Abstract
The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.
Highlights
Gravity driven free-surface flows, belonging to a major field of classical hydraulics problems, were not solved accurately and efficiently in the past, because of several design and measurement purposes
The Singular Integral Operators Method was applied to the determination of the free-surface profile of the unsteady flow over a spillway
There are some basic parameters of the unsteady spillway flows, like the discharge, the free surfaces and speeds which are necessary for the design of the spillways
Summary
Gravity driven free-surface flows, belonging to a major field of classical hydraulics problems, were not solved accurately and efficiently in the past, because of several design and measurement purposes. The spillway solutions are considerably more difficult to be determined than of the corresponding usual free-surface hydraulics problems, in open channel flow. L. Betts [12] applied the finite element method for the solution of free surface gravity flows. The complex variable function theory was further used for the solution of free surface potential flow problems. This method was applied in the specific cases where the geometry of the solid boundary consists of straight segments and the effort of gravity is neglected. An application is given to the determination of the free-surface profile of a spillway and comparing the outprints with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments. Whenever the S.I.O.M. was compared to the B.I.E.M. for the solution of problems where closed form solutions were available, the S.I.O.M. gave solutions much more close to the exact solutions
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