Q$3(30$ p$.)$ A falling head hydraulic conductivity test has been conducted on a clay sample. The soil sample was $55mm$ in diameter and $120mm$ tall. The standpipe had an inside diameter of $6mm.$ The water level in the bath surrounding the sample was $113mm$ above the laboratory countertop and the water level in the standpipe fell from a height of $303mm$ to $105mm$ from the top of the water level in the bath in $17$ hours $5$ minutes. Compute the hydraulic conductivity $($permeability$)$ of the soil.