Discontinuous solutions of the shallow water equations in a channel with an abrupt change in the cross sectional area

Flows in a channel with an abstract change in the cross sectional area are investigated within the limits of the one-layer shallow water model. A proof of the relations on the hydrodynamic discontinuity that arises in this case is given. The admissible stable flows at this discontinuity are distinguished. As an example, the problem of the flows that occur as a result of the failure of a dam when there is an abrupt change in the cross sectional area in a rectangular channel, the width of which is greater in the upper water race than in the lower water race, is solved.