Explain shock waves in compressible flow and the Rankine-Hugoniot relations.

Shock waves are discontinuous changes in flow properties occurring when supersonic flow encounters disturbance. Across a normal shock: velocity decreases (supersonic to subsonic), pressure and temperature increase abruptly, entropy increases (irreversible), and total pressure decreases. Rankine-Hugoniot relations connect upstream (1) and downstream (2) properties: ρ₂/ρ₁ = (γ+1)M₁²/((γ-1)M₁²+2), P₂/P₁ = (2γM₁²-(γ-1))/(γ+1), T₂/T₁ = P₂ρ₁/(P₁ρ₂). Oblique shocks form at angle β to flow direction, with downstream flow deflected by angle θ. Detached bow shocks form when θ exceeds maximum for given M₁. Understanding crucial for supersonic inlets, nozzles, and high-speed aerodynamics.