Abstract
The water surface profile analysis in open channel flows is carried out to predict the water depth of rivers and artificial channels by using the steady one-dimensional flow equation. If a singular point, which is defined as the intersection of the quasi-normal depth and the critical depth, exists in a flow, the classification of a singular point is done and then the water surface profile is calculated from the control section. It is known that the singular point analysis predicts the transitional profile from the high velocity flow (Fr>1) to the normal flow (Fr<1) through a singular point, which is never realized in actual flows. Using the unsteady flow equations, the stability analysis of the water surface profile near a singular point with respect to time is carried out. It is proved that the transition from the normal flow to the high velocity flow through the saddle point is stable and the other types of transitions are unstable and are never realized.
