Impact of a falling jet

Abstract

Given the complexity of the problem of the impact of a mass of liquid on a solid structure, various simplified models have been introduced in order to obtain some insight on particular aspects of the problem. Here the steady flow of a jet falling from a vertical pipe, hitting a horizontal plate and flowing sideways is considered. Depending on the elevation H of the pipe relative to the horizontal plate and the Froude number F, the flow can either leave the pipe tangentially or detach from the edge of the pipe. When the flow leaves tangentially, it can either be diverted immediately by the plate or experience squeezing before being diverted. 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 H. The pressure exerted on the plate is computed and discussed. For a fixed value of F, the maximum pressure along the plate goes through a minimum as H increases from small to large values. Results are presented for the three possible configurations: (i) tangential departure from the pipe and no squeezing, (ii) tangential departure from the pipe followed by squeezing of the liquid and (iii) detachment of the liquid from the pipe (with subsequent squeezing).