Impact of a rising stream on a horizontal plate of finite extent

Abstract

The steady flow of a stream emerging from a nozzle, hitting a horizontal plate and falling under gravity is considered. Depending on the length of the plate L and the Froude number F, the plate can either divert the stream or lead to its detachment. First, the problem is reformulated using conformal mappings. The resulting problem is then solved by a collocation Galerkin method; a particular form is assumed for the solution, and certain coefficients in that representation are then found numerically by satisfying Bernoulli's equation on the free surfaces at certain discrete points. The resulting equations are solved by Newton's method, yielding various configurations of the solution based on the values of F and L. The lift exerted on the plate is computed and discussed. If the plate is long enough, physically meaningful solutions are found to exist only for values of F greater than or equal to a certain critical value F0, which is to be determined. Results are presented, both for F > F0 where the detachment is horizontal and for F = F0 where the detachment point is a stagnation point at a 120° corner. Related asymmetric flows where the rising stream is inclined are also studied.