Describe flow through porous media and the Darcy-Forchheimer equation.

Flow through porous media (packed beds, filters, catalysts) is governed by resistance from viscous and inertial effects. Darcy's law for low Re (creeping flow): ΔP/L = μV/K, where K is permeability (m²), valid when Re_p < 1 based on pore dimension. For higher velocities, Forchheimer equation adds inertial term: ΔP/L = μV/K + βρV², where β is inertial resistance factor. Combined Darcy-Forchheimer: ΔP/L = (μ/α)V + C₂(½ρV²), where α is viscous permeability and C₂ is inertial factor. Ergun equation for packed beds: ΔP/L = 150μ(1-ε)²V/(ε³d_p²) + 1.75ρ(1-ε)V²/(ε³d_p), where ε is void fraction and d_p is particle diameter. Applications: oil reservoir simulation, groundwater flow, filtration system design, catalyst bed pressure drop.