Discussion
In a potential flow, the superposition of the stream functions of a uniform flow and a line source gives rise to a dividing streamline representing
Answer: A
The dividing streamline represents a Rankine's half-body.
A line source sends fluid outward in all directions; a uniform stream sweeps it downstream. Superposing them gives a stagnation point upstream of the source and a dividing streamline that wraps round the source and opens downstream to a constant width \(m/U\), where m is the source strength. Fluid inside never mixes with the outer flow, so the streamline can be replaced by a solid surface: a body with a rounded nose that extends to infinity, the Rankine half-body.
A circular cylinder needs a doublet with the uniform flow, a rotating cylinder adds a vortex to that, and a closed oval or elliptical shape needs a source and a sink of equal strength.
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