Approximate solution for gravity flow under a Tainter gate

摘要

An approximate shape of the free surface of an inviscid flow under a radial or Tainter gate as well as speed and direction of the flow along that free surface, in a sufficiently small neighbourhood of a common end point between the fixed and the free boundaries, has been presented. Conformal mapping, by Schwartz—Christoffel, has been applied to map the region of flow in the normalized complex potential plane onto the upper half-plane, and following Carter's method we are able to find the approximate solution. The effect of the Froude number as well as the shape of the radial gate on the free surface has been studied and the curves are plotted. The accuracy of the results is more than sufficient for practical purposes.