Example Problem

A company is designing a new chromatography column. The column consists of a packed bed of $+$ charged particles with a $2\mathrm{.}5{10}^{-6}m$ diameter, giving a porosity of $=0\mathrm{.}42.$ The typical diameter of chromatography columns is $0\mathrm{.}006m,$ but the length varies. The company is deciding how long their column should be$.$ The longer the column is$,$ the better the separation. But the chromatography equipment uses a pump that can deliver a maximum pressure of only $1\mathrm{.}4{10}^{7}Pa($assume the effluent leaving the column is $0Pa).$

Assume a fluid with $=820k\frac{g}{m^3},=0\mathrm{.}0012k\frac{g}{m}-s,$ and a flow rate of $1{10}^{-8}\frac{m^3}{s}.$ Based on this, calculate what would be the best column length $($in $cm).$