• Tags: viscosity, Stokes, terminal-velocity
• Difficulty: Moderate

When a small sphere falls through a viscous liquid, it reaches terminal velocity when: weight = buoyant force + viscous drag. (4/3)pir^3rho_sg = (4/3)pir^3rho_lg + 6pietarv_t. Solving: eta = 2r^2(rho_s - rho_l)g/(9v_t). Experiment: drop small steel balls into a tall cylinder of glycerine. Mark two horizontal lines well below the surface (to ensure terminal velocity is reached). Measure time to travel between the marks. v_t = distance/time. Repeat with balls of different radii. Plot v_t vs r^2: slope = 2*(rho_s - rho_l)g/(9eta). Stokes' law is valid only for laminar flow (Reynolds number Re = rho_lvd/eta < 0.1). Use small spheres and viscous liquids. Temperature control is important since viscosity is strongly temperature-dependent (roughly halves for every 25 degree C rise).