R. V. Southwell and G. Vaisey, “Relaxation Methods Applied to Engineering Problems: XIII, Fluid Motions Characterized by Free Streamlines,” Philosophical Trans- actions of the Royal Society of London. Series A, Ma- thematical and Physical Sciences, Vol. 240, No. 815, 1946, pp. 117-161.

has been cited by the following article:

• TITLE: Unsteady Spillway Flows by Singular Integral Operators Method

  AUTHORS: Evangelos G. Ladopoulos

  KEYWORDS: Unsteady Flows; Spillway; Free-Surface; Open Channel Hydraulics; Singular Integral Operators Method (S.I.O.M.); Constant & Linear Elements; Potential Flows

  JOURNAL NAME: Engineering, Vol.4 No.3, March 31, 2012

  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.