimensional (1-D) approach by sequential quadratic programming optimization. For the two-dimensional transitional choked flow, the 1-D optimization approach is utilized to calculate the free-surface elevation by using many 1-D streamtubes, for each streamtube bounded by the free-surface and a varied streamline below the free surface. Moreover, the extend von Mises transformation for given x=x(ξ) and stream function ψ=ψ(η) were used to find out the position of internal streamlines y=y(ξ,η) in the streamline coordinate (ξ,η). To this end, the elevations of all internal streamlines were obtained by solving the Laplace equation under the calculated free-surface elevation. Using them in this study, different shapes of a submerged obstacle were first investigated for the choked open-channel flow. Then the channel bottom with different slopes and curvatures are used to test their influences on the choked flow.
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