1. Pressure, Drag and Lift for Uniform Flow Over a Cylinder a 2 = 1

2. Pressure, Drag and Lift for Uniform Flow Over a Cylinder Along the cylinder, r = a, the velocity components become: u θ is maximum at θ = π/2 and 3 π /2; zero at θ = 0 and θ = π

3. The pressure distribution can be obtained using Bernoulli’s equation: dimensionless pressure coefficient C p

4. The drag on the cylinder may be calculated through integration of the pressure over the cylinder surface: The drag on the cylinder acts parallel to the flow. The lift is perpendicular to the flow: FxFx FyFy

5. Along the cylinder, r = a, the velocity components become: Pressure, Drag and Lift for Uniform Flow Over a Rotating Cylinder

6. The pressure distribution can be obtained using Bernoulli’s equation: dimensionless pressure coefficient C p

7. The drag and lift can be obtained by integrating the pressure over the cylinder surface p c : Still no drag for a rotating cylinder There is lift proportional to density, upstream velocity, and strength of vortex -- Kutta – Jukowski law Lifting effect for rotating bodies in a free stream is called Magnus effect

8. Example of Pressure, Drag and Lift for Uniform Flow Over a Cylinder 3 m u = 20 m/s The drag on the cylinder may be calculated through integration of the pressure over half the cylinder surface, from 0 to π. That’ll be with the outside pressure, inside pressure p 0 should also be considered:

9. 3 m u = 20 m/s

10. 3 m u = 20 m/s The lift on the object may be calculated through integration of the pressure over half the cylinder surface, from 0 to π.

11. 3 m u = 20 m/s

12. Lift for half-cylinder, 3 m high, influenced by wind (air density) hurricanetropical storm tropical depres -sion Gale Force

13. Lift for half-cylinder, 1 m high, influenced by flow (water density)