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The inviscid flow past a rotating circular cylinder can be generated by the superposition of

  • A.uniform flow, source and vortex
  • B.uniform flow, doublet
  • C.uniform flow, sink and vortex
  • D.uniform flow, doublet and vortex

Answer: D

The flow is built from a uniform flow, a doublet and a vortex.

A uniform flow plus a doublet gives the potential flow past a stationary circular cylinder: the doublet's streamline of zero value is a closed circle. Adding a free vortex at the centre superposes a circulation around the cylinder without changing the circle as a streamline, which models the rotation and produces the Magnus lift (Kutta-Joukowski lift per unit length is ρUΓ).

Uniform flow and a doublet alone describe a non-rotating cylinder. A source or a sink with a uniform flow gives an open half-body, not a closed cylinder, so adding a vortex to them does not represent a rotating cylinder either.

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