Complex Velocity Potential Problem

Ideal flow over a rotating cylinder can be modeled by combining the potential functions for uniform flow,

a doublet, and a free line vortex. The doublet and free vortex are centered about the same axis.

What is the complex potential function that describes this flow?

Determine expressions for the velocity components from the complex velocity potential.

Derive an expression for the pressure coefficient in terms of a spin ratio, $\frac{}{UR}.$ The pressure

coefficient is defined as $c_p=\frac{p-p_{}}{\frac{1}{2}{U}^2}$

Derive an expression for the lift force per unit depth into the page. The lift force should be in

terms of the air density, freestream speed $U,$ and the rotation rate $,$ and the cylinder radius

Draw streamlines using a computer for the cases following cases where the air velocity is $10\frac{m}{s}$

and the cylinder radius is $0\mathrm{.}2$ m :

a$.$ The cylinder is not rotating

b$.$ The cylinder is rotating such that the stagnation points are deflected $45$ upwards on the

cylinder. State the ratio $\frac{}{UR}$ that is required to achieve this deflection.