Flow Under A Gate

摘要

The potential flow of a heavy fluid under a gate is considered. The flow is assumed to emerge in the form of a jet with one free surface and one plane rigid surface. The acceleration due to gravity is acting in the direction perpendicular to the rigid surface. Most previous calculations are limited to large values of the Froude number. In the present paper we derive an efficient numerical scheme to compute solutions for all values of the Froude number F. The properties of our solutions can be described in terms of two critical values F1 approximately 2.0 and F2 approximately 1.8 of the Froude number F. For F < F2 there is no solution. For each value of F > F1, the solution is unique and qualitatively similar to the solutions obtained by previous investigators. However, for F2 < F < F1, we found that two different solutions are possible. As F approaches F1, a stagnation point appears on the free surface. Far downstream the flow is supercritical. The problem is solved numerically by series truncation for various values of the Froude number F. It is found that there are two flows for 1.80 < F < 1.87, one flow for F > 1.87 and no flows for F < 1.80.