$[20$ Points$]$ A falling$-$head permeability test was performed on a soil sample $97-mm$ in diameter and

$20-mm$ long. The standpipe had an inside diameter of $6\mathrm{.}0mm.$ The water level in the bath surrounding

the sample was $120mm$ above the laboratory countertop and the water level in the standpipe fell from a height of $510mm$ to $261mm$ above the countertop in $46$ hours and $35$ minutes. Compute the

hydraulic conductivity of the soil sample in units of $cm/$sec