Impact of fluid streams on horizontal walls

Abstract

The flow of a stream coming out of a pipe and hitting a horizontal wall is considered. Both cases of rising and falling flows are studied. First, for the rising flow, depending on the length of the wall L and the Froude number F, the wall can either divert the stream or lead to its detachment. The problem is reformulated using conformal mappings and the resulting problem is then solved by a collocation Galerkin method. A particular form is assumed for the solution, satisfying Bernoulli's equation on the free surfaces at certain discrete points. The resulting equations are solved by Newton's method. Solution profiles are presented for particular values of F and the question of the lift exerted on the wall is addressed. Then, the falling flow case is studied in the presence of a horizontal wall of infinite length. Depending on the elevation H of the pipe relative to the horizontal wall and F, the flow can either leave the pipe tangentially or detach from the edge of the pipe. Results are presented showing either a tangential departure from the pipe and no squeezing, or a tangential departure from the pipe followed by squeezing of the liquid. Finally, the cases of flows in the presence of stagnation points are discussed.