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1. Intermediate Aerodynamics: Potential Flow Theory Based on Katz & Plotkin’s 'Low-Speed Aerodynamics' Graduate Aerodynamics Course Instructor Name & Date

2. Introduction to Potential Flow Inviscid, incompressible, and irrotational flow results in potential flow. Governing equation: Laplace’s equation for velocity potential ∇²ϕ = 0. Importance: Reduces problem complexity by allowing elementary solutions.

3. Potential Flow Problem Setup Fluid domain V with solid boundaries S_B. Boundary conditions: - No normal flow: ∇ϕ ⋅ n = 0. - Far-field decay: lim (r→∞) (∇ϕ - v) = 0.

4. Green’s Identity in Potential Flow Green’s identity relates surface and volume integrals: ∫_S ((1/r) ∇ϕ - ϕ ∇(1/r)) ⋅ n dS = 0. Allows determination of ϕ at any point using boundary values.

5. Elementary Solutions Overview Types of singularities: 1. Point source/sink 2. Point doublet 3. Point vortex Each singularity satisfies ∇²ϕ = 0.

6. Point Source Velocity potential: ϕ = -σ / (4πr). Radial velocity: q_r = σ / (4πr²). Streamlines are radial; velocity decays with 1/r².

7. Point Doublet Velocity potential: ϕ = μ / (4π) n ⋅ ∇(1/r). Non-radial symmetry with a directional property. Streamlines resemble a source and sink in close proximity.

8. Principle of Superposition Superposition principle: Linear combination of solutions is also a solution. ϕ = Σ c_kϕ_k, ∇²ϕ = 0. Enables complex boundary problem solutions through elementary solutions.

9. Rankine Oval Combination of a source, sink, and uniform flow. Velocity potential: ϕ(x, z) = U∞x + (σ / 2π) ln(r₁ / r₂). Forms a closed streamline resembling an oval.

10. Flow Around a Cylinder Superposition of a doublet and free stream. Velocity potential: ϕ = U∞r cosθ + (μ / (2πr)) cosθ. Stagnation points at θ = 0, π.

11. Pressure Distribution on Cylinder Velocity components at surface: q_r = 0, q_θ = -2U∞ sinθ. Pressure coefficient: C_p = 1 - 4 sin²θ. Experimental vs. theoretical pressure distributions.

12. Flow Separation and Real Effects Symmetry in potential flow leads to zero drag. Real flow: Separation and wake formation behind cylinder. Visual comparison: Theoretical vs. experimental streamlines.

13. Kutta-Joukowski Theorem Circulation Γ generates lift. Lift per unit span: L = ρ U∞ Γ. Valid for incompressible, inviscid, irrotational flow.

14. Flow Around a Sphere Superposition of a free stream and three-dimensional doublet. Velocity potential: ϕ = U∞r cosθ + (μ / (4πr²)) cosθ. Pressure coefficient: C_p = 1 - (9/4) sin²θ.

15. Experimental Drag Coefficients Drag coefficient comparison for spheres and cylinders. Variation with Reynolds number.

16. Summary Potential flow simplifies complex flow problems. Elementary solutions (source, doublet, vortex) form building blocks. Real flow effects like separation highlight limitations.

17. Questions Invite student questions and discussion.