A uniform flow of speed U_\infty = 20 m/s combines with a doublet of strength \kappa = 80 m^3/s to model flow over a cylinder. What is the radius R (in meters) of the equivalent circular cylinder?

Answer Key:

2.0

### Solution: Cylinder radius in potential flow is R = \sqrt{\kappa / (2 \pi U_\infty)}... wait! In standard notation \psi = U_\infty r sin heta (1 - R^2/r^2), where doublet stream function is - \mu sin heta / (2\pi r) or with \kappa = 2\pi U_\infty R^2. If R = \sqrt{\kappa / U_\infty} or \kappa = U_\infty R^2, let's specify \kappa / U_\infty = R^2 ==> R^2 = 80 / 20 = 4 ==> R = 2.0 m.

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