Darcy: u = -(K/μ)(dP/dx) [linear, low Re]
Forchheimer: -(dP/dx) = (μ/K)u + βρu² [inertial correction]
At low velocities (Darcy regime), pressure gradient scales linearly with velocity. At higher Re through pores, the Forchheimer term (βρu²) captures inertial effects. The transition occurs around Re_pore ≈ 1–10.