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A free-streamline theory is given for the steady flow of an inviscid, stratified fluid into a line sink, with the fluid stagnant above the dividing streamline. It is shown that an infinite number of such solutions exist for 0.33 ≤ F1 ≤ ∞. A constructive procedure is used to obtain the solutions. Error estimates are given through suitable perturbation schemes. An answer to the question of uniqueness is presented with F1 = 0.33 given as the unique Froude number for all separated flows.
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Timothy W. Kao (1970) studied this question.
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