Open channel flows with submerged obstructions

Free-surface flows past a submerged triangular obstacle at the bottom of a channel are considered. The flow is assumed to be steady, two-dimensional and irrotational; the fluid is treated as inviseid and incompressible and gravity is taken into account. The problem is solved numerically by series truncation. It is shown that there are solutions for which the flow is suberitical upstream and supercritical downstream and other flows for which the flow is supercritical both upstream and downstream. The latter flows have limiting configurations with a stagnation point on the free surface with a 120° angle at it. It is found that solutions exist for triangular obstacles of arbitrary size. Local solutions are constructed to describe the flow near the apex when the height of the triangular obstacle is infinite.