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:

\[ \text{Lift per unit span} = \rho \cdot \Gamma \cdot V_\infty \]
Where:
  \( \text{Lift per unit span} = 6 \, \text{N/m} \),
  \( \rho = 1.225 \, \text{kg/m}^3 \) (density of air),
  \( V_\infty = 30 \, \text{m/s} \) (free-stream velocity),
  \( \Gamma \) is the circulation.

Rearranging the formula to solve for \( \Gamma \):
\[ \Gamma = \frac{\text{Lift per unit span}}{\rho \cdot V_\infty} \]

Substituting the given values:
\[ \Gamma = \frac{6}{1.225 \times 30} = \frac{6}{36.75} \approx 0.163 \, \text{m}^2/\text{s} \]

When rounded to two decimal places, the circulation is approximately 0.16 m²/s.