Stokes Law
Stokes’ law for the terminal speed of a small ball falling through a viscous fluid, with a correction for the wall of the tube. Use it for falling-ball viscometer experiments, with ball diameter as x and terminal speed as y.
Parameters
- Viscosity of the fluid.
- The ball’s density minus the fluid’s density, times the gravitational acceleration g.
- Inner diameter of the tube, which enters through the wall factor 1 − 2.1x/K₁.
Tips
- The data determine K₀ and a₀ only through their ratio K₀/a₀. Fix K₀ at its value from the measured densities to fit the viscosity a₀; with both free, the fit is not full rank.
- Fix K₁ at the measured tube diameter as well, unless you are testing the wall correction.
- curve.fit does not estimate starting values for this model, so enter a guess for every free parameter.
- Use one consistent set of units, for example SI: x and K₁ in m, y in m/s, K₀ in N/m³ and a₀ in Pa·s.