Question

The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).

Hint:

For a spinning cylinder in a potential flow, the lift per unit span is directly proportional to the circulation and free-stream velocity. The formula \( {Lift per unit span} = \rho \cdot \Gamma \cdot V_\infty \) can be used to calculate the circulation.

Answer 1

To find the circulation \( \Gamma \) around the spinning circular cylinder, we use the relationship between the lift per unit span and circulation for a cylinder in potential flow: \[ {Lift per unit span} = \rho \cdot \Gamma \cdot V_\infty \] Where:
\( {Lift per unit span} = 6 \, {N/m} \),
\( \rho = 1.225 \, {kg/m}^3 \) (density of air),
\( V_\infty = 30 \, {m/s} \) (free-stream velocity),
\( \Gamma \) is the circulation.
Rearranging the formula to solve for \( \Gamma \): \[ \Gamma = \frac{{Lift per unit span}}{\rho \cdot V_\infty} \] Substituting the given values: \[ \Gamma = \frac{6}{1.225 \times 30} = \frac{6}{36.75} \approx 0.163 \, {m}^2/{s} \] When rounded to two decimal places, the circulation is approximately 0.16 m\(^2\)/s.