• 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. $\frac{4}{3}$pi$r^3$$rho_s$g = $\frac{4}{3}$pi$r^3$$rho_l$g + 6pietar$v_t$. Solving: eta = 2*$r^2$($rho_s$ - $rho_l$)$\frac{g}{9*v_t}$. 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. $v_t$ = $\frac{distance}{time}$. Repeat with balls of different radii. Plot $v_t$ vs $r^2$: slope = 2*($rho_s$ - $rho_l$)*$\frac{g}{9*eta}$. Stokes' law is valid only for laminar flow (Reynolds number Re = $rho_l$vd/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).