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

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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

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

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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

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

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

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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

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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:

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3 m u = 20 m/s

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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.

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3 m u = 20 m/s

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

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

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Lecture #19: Fluid Dynamics I

Lecture #19: Fluid Dynamics I

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