Stokes Drag and Terminal Velocity

A sphere falling through fluid experiences gravitational force F_g = mg and drag F_drag. In the Stokes regime (Re ≪ 1), F_drag = 6πηrv. At terminal velocity these balance. At high Re, the drag law changes — use the standard drag equation F = ½ρC_D A v².

Particle radius r 0.005 m Density ρ_p 2000 kg/m³ Fluid viscosity η 0.001 Pa·s Fluid density ρ_f 1000 kg/m³

Theoretical terminal velocity Stokes: — m/s
Re at v_t: —
Regime: —
Stokes valid if Re < 1
Newton drag if Re > 1000

Current simulation Velocity: — m/s
Re: —
C_D: —
F_grav: — N
F_drag: — N
Net accel: — m/s²

Stokes: F = 6πηrv
Newton: F = ½ρ_f C_D πr² v²
Transition: C_D = 24/Re + 6/(1+√Re) + 0.4