Flow through Slit in Dam

Abstract

The problem of gravity-driven free-surface flows is difficult to solve due to the nonlinear character of the boundary condition. Using methods based on complex analysis, only flows past simple geometrical boundaries have been investigated. The fluid flow from a reservoir, through a slit with an arbitrarily curved boundary, into downstream in the pattern of a free jet has both characters of free jet and flow from a sluice gate. The solution of the problem is more difficult to obtain than either free jet or flow under a sluice gate. When the total energy head, namely, the depth of water in reservoir is given, not only the velocity on the solid boundary and the profiles of the free surfaces need to be calculated, but also the discharge needs to be determined. In the present paper, by using the theory of the boundary-value problem of analytical function and the substitution of variables, the boundary-integral equations in the physical plane are derived. According to the consistency between the discharge and the uniform velocity at far upstream, the writers present a synchronous iterative method for the discharge and flow pattern. The profile of the free surfaces, the velocity and pressure distributions on the walls, and the discharge are calculated. The computed results agree well with the measured results.