Homework Help: Falling object viscometer non-transparant liquid

1. Jun 25, 2012

periclaas

For a coursework, I need to derive the equations behind a viscometer. This viscometer has a free falling object in a non-transparent viscus fluid but it doesn't necessarily need to be the traditional sphere. The restriction only is that the object is connected to a thin stick which is used to pull the object up after a run. The stick is also used for accurate time measurements and it additional weight can be placed on it for rapid extra measurements.

The most straight forward way is using a sphere of considerable size ($d_{stick} \ll d_{sphere}$) and Stokes law to get an expression for the viscosity ($\eta = \frac{g d^2}{18 v} \left(\rho_s - \rho \right)$ if Re<1). There are correction factors available to extent and improve the expressions so this is an option.

I was wondering if other objects (e.g. axial falling cylinder, flat plate) can be used and how to relate their drag coefficients (which are normally documented as an empirical constant) to the viscosity?