Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary

Dun, C.R. and Hocking, G.C. (1995) Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary. Journal of Engineering Mathematics, 29 (1). pp. 1-10.

Abstract

A series truncation method is used to compute the flow into a line sink from a region of fluid with a free surface and a sloping wall beneath the sink. The method admits a well-known exact solution for a particular value of the slope. Solutions with a cusp above the sink, and with a stagnation point above the sink are computed for all values of the slope, and compared with results at both ends of the range, i.e. with results for both a vertical wall and a horizontal bottom, with good agreement.