Explain potential flow theory and its limitations in real flow analysis.

Potential flow theory assumes inviscid, irrotational (∇×V=0) flow where velocity derives from scalar potential: V = ∇φ. Satisfies Laplace equation ∇²φ = 0, allowing superposition of elementary solutions: uniform flow, source/sink, doublet, vortex. Superposition creates complex flows: cylinder with circulation (Magnus effect), Rankine bodies, airfoil flows. Stream function ψ defines streamlines (ψ = constant). Limitations: cannot predict drag on symmetric bodies (d'Alembert's paradox), ignores viscous effects and boundary layers, cannot capture flow separation or wakes, misses rotational flows in turbomachinery. Practical use: initial estimates of pressure distribution, panel methods for external aerodynamics, combined with boundary layer analysis, starting point for wing design. Must be supplemented with viscous corrections for accurate force predictions.