Potential Flow at a Two-Dimensional Conduit Outlet

A theory is presented to describe the potential flow of liquid at a two-dimensional conduit outlet. A detailed description of the flow is given by an integro-differential equation derived from the solution of a boundary-value problem of Dirichlet type is an infinite strip in the complex potential plane. The integro-differential equation, in which the main parameters are the approach Froude number, F, and an unknown location of the hydraulic grade line, is solved numerically for flows with F=0.9, 1, 2, 3, and 4. Thus, the relationship between the location of the hydraulic gradient and F is obtained, which furnishes a limiting value of F for the case when the total head is equal to the evaluation of the top of the conduit. The geometry of the free surfaces and pressure distributions on the boundaries of the conduit and in the body of the flow are given for different values of F.