Singular integral equations in potential flows of open-channel transitions

The free-surface profile of potential flows is calculated in open-channel transitions by using singular integral equation methods. Thus in such free-surface hydraulics applications the analysis of fluid motion is very complicated, as both the subcritical and supercritical flows are presented simultaneously. For the numerical solution of the singular integral equations are used both constant and linear elements.An application is finally given to the determination of the free-surface profile in an open-channel contraction and comparing the numerical results with corresponding results by finite differences.