, Volume 29, Issue 1, pp 1-10

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

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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.